Free Essay

In: Other Topics

Submitted By mamat

Words 10336

Pages 42

Words 10336

Pages 42

INTRODUCTION

1.1 BACKGROUND OF INDUSTRIAL TRAINING

All final year students of Bachelor of Sciences (Hons) (Statistics), Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA (UiTM) are required to undergo the industrial training. The students will be placed in the government or private organizations of their choice for a period of three months, during which they are also required to design a research project. The following one month will be allocated for data analysis, report writing and oral presentation. This training is very beneficial and important to expose students to the various aspects of industrial practices and ethics. The students are also able to apply the theories and knowledge that they have learned to the projects assigned to them.

1.2 OBJECTIVES OF INDUSTRIAL TRAINING

The objectives of the industrial training are: ❖ To expose students to the real working environment ❖ To train students being familiar with the organization structure, operations, and administration. ❖ To acquire real experience in solving research problems and apply appropriate statistical data analysis. ❖ To enable students to integrate the theory learned at UiTM with practice. ❖ To cultivate cooperative networking between industries and UiTM

1.3 INDUSTRIAL TRAINING ATTACHMENT

I had undergone my industrial training at Socio Economic and Environmental Research Institute (SERI) at Penang from 3rd January 2011 until 31st March 2011. I was directly supervised by Dr Chan Huang Chian and Ms Ong Wooi Leng who were Senior Research Fellow and Research Analyst respectively in the company. SERI is located at No.10 Brown road, 10350 Penang, Malaysia.

1.3.1 Profile of Organization

[pic]

Figure 1.1: SERI’s logo

The Socio-Economic & Environmental Research Institute (SERI) is an independent non-profit Penang-based think tank and research institute set up on March 1997, and officially launched on 8 November 1997 by the Chief Minister of Penang, YAB Tan Sri Dr. Koh Tsu Koon, with a focus on facilitating sustainable, continuous and balanced development for the state of Penang. It is under the charge of Board of Directors which oversees the smooth operation of the institute by providing guidelines, which helps sets its research agenda and manage its finance.

Right from the beginning, SERI has been a unique institution with a difference. Unlike many other larger think tanks, SERI has retained its compact structure and slim set-up, allowing the Institute to respond rapidly to new challenges.

While the role of a "thinking institution" has always characterized the modus operandi of the Institution, as seen in the active involvement of SERI in policy analysis and in its provision of economic advisory services to the Penang state government, SERI’s primary objective is to help Penang achieve a sustainable level of balanced development in the long term.

To achieve this, SERI collaborates closely with the Penang state government, local government-linked agencies and several international organizations including UNDP, CIDA and APO, on various projects that have gone beyond the fulfillment of tasks normally associated with a regular policy "think-tank". Aside from providing in-depth economic analysis and research focus, SERI’s also acts as a platform for disseminating information and facilitating community-centered projects that help to create a better quality of life and physical environment for the people of Penang.

Today, SERI has firmly established itself as one of Malaysia’s leading independent research organizations, regularly consulted by local government, local and international NGOs on a diverse range of issues from education and sustainability to economics and human resource issues.

(www.seri.com.my, 2011)

1.3.1.1 SERI’s Mission

SERI is poised to be a force of change by delivering far-reaching and realistic policy solutions that would produce a fair, more inclusive and environmentally sustainable Penang.

(www.seri.com.my, 2011)

1.3.1.2 SERI’s Vision

SERI will provide a progressive forum to engage the Penang state government, local councils, government-linked agencies, international organizations and the public by way of research and dialogue.

Its strong networks in government, academia, corporate and voluntary sectors will enable SERI to deliver well-researched and clearly argued policy analysis, reports and publications which will play a vital role in initiating the momentum of progressive thought.

(www.seri.com.my, 2011)

1.3.1.3 SERI’s Organization

SERI was established as the think tank of Penang to formulate strategic planning and policy recommendations that seek the betterment of the quality of life for its clients through adherence to the principles of sustainable development.

The three main thrusts of SERI are: • Economic policies • Social inclusiveness policies • Environmental policies

(www.seri.com.my, 2011)

Board of Director

|1. |Dato’ Dr. Haji Sharom Ahmat |Chairman |

|2. |YB DCM I Dato’ Mansor Othman |Director |

|3. |YB DCM II Prof Dr. Ramasamy a/l Palanisamy |Director |

|4. |Dato’ Seri Chet Singh |Director |

|5. |YB Liew Chin Tong |Executive Director |

|6. |Dato’ Dr. Leong Yueh Kwong |Director |

|7. |Dato’ Seri Nazir Ariff |Director |

|8. |Dato’ Rosli Jaafar |Director |

|9. |Dr. Tan Liok Ee |Director |

|10. |Tuan Hj Zaini b. Hussain |Director |

|11. |Ir. Jaseni b. Maidinsa |Director |

|12. |Dr. Michael Lim Mah Hui |Director |

|13. |En. Hamdan Majeed |Director |

Executive Director, Centre Chair, Fellows and Editor:

|1. |Executive Director: |YB Liew Chin Tong |

|2. |Chair, Centre for Economics cum Fellow: |Dato’ Dr. Toh Kin Woon |

|3. |Chair, Centre for Environmental & Sustainability Studies: |Dato’ Dr. Leong Yueh Kwong |

|4. |Senior Research Fellow: |Dato’ Dr. Goh Ban Lee |

|5. |Senior Research Fellow: |Dr. Chan Huan Chiang |

|6. |Senior Visiting Fellow: |Prof Woo Wing Thye |

|7. |Senior Visiting Fellow: |Prof Muhamad Jantan |

|8. |Senior Visiting Fellow: |Prof Suresh Narayanan |

|9. |Senior Visiting Fellow: |Prof Jimmy Lim Cheok Siang |

|10. |Senior Visiting Fellow: |Dr. Michael Lim Mah Hui |

|11. |Senior Visiting Fellow cum Editor: |Dr. Ooi Kee Beng |

|12. |Senior Visiting Fellow: |Dr. Francis Hutchinson |

|13. |Senior Visiting Fellow: |Dr. Hin Lin Yee |

|14 |Senior Visiting Fellow: |Prof Chee Kim Loy |

|15 |Senior Visiting Fellow: |Dr. Anthony Chin |

|16 |Senior Visiting Fellow: |Dr. Din Merican |

|17 |Senior Visiting Fellow: |Mr. Yoon Chon Leong |

| | | |

| |Staff Strength: | |

|1 |General Manager: |Mr. Lim Wei Seong |

|2 |Manager, Strategy & Policy Studies: |Mr. Khor Hung Teik |

|3 |Manager, Special Projects: |Cik Fatimah Hassan |

|4 |Deputy Editor: |Ms. Rosalind Claire Chua |

|5 |Assistant Manager |Mr Richard Ho Weng Keong |

|6 |Research Analyst |Ms Ong Wooi Leng |

|7 |Research Analyst |En. Mohd Firdaus b. Habib Mohd |

|8 |Publication Officer |Mr Jeffrey Hardy Quah |

|9 |Research Officer |Mr Ben Wismen |

|10 |Research Officer |Cik Athirah binti Azhar |

|11 |Research Officer |Mr. Daniel Lee |

|12 |Communication Executive |Mr. Daniel Lim |

|13 |Administrative & Finance Executive |Ms. Maggie Loo |

|14 |Administrative cum PEM Business Executive |Puan Nor Faezah Bt Abdul Aziz |

|15 |Account cum Admin Clerk |Cik Nor Farah Ishak |

|16 |Caretaker: |Pakcik Nordin |

1.4 INDUSTRIAL TRAINING TASK

I have completed my industrial training at Socio Economic & Environmental Research Institute (SERI), Penang. During my three month training there, I was assigned at Statistics Department which focuses on economic research using secondary data. From there, I gained a lot of experience. I have learnt a lot of things that were useful for preparing me into the working environment. I was assigned into various tasks during the practical training. These tasks include:

i. To source and gather the data from respective departments such as Department of Statistics, Bank Negara Malaysia, Department of Environment and Penang Council municipal, and etc.

ii. To assist in prepared report for quarterly bulletins, Penang Statistics 2010.

iii. To update data of Industrial Production Index and do analysis for consumption goods and Industrial production Index.

iv. To write an article for Penang Economic Monthly.

v. To present an analysis of data that has been done.

CHAPTER 2

FORECASTING INDUSTRIAL PRODUCTION INDICES IN MALAYSIA USING ARIMA MODEL

2.1 INTRODUCTION

This chapter describes the background of the study which is Section 2.2, Section 2.3 and 2.4 give the problem and objective of the study respectively. Section 2.5 states the significant of the study while literature review is in Section 2.6.

2.2 BACKGROUND OF THE STUDY

Department of statistics defines the industrial production Index (IPI) as a measure of the rate of change in the production of industrial commodities in real terms over time. These commodities are obtained from the Manufacturing, Mining and Electricity sectors. Moreover, the Industrial Production Index is sensitive to consumer demand and interest rate.

As such, Industrial Production becomes as important tool for future GDP and economic performance forecasts. Industrial Production figures are also used to measure inflation by central banks as high levels of industrial production may lead to uncontrolled levels of consumption and rapid inflation. Industrial Production index also measure the fluctuation in the Malaysia economy growth where it reacts quickly ups and down in business cycle.

As industrial production is considered as one of the best barometers for the economic well-being of a nation, it is important for a national company, to be well informed of the trend in industrial production for the use of their strategic planning.

Thus, in this study an approach model will be proposed for Malaysian Industrial Production Index (IPI). This proposed model will be used to generate forecasting values of Malaysian IPI.

2.3 PROBLEM STATEMENT

Recently, Malaysian economy has experienced economic fluctuations throughout its history and it affects the whole community including household, workers and investors. One of the main tasks of the economy watcher is to extract reliable signals from high frequency indicators to provide the decision-maker with an early picture of the short-term economic situation.

The index of industrial production (IPI) is probably the most important and widely analyzed high-frequency indicator given the relevance of manufacturing activity as a driver of the whole business cycle. This can be seen by the extensive comments and reactions of business analysts as soon as the IPI is published. (Golinelli and Parigi, 2007)

Indeed, the IPI is a crucial variable in the forecasting process of the short-term evolution of GDP in most countries. However, the IPI itself is characterized by a significant publication delay, which limits its usefulness and motivates the great efforts to compute reliable and updated forecasts. The efforts of statistical institutes to shorten the delay of the first release imply a greater degree of revision of the early estimates, which leads to the usual problem of assessing the ability of alternative forecasting methods using real-time data.

Moreover, these economic fluctuations that reacts in industrial production are difficult to predict because there can be numerous factors that cause the changes in the economic conditions whether mining, manufacturing or electricity.

So, it is important for government to control the economic fluctuation in order to control the rate of change in the production of industrial commodities in real terms over time. To have a proper control, there is a need to study the trend of industrial production index, model them by using proper techniques and use the model for prediction purposes.

2.4 OBJECTIVES OF THE STUDY

The main objectives of this study are as follow:

i. To propose the best ARIMA model for Industrial Production Index in Malaysia.

ii. To forecast monthly Industrial Production Index in Malaysia for the year 2011 using Time Series Model.

2.5 SIGNIFICANCE OF THE STUDY

It is hoped that this study can be used to assist SERI in understanding the trend of Industrial Production Index, guiding the company in making decision and serving as a benchmark for improving SERI’s existing strategies for services to the Penang State government.

Besides, it can be use as a reference series in the compilation of cyclical indicators which help to predict the future turning points in business cycle to formulate strategic planning and policy recommendation.

In addition, it gives more current view of business activities and general pictures of which sectors of the economy are growing and which are not since Industrial Production Index is important to serve as leading indicator of economic health.

Lastly, it is hoped that the company will continue to use any statistical technique to forecast Industrial Production index.

2.6 LITERATURE REVIEW

Box-Jenkins approach is synonymous with the general ARIMA modeling. The term ARIMA is in short stands for the combination that comprises of Autoregressive/Integrated/moving Average models. The Autoregressive (AR) model was first introduced by Yule (1926) and later generalized by Walker (1931). Moving Average (MA) models was first introduced by Slutzky (1937) and the combination of these two models was introduced in 1938 by Wold. This approach was first introduced by George E.P. Box (University of Wisconsin, USA) and Gwilym M.Jenkins (University of Lancester,UK) in 1976. They provided a comprehensive explanation of the technique of analyzing the time series data to be used in the univariate ARIMA models.

A study by Pedro Revilla (1991) on “Spanish Methods to Improve Timeliness in the Industrial Production Indices” found that, it is necessary to use models that have stochastic processes as a theoretical framework, such as time series analysis models. In this case, the use of very simple time series models is proposed: univariate ARIMA models (Box-Jenkins, 1970) and univariate ARIMA with Intervention Analysis models (Box - Tiao, 1975). From a theoretical point of view, multivariate models (that picked up the correlation of all the variables) would be appropriate in surveys with more than one variable. However, the difficulty of their practical use suggests the desirability of a univariate environment. ARIMA modelling (in addition to their common use in seasonal adjustment) may be used in statistical offices for data editing and imputation, the description of the data´s characteristics for analysis and quality control (Revilla et al., 1991), and linking series.

Besides, a study by Bodo and Signorini (1987) on “ Short term forecasting of the Industrial Production Index “ found that, the simplest methods of forecasting the future values of Industrial Production Index were seasonal Holt-Winters method and two ARIMA models. On that study there were present several methods for obtaining earlier estimates, including (a) simple univariate models, (b) an OLS model that employs data on electric power input, corrected for the effects of temperature and (indirectly) of the manufacturing output mix, (c) a transfer-function model based on business surveys. The results are satisfactory. The best single forecasts are those based on the electric power input, but combining these with business surveys gives even better predictions.

Another research by Francis et al (1991) found that, a forecaster can nowadays consider a wide variety of time series models that describe seasonal variation and nonlinear regime-switching behaviour. So, they examine the forecasting performance of various models for seasonality and nonlinearity for quarterly industrial production series of 18 OECD countries. They find that the accuracy of point forecasts varies widely across series, across forecast horizons and across seasons. However, in general, linear models with fairly simple descriptions of seasonality outperform nonlinear at short forecast horizons, whereas nonlinear models with more elaborate seasonal components dominate at longer horizons. Finally, none of the models is found to render efficient forecasts and hence, forecast combination is worthwhile.

Mei Tseng et al (2002) found the Seasonal Time Series ARIMA (SARIMA) model was also able to forecast certain significant turning points of the test time series. This model was used to forecast two seasonal time series data of total production value for Taiwan machinery industry and the soft drink time series. The forecasting performance was compared among four models, i.e., the SARIMABP and SARIMA models and the two neural network models with differenced and deseasonalized data, respectively. Among these methods, the mean square error (MSE), the mean absolute error (MAE), and the mean absolute percentage error (MAPE) of the SARIMA model were the lowest.

Next, a study by Golinelli and Parigi (2007) on “Forecasting industrial production: The role of information and methods” used five alternative forecasting methods for each prediction horizon: the ARIMA model; the average of the single equation SM; the average of the multiple-equation SM; the average of the FM; and the overall average of the SM and FM models. All forecasts are computed with the latest available data, given the unavailability of a real-time dataset for some indicators (specifically two-digit Ateco data for the IPI). However, the first two columns report the smallest RMSEs and their ratios with respect to the ARIMA model.

CHAPTER 3

METHODOLOGY

3.1 INTRODUCTION

This chapter describes the data used in the study, the method of data analysis and the criteria used to compare the performance of forecasting models used. Section 3.2 describes the method of data collection. Section 3.3 gives methods used to analyze data. Section 3.4 discuses the criteria used in assessing the performance of identified best forecasting models using ARIMA.

3.2 DATA DESCRIPTION

Secondary data are used in this study. This data referred to the business cycles which are generally measured by the Industrial Production Index. In this study, data for monthly in Malaysia from January 2005 until February 2011 are used. The data are derived from Department of Statistics to identify economic performance.

3.3 METHOD OF DATA ANALYSIS

Box-Jenkins Methodology is used in this study to determine the best Autoregressive/Integrated/moving Average (ARIMA) model in forecasting the Industrial Production Index. The computation is done using MINITAB software version 15.

3.3.1 BOX-JENKINS METHODOLOGY

ARIMA modeling was commonly applied to time-series analysis, forecasting and control. The application of the Box-Jenkins methodology lies on the assumption that concerns the characteristic of the initial data series and also must be through several steps as described below.

The Assumption of Box-Jenkins Methodology

Basically, it assumed that the data series is stationary. Where such assumption was not met, then the necessary procedures will be performed in order to achieve stationary in the series. Incidentally, for most economics or business data series, non-stationary is the norm. A series is said to be ‘stationary’ if it fluctuates randomly around some fixed values, generally either around the mean value of the series or it can be some other constant values or even zero value. More specifically, it can be said that

‘A series is stationary if it does not show growth or decline over time’. The series that does not depicts this characteristics was called ‘non-stationary series’ and such series can be made stationary (by removing the trend) by taking successive differences of the data.

The Stages in the ARIMA models

The basis of Box-Jenkins modeling approach consists of three main stages. These are:

Stage Process

1. Model Identification

2. Model Estimation and Validation

3. Model Application

Figure 3.1 shows the diagrammatic representation of these stages. However prior to the implementation of these stages, the data series need to be prepared such as; stabilizing the variance by transforming the data, checking for inconsistent or missing values and achieving the stationary condition. A simple plotting of line chart and analyzing the autocorrelation function (ACF) and partial autocorrelation function (PACF) can significantly help to ease the work of data preparation.

Figure 3.1: ARIMA Modeling Process.

(Dr Mohd Alias Lazim, 2007. Introductory Business Forecasting a Practical Approach)

Step 1: Model Identification.

The first step in the application of the Box-Jenkins methodology is to identify the class of model most suitable to be applied to the given data set. This is done by computing, analyzing and plotting various statistics based on historical data. Common statistics used to identify the model type is the autocorrelation and the partial autocorrelation coefficients.

However, model identification based on observing the ACF and PACF method can be the trickiest part of the application of the Box-Jenkins methodology. This is because it is very difficult to exactly pinpoint the exact model type based on the ACF and PACF alone.

The identification of the Box-Jenkin’s Model provides four-step procedure in order to identify the possible general form of an ARIMA model. The steps were:

Construct a time plot for the original data series. Try to identify any unusual observation. If such observation exists, decide whether a transformation is necessary. If necessary, transform to achieve stationary in variance, for example. Plot also the ACF and PACF to confirm the stationary condition of the series.

i. If data series appears non-stationary, perform the first difference. For non-seasonal data series the first different is sufficient. If seasonality exists, perform the seasonal difference. If the non-stationary condition persists after the seasonal difference, then perform the non-seasonal difference. Plot also the ACF and PACF of the final series to confirm its stationary condition.

ii. When stationary condition has been achieved, examined the ACF and PACF to see whether any discernible pattern of the data series exists. The ACF and PACF may reveal the type of AR and MA model appropriate. Model with seasonal component is suggested by larger autocorrelation/partial autocorrelation at seasonal lags, example at lags 12, 24 for monthly data and lags 4, 8 etc. for quarterly data.

iii. In the model identification stage, it may be slightly easier to select pure AR or pure MA models. But when selecting a mixed ARIMA model, the process to decide on the values of p and q is much more difficult especially for model with seasonal component. Hence, it is worth considering several possible models in order to minimize the chance of not picking the most appropriate model form. To finally determine the best fitted model, one needs to use several statistical measures such as the MSE, AIC/BIC or the Box-Pierce (Ljung-Box) statistic.

Step 2: Model Estimation and Diagnostic Testing.

The Box-Jenkins models are usually estimated based on sample statistic that must be tested to ensure their validity as estimates of the true population parameter values. In this case there are three components of the validation. In this case, there were three components of the validation process:

i. Statistical validation or residual diagnostics,

ii. Parameter validation, and

iii. Model validation.

However, the common statistical measure used when validation the ARIMA models was The Box-Pierce Q Statistic.

The Box-Pierce Q Statistic

The Box-Jenkins framework assumes that the residuals (error terms) were not correlated with each other, i.e. it is assumed that there is no systematic pattern in the residuals.

In short, the residuals are independent of one another. When there is systematic pattern in the behavior of the residuals, then it said to be mis-specified. Mis-specification is a symptom that indicates that important parameters may have been omitted or alternatively unimportant parameter(s) is included in the model. A procedure to check for mis-specification is to check for the presence of correlation among the residuals, carried out by calculating the chi-squared value of the error terms.

Such test procedure is commonly known as portmanteau test. Hence, other naming this procedure as ‘model validation’, it is also common among forecasters and modelers to call it ‘test for mis-specification’.

One such test is the Box-Pierce Q Statistics. The test statistic is given as,

[pic] (3.1)

which was approximately distributed as a chi-squared distribution with

(h-p-q) degrees of freedom. In this equation,

T is the number of observations in the time series

h is the maximum lags being tested

p is the number of AR terms

q is the number of MA terms

rk is the simple autocorrelation of the residual terms, and

d is the degrees of differencing applied to original data

(Dr Mohd Alias Lazim, 2007. Introductory Business Forecasting a Practical Approach)

An alternative update version (believed to be much closer to the [pic] distribution) of this test is the Ljung-Box statistic given as,

[pic] (3.2)

which is also distributed as a chi-squared distribution with (h-p-q) degrees of freedom.

(Dr Mohd Alias Lazim, 2007. Introductory Business Forecasting a Practical Approach)

If the residuals are white noise the Q or Q* statistics was distributed as

[pic] with (h-p-q) degrees of freedom.

In other word if the calculated chi-squared value was larger than the tabulated [pic] for (h-p-q) degrees of freedom then reject H0 (which states that the residuals are white noise).

By accepting H1 (which states that the residuals are not white noise), the model was therefore, considered mis-specified or inadequate. Likewise, if the Q statistic was less than [pic] with (h-p-q) degrees of freedom, accept the H0 (the model is adequate).

In addition, it is possible in the Box-Jenkins methodology that two or more models may have the same results of accepting the H0. Therefore, when choosing the best model, one has to supplement the testing procedure with other statistics such as the AIC or BIC or the MSE. However, when deciding on the best model choice, the concept of parsimony is highly applicable in that the simpler model is usually the possible main choice.

Step 3: Model Application

If all test criteria are met and that the model’s fitness has been confirmed, it is then ready to be used to generate the forecasts values. The forecast values may be in term of single-valued items or in terms of confidence intervals. The confidence interval estimates provide the probabilistic measures of certainly and uncertainly associated with the forecast value.

The process of determining the final or ‘best’ model in an iterative one as indicates by Figure 3.1. This means that, before the final model is arrived at the process of formulating and estimating the model has to be performed repeatedly, going back and forth, between the first two phases, each time revising and improving the model until one estimated model, which is superior to all other competing models, is found. Main criterion used is based on the model’s forecasting performance, either within sample or outside sample evaluation.

The next critical stage is to develop a system to monitor the forecast values produced. If on the basis of subsequent information, it is found that the model fails to produce reliable forecast values or fails to explain the phenomena being investigated then it needs to be revised and updated.

Hence, the process begins anew. At this stage two possibilities may occur;

i. New or latest data are collected and incorporated into existing series.

ii. New model is formulated and re-estimated.

The Basic Model of the Mixed Autoregressive Integrated Moving Average (ARIMA) Model.

When the stationary assumption of the variable is not met, then the ARIMA modeling is formulated. In this information, it is necessary that the data series needs, firstly, to be differenced in order to achieve stationary. The model, thus, obtained is represented in general term as ARIMA(p,d,q) where as stated earlier the symbol ‘d’ denotes the number of time the variable Yt needs to be differenced in order to achieve stationary. A simple case of the model as represented by ARIMA(1,1,1) is written as,

wt =μ + ϕ1wt-1 - ϴ1ԑt -1 + ԑt (3.3)

Where wt = Yt- Yt-1 represents the first difference of the series and is assumed stationary. In this case, the values of p=1, d=1, and q=1.

Now moving all the lag variables to the right, the equation can now be written as,

Yt=Yt-1 + ϕ1Yt-1 – ϕ1Yt-2 -ԑt - ϴ1ԑt-1 (3.4)

There are cases where the first difference may not render the series stationary. If the second difference is necessary, then the series is integrated of the second order where the value of ‘d’ is 2. For example, in ARIMA (1,2,1), the autoregressive and the moving average models are both of the first order with ‘p’ and ‘q’ equal to 1 and ‘d’ equal to 2. Note that, in the general applications of the model the values of p, d and q rarely exceed 2.

(Dr Mohd Alias Lazim, 2007. Introductory Business Forecasting a Practical Approach)

3.4 Choosing the Best Model

The criterion used to differentiate between a poor forecast model and a good forecast model is called the ‘error measure’. Thus, a particular model is considered better than the others if it meets this certain set of criterion. The measurement of the ‘error measure’ is done by choosing an error measure that has the smallest value. There are several forms of error measures that are commonly being used by forecasters and researchers: i. Mean Squared Error (MSE)

ii. Mean Absolute Percentage Error (MAPE)

Mean Squared Error (MSE)

MSE is the standard error measure for assessing the model’s fitness to a particular data and comparing the model’s forecasting performance. For the one step ahead forecast, the equation is written as

[pic] (3.5)

for which [pic] (3.6)

where,

[pic] [pic] is the actual observed value in time t.

[pic][pic] is the fitted value in time t generated from the origin (t = 1,2,3,…,n)

n is the number of out-of-sample error terms generated by the model.

(Dr Mohd Alias Lazim, 2007. Introductory Business Forecasting a Practical Approach)

Mean Absolute Percentage Error (MAPE)

This can be the most widely used unit free measure. When measuring a series, MAPE is written as,

MAPE = [pic] (3.7)

where,

n denotes effective data points and,

[pic] is defined as the absolute percentage error calculated on the fitted values for a particular forecasting method.

(Dr Mohd Alias Lazim, 2007. Introductory Business Forecasting a Practical Approach)

CHAPTER 4

RESULTS AND DISCUSSION

4.1 INTRODUCTION

Results and discussion of ARIMA model for Industrial Production Index are presented in Section 4.2. ARIMA model for Mining Index is discussed in Section 4.3, followed by ARIMA model for Electricity and Manufacturing Index in Section 4.4 and 4.5 respectively.

4.2 BOX-JENKINS MODEL FOR INDUSTRIAL PRODUCTION INDEX

4.2.1 Initial Data Investigation

At the initial stage, a simple data investigation was conducted to understand the basic pattern of the series and, hence to identify any unusual observation or characteristic existing. This is done by constructing a simple time plot (Figure 4.1) and fitting a linear trend line. A cursory observation indicates that the series is not stationary.

The series, however, does not indicate presence of seasonal effect though significantly small values at time points 26th and 38th were observed which could be constructing as irregular effects. For this example, no specific action will be made on these irregularities.

[pic]

Figure 4.1: Time Plot of Yt and the Trend Line

The ACF and PACF were also plotted so as to collect more conclusive evidence on its stationary conditions. Figure 4.2 shows the decaying pattern of the autocorrelations whilst for the partial autocorrelation in Figure 4.3 such pattern was not visibly noticeable. Three values of the autocorrelations exceed the significant limit.

[pic] Figure 4.2: The Autocorrelation Function (ACF) for Yt

[pic]

Figure 4.3: The Partial Autocorrelation Function (PACF) of Yt

Then, the next step is to perform the first order differencing and the resulting series is plotted as shown in Figure 4.4.

[pic]

Figure 4.4: Time Plot of Zt = Yt-Yt-1 and Trend Line

4.2.2 Performing the First Differencing

The first differencing was performed in order to render the original series stationary. Let the series in first difference be Zt such that,

Zt = Yt-Yt-1 (4.1)

A time plot of Zt = Yt-Yt-1 is given in Figure 4.4. The fitted trend line does not indicate presence of trend component. Thus, the stationary assumption was met.

Then, further evidence of the stationary condition is obtained by plotting the ACF and PACF as shown in Figure 4.5 and Figure 4.6. The decaying pattern in both the ACF and PACF has disappeared.

However, for the ACF the rate of decay is much faster in which the values of autocorrelation change from positive and negative. On the other hand the PACF show several spikes, the most significant at lag 1 ( exceeding the 2 standard error line) and the second at lag 12 ( barely touching the 2 standard error line).

[pic]

Figure 4.5: The Autocorrelation Function (ACF) of Zt = Yt-Yt-1

[pic]

Figure 4.6: The Partial Autocorrelation Function (PACF) of Zt = Yt-Yt-1

Therefore, from the ACF and PACF (Figure 4.5 and 4.6) one can conclude that the series is now stationary. However, the series may not necessarily be perfectly stationary because in most economic or business data series such condition may not be easily achievable because of the unexplainable factors inherent in such data sets.

4.2.3 Model Identification

The third stage in this analysis is to perform model identification. The process of identifying the suitable models to be fitted to the data series involved the analysis of the ACF and the PACF of the stationary series as depicted in Figure 4.5 and Figure 4.6.

However, it need to be reiterated that it is not easy to exactly specify the model class based on the evidence as provided by the ACF and PACF since we cannot summarily judge the impact of the magnitude of the spikes on the model. Close scrutiny and careful judgment 0f the location and size of the spikes are essential to determine the number of lags required.

As a way out of this predicament several possible models will be specified, estimated and then performed the necessary validation/diagnostic tests. The model picked is the one that gives the superior results.

Based on the Figure 4.5 and Figure 4.6 and the number of significant spikes, the following four models have been identified and estimated using Minitab.

• ARIMA(2,1,2)

• ARIMA(2,1,1)

• ARIMA(1,1,1)

4.2.4 Model Validation and Diagnostics checking

In a well fitted model the residuals obtained are expected to have the property of white noise. Hence, model validation and diagnostic checking involved analyzing the residuals for resemblance of white noise characteristic. A simple technique is to observe the ACF and PACF of the residuals. If the residuals are white noise, then it is expected that no significant partial autocorrelations coefficients exist. Hence, the stationary condition of the residuals is achieved.

More sophisticated technique of establishing the stationary condition of the residuals is to check the Ljung-Box Q Statistic. This statistic is provided by the Minitab software.

The hypotheses are,

H0: the errors are random (white noise)

H1: the errors are nonrandom (not white noise)

The summary of the various statistics obtained from fitting the models using the Minitab are tabulated in Table 4.1.

Table 4.1: Summary of Portmanteau Test for Index of Industrial production

| |Model |

|Statistics | |

| |ARIMA (2,1,2) |ARIMA (2,1,1) |ARIMA (1,1,1) |

|Chi-Square |8.8 |10.8 |10.0 |

|DF |7 |8 |9 |

|Critical value |14.05 |15.50 |16.91 |

|Decision |Accept H0 |Accept H0 |Accept Ho |

|(5% sig.level) | | | |

|conclusion |The errors are white |The errors are white |The errors are white |

| |noise |noise |noise |

|MSE |18.036 |18.491 |18.503 |

|MAPE |3.163 |2.992 |3.094 |

|Rank MSE |1 |2 |3 |

|Rank MAPE |3 |1 |2 |

4.2.5 Results and Conclusion

Checking the values of the chi-square and comparing them against the critical values, we can accept the null hypothesis that the errors for each of the models are white noise. Hence, the conclusion is that the models are well specified and adequate. However, we only need one model among the four well specified models. Thus, based on the smallest chi-square, ARIMA (2,1,1) is the best.

However, in order to ensure that the above decision is correct further analysis using the respective MSE’s as comparison was performed. Based on the smallest MSE, the result points towards ARIMA(2,1,2).

Then, we compare the models using MAPE where the smallest MAPE is the best model. Based on the Table 4.1, the smallest MAPE is ARIMA (2,1,1). On the other hand, by applying the concept of parsimony, ARIMA (1,1,1) though having slightly larger values of the MSE and chi square will be the obvious choice.

Thus, we can conclude that the best ARIMA model for Industrial production Index is ARIMA (2,1,1).

4.2.6 Generating Forecast Values using ARIMA (2,1,1)

Table 4.2 shows the forecast value for the year 2010 and 2011 using ARIMA(2,1,1). Then, Figure 4.7 indicates the graph of forecast value for 2011. The graph shows that the Industrial production index is increase gradually over year.

Table 4.2: Forecast Value for year 2010 and 2011

|Year |Month |Actual |Forecast |

|2010 |Jan |108.24 |102.89 |

| |Feb |96.16 |104.09 |

| |Mar |110.79 |103.82 |

| |Apr |107.63 |104.33 |

| |Mei |109.99 |104.36 |

| |June |106.76 |104.63 |

| |July |108.75 |104.73 |

| |Aug |107.23 |104.90 |

| |Sept |106.35 |105.01 |

| |Oct |110.15 |105.14 |

| |Nov |106.33 |105.24 |

| |Dec |108.88 |105.34 |

|2011 |Jan | |105.43 |

| |Feb | |105.52 |

| |Mar | |105.60 |

| |Apr | |105.67 |

| |Mei | |105.74 |

| |June | |105.81 |

| |July | |105.88 |

| |Aug | |105.94 |

| |Sept | |106.00 |

| |Oct | |106.06 |

| |Nov | |106.12 |

| |Dec | |106.17 |

[pic]

Figure 4.7 : Forecast Value for Industrial Production Index for the Year 2011.

4.3 BOX-JENKINS MODEL FOR MINING

4.3.1 Initial Data Investigation

In this step, the data series was investigated by plotting the time chart ACF and PACF. The result clearly indicates that the series not only is not stationary but also contains the seasonal component as evidence from Figure 4.8. Note the regular peaks and trough in Figure 4.9 and the Figure 4.10 shows the pattern like wave and to a slightly lesser extent in Figure 4.10. All these characterize the behavior of the data with seasonal effect present.

[pic]

Figure 4.8: Time Plot of Yt

[pic]

Figure 4.9: The Autocorrelation Function (ACF) of Yt

[pic]

Figure 4.10: The Partial Autocorrelation Function (ACF) of Yt

4.3.2 Performing Seasonal Differencing

Since this is monthly series, the seasonal differences is given as Zt = Yt- Yt-12. The series shows decline over time in Figure 4.11. In other words, the data series indicate presence of trend component. However, in order to ensure that the above decision is correct further analysis by observing Figure 4.12 and Figure 4.13, one can conclude that the series in seasonal difference, Zt, is not stationary. Note the ACF and PACF which depict the decaying and undulating characteristics.

[pic]

Figure 4.11: Time Plot of Series in Seasonal Differencing, Zt = Yt- Yt-12

[pic]

Figure 4.12: The Autocorrelation Function (ACF) of Zt

[pic]

Figure 4.13: The Partial Autocorrelation Function (ACF) of Zt

4.3.3 Performing Non-Seasonal Differencing

Non-seasonal differencing, Wt = Zt-Zt-1 was performed and the time plot was obtained. The time plot in Figure 4.14 does not show the presence of trend whilst the ACF indicates significant spikes at certain lags. In fact Figure 4.15 and Figure 4.16 confirmed that the series is now stationary.

[pic]

Figure 4.14: Time Plot of Wt

[pic]

Figure 4.15: The Autocorrelation Function (ACF) of Wt.

[pic]

Figure 4.16: The Partial Autocorrelation Function (ACF) of Wt

In order to determine the best model formulations to be fitted to the data series one needs to observe for significant spikes in Figure 4.15 and Figure 4.16. Since, the series contains the seasonal component then general formulation is written as ARIMA (p,d,q)(P,D,Q)12.

To identify the non-seasonal part, one needs to observe the significant spikes at lags other 12, 24 or 36, though lags 36 and beyond are uncommon for most series.

As mentioned earlier, to be able to exactly identify the right model formulation is rather difficult because of the nature of the economic/business data series. Hence, several models believed to be the best possible formulations are identified and estimated.

4.3.4 Model Identification

From Figure 4.15, two significant spikes are observed. One at lag 1 and one at lag 11. These two spikes can be used to specify the non seasonal MA part of the model. Another significant spike is also observed at lag 12 to suggest the seasonal SMA part of the model.

Similarly, to identified the AR part of the model one needs to observe the PACF, i.e Figure 4.16. Three significant spikes are observed at lag 1 and others at lag 2 and at lag 10 to suggest the non seasonal AR part of the model. However, there is no significant spike at lag 12 to indicate the seasonal SAR part of the model.

However, even if these observations are made we cannot be perfectly sure of the correct values of the respective p, q, P, and Q that can be assigned to the model. Hence, to ensure that a well specified model is not missed out, several model formulations will be identified and estimated. Subsequently by using the statistic available from the specified software a final decision will be made on the best model formulation. Three models specified are:

ARIMA (3,1,0)(0,1,1)12

ARIMA (3,1,1)(0,1,0)12

ARIMA (3,1,0)(0,1,0)12

4.3.5 Model Validation and Diagnostic Checking

In a well fitted model the residuals obtained are expected to have the property of white noise. Hence, model validation and diagnostic checking involved analyzing the residuals for resemblance of white noise characteristic. A simple technique is to observe the ACF and PACF of the residuals. If the residuals are white noise, then it is expected that no significant partial autocorrelations coefficients exist. Hence, the stationary condition of the residuals is achieved.

More sophisticated technique of establishing the stationary condition of the residuals is to check the Ljung-Box Q Statistic. This statistic is provided by the Minitab software.

The hypotheses are,

H0: the errors are random (white noise)

H1: the errors are nonrandom (not white noise)

To pick the best model, all test statistics are summarized as in Table 4.3 and evaluated.

Table 4.3: Summary of Portmanteau Test for Mining

| |Model |

|Statistics | |

| | ARIMA | ARIMA | ARIMA |

| |(3,1,0)(0,1,1)12 |(3,1,1)(0,1,0)12 |(3,1,0)(0,1,0)12 |

| | | | |

|Chi-Square |11.3 |13.10 |14.0 |

|DF |7 |7 |8 |

|Critical value |14.06 |14.06 |15.50 |

|Decision |Accept Ho |Accept Ho |Accept Ho |

|(5% sig.level) | | | |

|conclusion |The errors are white |The errors are white noise|The errors are white |

| |noise | |noise |

|MSE |6.702 |12.668 |12.269 |

|MAPE |1.995 |2.770 |2.750 |

|Rank MSE |1 |3 |2 |

|Rank MAPE |1 |2 |3 |

4.3.6 Results and Conclusion

Except for the first model, all other models are well specified since the errors are white noise, i.e. by accepting the null hypothesis as a result of achieving smaller chi square values as compared to the respective critical value at the respective DF (Degrees of Freedom). To ease the problem of deciding one among the four models another criterion will be invoked, i.e. the concept of parsimony and the size of their respective MSE and MAPE. On these account, model 1, ARIMA (3,1,0)(0,1,1)12, is therefore the winner since it has the smallest MSE and also smallest MAPE.

4.3.7 Generating Forecast Values using ARIMA (3,1,0)(0,1,1)12.

Table 4.4 shows the forecast value for the year 2010 and 2011 using

ARIMA (3,1,0)(0,1,1)12. Then, Figure 4.17 indicates the graph of forecast value for 2011.

Table 4.4: Forecast Value for year 2010 and 2011

|Year |Month |Actual |Forecast |

|2010 |Jan |103.34 |98.19 |

| |Feb |88.24 |87.57 |

| |Mar |98.74 |96.50 |

| |Apr |94.22 |90.02 |

| |Mei |96.43 |93.16 |

| |June |90.85 |86.87 |

| |July |92.74 |93.56 |

| |Aug |90.16 |90.01 |

| |Sept |95.76 |89.88 |

| |Oct |95.29 |92.54 |

| |Nov |92.54 |88.62 |

| |Dec |94.93 |94.04 |

|2011 |Jan | |93.99 |

| |Feb | |83.53 |

| |Mar | |92.21 |

| |Apr | |85.46 |

| |Mei | |88.48 |

| |June | |82.04 |

| |July | |88.55 |

| |Aug | |84.83 |

| |Sept | |84.54 |

| |Oct | |87.02 |

| |Nov | |82.94 |

| |Dec | |88.19 |

[pic]

Figure 4.17 : Forecast Value for Mining for the Year 2011.

4.4 BOX-JENKINS MODEL FOR ELECTRICITY

4.4.1 Initial Data Investigation

At the initial stage, a simple data investigation was conducted to understand the basic pattern of the series and, hence to identify any unusual observation or characteristic existing. This is done by constructing a simple time plot (Figure 4.18) and fitting a linear trend line. A cursory observation indicates that the series is not stationary. The series, however, does not indicate presence of seasonal effect though significantly a small value at time points 26th was observed which could be constructed as irregular effects. For this example, no specific action will be made on these irregularities.

[pic]

Figure 4.18: Time Plot of Yt and the Trend Line

The ACF and PACF were also plotted so as to collect more conclusive evidence on its stationary conditions. Figure 4.19 shows the decaying pattern of the autocorrelations whilst for the partial autocorrelation in Figure 4.20 such pattern was not visibly noticeable. Two values of the autocorrelations exceed the significant limit.

[pic]

Figure 4.19: The Autocorrelation Function (ACF) of Yt

[pic]

Figure 4.20: The Partial Autocorrelation Function (PACF) of Yt

Then, the next step was to perform the first order differencing and the resulting series is plotted as shown in Figure 4.21.

4.4.2 Performing the First Differencing

The first differencing was performed in order to render the original series stationary. Let the series in first difference be Zt such that,

Zt = Yt-Yt-1 (4.2)

A time plot of Zt = Yt-Yt-1 is given in Figure 4.21. The fitted trend line does not indicate presence of trend component. Thus, the stationary assumption was met.

[pic]

Figure 4.21: Time Plot of Zt = Yt-Yt-1 and Trend Line

Then, further evidence of the stationary condition is obtained by plotting the ACF and PACF that shown in Figure 4.22 and Figure 4.23. The decaying pattern in both the ACF and PACF has disappeared.

However, for the ACF the rate of decay is much faster in which the values of autocorrelation change from negative and positive and vice versa. On the other hand the PACF show several spikes, the most significant at lag 1 (exceeding the 2 standard error line).

[pic]

Figure 4.22: The Autocorrelation Function (ACF) of Zt = Yt-Yt-1

[pic]

Figure 4.23: The Partial Autocorrelation Function (PACF) of Zt = Yt-Yt-1

Therefore, from the ACF and PACF (Figure 4.22 and 4.23) one can conclude that the series is now stationary. However, the series may not necessarily be perfectly stationary because in most economic or business data series such condition may not be easily achievable because of the unexplainable factors inherent in such data sets.

4.4.3 Model Identification

The third stage in this analysis is to perform model identification. The process of identifying the suitable models to be fitted to the data series involved the analysis of the ACF and the PACF of the stationary series as depicted in Figure 4.22 and Figure 4.23.

From Figure 4.22, one significant spike is observed at lag 1. This spike can be used to specify the MA part of the model.

Similarly, to identified the AR part of the model one needs to observe the PACF, i.e Figure 4.23. There is also a significant spike at lag 1 to suggest the AR part of the model.

Based on the Figure 4.22 and Figure 4.23 and the number of significant spikes, the following three models have been identified and estimated using Minitab.

• ARIMA(1,1,1)

• ARIMA(1,1,0)

• ARIMA(0,1,1)

4.4.4 Model Validation and Diagnostics checking

In a well fitted model the residuals obtained are expected to have the property of white noise. Hence, model validation and diagnostic checking involved analyzing the residuals for resemblance of white noise characteristic. A simple technique is to observe the ACF and PACF of the residuals. If the residuals are white noise, then it is expected that no significant partial autocorrelations coefficients exist. Hence, the stationary condition of the residuals is achieved.

More sophisticated technique of establishing the stationary condition of the residuals is to check the Ljung-Box Q Statistic. This statistic is provided by the Minitab software.

The hypotheses are,

H0: the errors are random (white noise)

H1: the errors are nonrandom (not white noise)

The summary of the various statistics obtained from fitting the models using the Minitab are tabulated in Table 4.5.

Table 4.5: Summary of Portmanteau Test for Electricity

| |Model |

|Statistics | |

| |ARIMA (1,1,1) |ARIMA (1,1,0) |ARIMA (0,1,1) |

|Chi-Square |18.1 |17.10 |20.6 |

|DF |9 |10 |10 |

|Critical value |16.91 |18.30 |18.30 |

|Decision |Reject H0 |Accept H0 |Reject H0 |

|(5% sig.level) | | | |

|conclusion |The errors are not white |The errors are white noise |The errors are not white |

| |noise | |noise |

|MSE |30.26 |29.57 |31.77 |

|MAPE |3.930 |3.897 |4.116 |

4.4.5 Results and Conclusion

Checking the values of the chi-square and comparing them against the critical values, we can accept the null hypothesis that the errors for each of the models are white noise. Hence, the conclusion is only one models are well specified and adequate.

Thus, we can conclude that the best ARIMA model for Electricity is

ARIMA (1,1,0).

4.4.6 Generating Forecast Values using ARIMA (1,1,0)

Table 4.6 shows the forecast value for the year 2010 and 2011 using ARIMA (1,1,0). Then, Figure 4.24 indicates the graph of forecast value for 2011. The graph shows that the Electricity increase gradually over year.

Table 4.6: Forecast Value for year 2010 and 2011

|Year |Month |Actual |Forecast |

|2010 |Jan |119.76 |115.34 |

| |Feb |108.27 |117.03 |

| |Mar |126.43 |116.64 |

| |Apr |123.62 |117.45 |

| |Mei |127.70 |117.56 |

| |June |120.60 |118.08 |

| |July |123.88 |118.36 |

| |Aug |123.63 |118.78 |

| |Sept |115.15 |119.13 |

| |Oct |126.75 |119.51 |

| |Nov |118.43 |119.87 |

| |Dec |120.09 |120.25 |

|2011 |Jan | |120.61 |

| |Feb | |120.99 |

| |Mar | |121.36 |

| |Apr | |121.73 |

| |Mei | |122.10 |

| |June | |122.47 |

| |July | |122.83 |

| |Aug | |123.20 |

| |Sept | |123.57 |

| |Oct | |123.94 |

| |Nov | |124.31 |

| |Dec | |124.68 |

[pic]

Figure 4.24: Forecast Value for Electricity for the Year 2011.

4.5 BOX-JENKINS MODEL FOR MANUFACTURING

4.5.1 Initial Data Investigation

At the initial stage, a simple data investigation was conducted to understand the basic pattern of the series and, hence to identify any unusual observation or characteristic existing. This is done by constructing a simple time plot (Figure 4.25) and fitting a linear trend line. A cursory observation indicates that the series is not stationary. The series, however, does not indicate presence of seasonal effect though significantly a small value at time points 25th was observed which could be constructed as irregular effects. For this example, no specific action will be made on these irregularities.

[pic]

Figure 4.25: Time Plot of Yt and the Trend Line

The ACF and PACF were also plotted so as to collect more conclusive evidence on its stationary conditions. Figure 4.26 shows the decaying pattern of the autocorrelations whilst for the partial autocorrelation in Figure 4.27 such pattern was not visibly noticeable. A spike of the autocorrelations exceeds the significant limit at lag 1.

[pic]

Figure 4.26: The Autocorrelation Function (ACF) of Yt

[pic]

Figure 4.27: The Partial Autocorrelation Function (PACF) of Yt

Then, the next step was to perform the first order differencing and the resulting series is plotted as shown in Figure 4.28.

4.5.2 Performing the First Differencing

The first differencing was performed in order to render the original series stationary. Let the series in first difference be Zt such that,

Zt = Yt-Yt-1 (4.3)

A time plot of Zt = Yt-Yt-1 is given in Figure 4.28. The fitted trend line does not indicate presence of trend component. Thus, the stationary assumption was met.

[pic]

Figure 4.28: Time Plot of Zt = Yt-Yt-1 and Trend Line.

Then, further evidence of the stationary condition is obtained by plotting the ACF and PACF that shown in Figure 4.29 and Figure 4.30. The decaying pattern in both the ACF and PACF has disappeared.

However, for the ACF the rate of decay is much faster in which the values of autocorrelation change from negative and positive and vice versa. On the other hand the PACF show several spikes, the most significant at lag 1 (exceeding the 2 standard error line) and another at lag 17(exceeding the 2 standard error line).

[pic]

Figure 4.29: The Autocorrelation Function (ACF) of Zt = Yt-Yt-1

[pic]

Figure 4.30: The Partial Autocorrelation Function (PACF) of Zt = Yt-Yt-1

Therefore, from the ACF and PACF (Figure 4.29 and 4.30) one can conclude that the series is now stationary. However, the series may not necessarily be perfectly stationary because in most economic or business data series such condition may not be easily achievable because of the unexplainable factors inherent in such data sets.

4.5.3 Model Identification

The third stage in this analysis is to perform model identification. The process of identifying the suitable models to be fitted to the data series involved the analysis of the ACF and the PACF of the stationary series as depicted in Figure 4.29 and Figure 4.30.

From Figure 4.29, one significant spike is observed at lag 1. This spike can be used to specify the MA part of the model.

Similarly, to identified the AR part of the model one needs to observe the PACF, i.e Figure 4.30. There are two significant spikes at lag 1 and lag 17 to suggest the AR part of the model.

Based on the Figure 4.29 and Figure 4.30 and the number of significant spikes, the following three models have been identified and estimated using Minitab.

• ARIMA(1,1,1)

• ARIMA(1,1,0)

• ARIMA(0,1,1)

4.5.4 Model Validation and Diagnostics checking

In a well fitted model the residuals obtained are expected to have the property of white noise. Hence, model validation and diagnostic checking involved analyzing the residuals for resemblance of white noise characteristic. A simple technique is to observe the ACF and PACF of the residuals. If the residuals are white noise, then it is expected that no significant partial autocorrelations coefficients exist. Hence, the stationary condition of the residuals is achieved.

More sophisticated technique of establishing the stationary condition of the residuals is to check the Ljung-Box Q Statistic. This statistic is provided by the Minitab software.

The hypotheses are,

H0: the errors are random (white noise)

H1: the errors are nonrandom (not white noise)

The summary of the various statistics obtained from fitting the models using the Minitab are tabulated in Table 4.6.

Table 4.7: Summary of Portmanteau Test for Manufacturing

| |Model |

|Statistics | |

| |ARIMA (1,1,1) |ARIMA(1,1,0) |ARIMA (0,1,1) |

|Chi-Square |8.4 |8.4 |8.7 |

|DF |9 |10 |10 |

|Critical value |16.91 |18.30 |18.30 |

|Decision |Accept Ho |Accept Ho |Accept Ho |

|(5% sig.level) | | | |

| | | | |

|conclusion |The errors are white noise|The errors are white |The errors are white |

| | |noise |noise |

|MSE |25.63 |25.06 |26.09 |

|MAPE |3.559 |3.559 |3.574 |

|Rank MSE |2 |1 |3 |

|Rank MAPE |2 |1 |3 |

4.5.5 Results and Conclusion

Checking the values of the chi-square and comparing them against the critical values, we can accept the null hypothesis that the errors for each of the models are white noise. Hence, the conclusion is that the three models are well specified and adequate. However, we only need one model among the three well specified models. Thus, based on the smallest chi-square, ARIMA (1,1,1) and ARIMA(1,1,0) is the best.

However, in order to ensure that the above decision is correct further analysis using the respective MSE’s as comparison was performed. Based on the smallest MSE, the result points towards ARIMA (1,1,0).

Then, we compare the models using MAPE where the smallest MAPE is the best model. Based on the Table 4.6, the smallest MAPE is also ARIMA (1,1,0). On the other hand, by applying the concept of parsimony, ARIMA (0,1,1) though having slightly larger values of the MSE and chi square will be the obvious choice.

Thus, we can conclude that the best ARIMA model for Manufacturing is ARIMA (1,1,0).

4.5.6 Generating Forecast Values using ARIMA (1,1,0)

Table 4.7 shows the forecast value for the year 2010 and 2011 using ARIMA (1,1,0). Then, Figure 4.31 indicates the graph of forecast value for 2011. The graph shows the upward trend.

Table 4.8: Forecast Value for year 2010 and 2011

|Year |Month |Actual |Forecast |

|2010 |Jan |109.53 |105.59 |

| |Feb |98.86 |105.98 |

| |Mar |115.14 |106.09 |

| |Apr |112.62 |106.31 |

| |Mei |114.89 |106.49 |

| |June |113.14 |106.68 |

| |July |115.07 |106.87 |

| |Aug |113.94 |107.06 |

| |Sept |110.64 |107.25 |

| |Oct |115.78 |107.44 |

| |Nov |111.85 |107.63 |

| |Dec |114.56 |107.82 |

|2011 |Jan | |108.02 |

| |Feb | |108.21 |

| |Mar | |108.40 |

| |Apr | |108.59 |

| |Mei | |108.78 |

| |June | |108.97 |

| |July | |109.16 |

| |Aug | |109.35 |

| |Sept | |109.54 |

| |Oct | |109.73 |

| |Nov | |109.92 |

| |Dec | |110.11 |

[pic]

Figure 4.31: Forecast Value for Manufacturing for the Year 2011.

CHAPTER 5

CONCLUSIONS AND RECOMMENDATIONS

1. INTRODUCTION

Section 5.2 of this chapter gives conclusion of this study. Then, some recommendation can be found in Section 5.3

2. CONCLUSION

In conclusion, based on the analysis and results from the previous chapter, we can conclude that, all the original data series have irregular effect except Mining that has seasonal effect. Thus, performing first differencing is needed in order to achieve stationary series. Seasonal differencing was applied in Mining since the data series indicate the presence of trend component.

The best ARIMA model was evaluated in order to forecast the Industrial Production Index (IPI) and all the IPI division in Malaysia. Based on the smallest MSE and MAPE, ARIMA (2,1,1) was proposed as the best ARIMA model to forecast Industrial Production Index.

We found that, the Box-Jenkins model was also appropriate to forecast the value of IPI division such as Mining, Manufacturing and Electricity. ARIMA (1,1,0) is the best ARIMA model to forecast Electricity. While ARIMA(3,1,1)(0,1,1)12 and ARIMA(1,1,0) is the best ARIMA model to forecast Mining and Manufacturing respectively.

3. RECOMMENDATION

We recommend that Box-Jenkins Model should be used to forecast Industrial Production Index in order to identify Malaysia economic performance. It is important to provide a clear illustration of the Malaysia economy and shape the strategies direction by using the generated value of the forecasting.

Other than that, other models such as seasonal Holt-Winters model should be tried to fit the Industrial Production Index to generate an accurate result in order to forecast IPI’s value.

REFERENCES

1. Bodo, G. & Signorini, L.F (1987). Short-term forecasting of the industrial production index. International Journal of Forecasting. 3(2) p. 245-259.

2. Francis, X. & Glenn, D.R (1991). Forecasting Output with the Composite Leading Index: A Real- Time Analysis. Journal of the American Statistical Association. 86(415) p.603-610.

3. Fang-Mei Tseng (2002). Combining neural network model with seasonal time series ARIMA model. Technological Forecasting and Social Change 69(1) p. 71-87.

4. Jeffrey A. Miron and Christina D. Romer (1989) .New Monthly Index of Industrial Production, 1884-1940. The Journal of Economic History. 50(2) p.321-337.

5. Joseph H. Davis (2004). An Annual Index of U. S. Industrial Production, 1790–1915. Journal of Forecasting. 119(4) p.1177-1215.

6. K. D. Patterson (1995) A State Space Approach to forecasting the Final Vintage of Revised Data with an Application to the Index of Industrial Production. Journal of Forecasting. 14(4) p.337–350.

7. Mohd Alias Lazim (2007). Introductory Business Forecasting a Practical Approach, Second Edition. University Publication Centre (UPENA), Universiti Teknologi MARA.

8. Peter, K. (1987). The Cyclical Component of U. S. Economic Activity. The Quarterly Journal of Economics. 102(4) p.797-814.

9. Philip Hans Franses, Dick van Dijk (2005). The Forecasting Performance of Various models for Seasonality and Nonlinearity for quarterly Industrial Production . International Journal of Forecasting. 21(1) p. 87-102.

10. Revilla, P. (1991). Spanish Method to Improve Timeliness in the Industrial Production Indices. Spain: National statistical Institute.

11. T. Terasvirta, H. M. Anderson (1992) .Characterizing Nonlinearities in Business Cycles Using Smooth Transition Autoregressive Models. Journal of Applied Econometrics. 7(S1) p. S1-S201.

-----------------------

Model Identification

Stage 1

Model estimation

Stage 2

Model Validation:

Diagnostic & Statistical Test (Portmanteau test, AIC, BIC)

If test fail: Revise model

If pass test:

Apply Model

Stage 3…...

Premium Essay

...Products Liability Research Paper: Brazilian Blowout By Tekendrea Fayne LEG500011VA016-1126-001: Law, Ethics & Corp. Governance Francis Hatstat Strayer University September 9, 2012 Premises Brazilian Blowout Professional Treatments are use of innovative and breakthrough bonding technologies, these treatments actually improve the health and condition of the hair by creating a protective protein layer around the hair shaft to eliminate frizz and smooth the cuticle. These treatments aim to smooth out unruly curls and waves and to reduce frizz. However, the treatments do not guarantee completely straight hair. If the Brazilian Blowout is performed correctly, about 50 to 80 percent of the curl can be reduced depending on the original hair texture. Treatments last around 10–12 weeks and repeating the treatment every few months will allow for treatment of new growth. Depending on the treatment used downtime, after it is performed ranges from no-wait to a 72 hour period in which the recipient cannot wash or wet the hair, exercise, tuck the hair behind the ears, or pin it up with any hair clip, pony tail holder or headband, as doing so may compromise the result of the treatment. The treatment on average cost about $150–$600 depending on the hair length. FDA states that Brazilian Blowouts are hazardous to the health of the women who use them and hairdressers who apply them. The concern is over the “alleged” presence of formaldehyde in the hair smoothing...

Words: 1664 - Pages: 7

Premium Essay

...Product refers to the fashion items and services that a company will offer its target market. Company history may play a major role here; many firms have a long-standing record in producing specific lines. For instance, when a sportswear company may try to develop products on sports equipment but will not usually decide also to make and sell bras or evening gowns. Product element is fundamental to the fashion design industry. The continual process of new product development and resulting change drives the whole industry and answers the demand from consumers for a constant stream of new ideas and offerings. . Without the constant generation and introduction of new ideas, the concept of fashion may not exist, the seasonal fashion shows and collections may fade out. Axiomatically, if consumers were not constantly engaged in the process of looking for new products to satisfy their emerging needs, the fashion process could not function either. All of the three brands, H&M, DKNY and PRADA are at the maturity stage of the product life cycle. They all have a long brand history. Miuccia Prada designed Prada in 1988. DKNY was founded by Donna Karan in 1989 in New York. H&M was founded in 1947 in Sweden. At this stage, their products have achieved acceptance by most potential buyers. There is a slow down in sales growth in total. These companies may try to increase their advertising and sales promotion to remind and inform the public of their products and events. They can also......

Words: 372 - Pages: 2

Free Essay

... MARKET RESEARCH NAMKEEN MARKET IN INDIA Table of contents 1. | | Title | | 2. | | Introduction | | 3. | | Namkeen market | | | 3.1. | Key players/ Brands | | | 3.2. | Market share | | | 3.3. | Sub category/ variety | | 4. | | Price, SKU & Packaging | | 5. | | Concept of Namkeen market | | | 5.1. | Market size | | | 5.2. | Market type | | | 5.3. | Market segment | | 6. | | Positioning | | 7. | | Trends | | 8. | | Campaign | | 9. | | References | | TITLE To study Namkeen market in India INTRODUCTION The country of India is the 2nd largest food producer in the world. With a continuous and rapid growth, this industry is most likely to double itself in the coming 10 years. From time to time, the country involves different kinds of new technologies related to food processing, which are updated on regular intervals as well so as to meet the modern requirement of the citizens of India. Starting from vegetarian to non-vegetarian food, milk to milk products, junk to health food,Namkeen, soft drinks to alcoholic beverages, the country manufactures all kinds of food products. Some of the most prominent sub-divisions of Indian food industry are soft drink bottling, fishing, confectionery manufacturing, aqua-culture, poultry and meat processing, grain-milling, alcoholic beverages, fast-food manufacturing, ready-to-eat cereals processing etc. Initially Namkeen in India was usually made at home but with the increasing number of......

Words: 2100 - Pages: 9

Premium Essay

...Product quality The collection of features and characteristics of a product that contribute to its ability to meet given requirements . To consumers, a high-quality product is one that well satisfies their preferences and expectations. This consideration can include a number of characteristics, some of which contribute little or nothing to the functionality of the product but are significant in providing customer satisfaction. A third view relating to quality is to consider the product itself as a system and to incorporate those characteristics that pertain directly to the operation and functionality of the product. First is the view of the manufacturer, who is primarily concerned with the design, engineering, and manufacturing processes involved in fabricating the product. Quality control (QC) is the collection of methods and techniques for ensuring that a product or service is produced and delivered according to given requirements. In general business, product features are all the qualities and characteristics of a product– its size, shape, materials, and its functionalities and capabilities Brand Name, term, design, symbol, or any other feature that identifies one seller's good or service as distinct from those of other sellers." [1] Packaging is the science, art, and technology of enclosing or protecting products for distribution, storage, sale, and use. Packaging also refers to the process of design, evaluation, and production of packages. Packaging can......

Words: 258 - Pages: 2

Free Essay

...find out the “competitive analysis of packaged food industry in context of traditional sweets, snacks, namkeens opportunities and challenges ahead” and also the “Findings and Result of New Product Development”. In the training program I had tried my level best to arrange the work in systematic and chronological way. This endeavor work shall provide the Bikano marketing department, an idea about the market condition and the behaviour of consumers and wholesalers about their product. Therefore, it hoped with all sincerity that this work shall be of definite use to the organization. ACKNOWLEDGEMENT “Acknowledgement is an art, one can write glib stanzas without meaning a word, on the other hand one can make a simple expression of gratitude.” As anyone who has written a project work, or research work, it is quite impossible to acknowledge by name every individual who has played some part of this work. I feel it difficult to express in words my profound sense of gratitude to most respected persons who helped me to make this work possible. I acknowledge my gratitude to respected mentors. Ms.Pooja Jain who have been kind enough to suggest improvement of this work and make it broad, based. I would like to thank Mrs. Sangeeta Goel the Marketing manager, Mr. Nagesh Mishra the Research analyst of Bikanerwala food Pvt. Ltd. for their support and encouragement. Finally, of course great debt are owed to the Bikanerwala company for giving us an opportunity to be part of......

Words: 8944 - Pages: 36

Premium Essay

...Product The marketing mix starts with product part so in this section of the paper will be discussed what does the consumer want and need from the product, the main characteristics and features of the product and also the best ways to choose branding and packaging. Low-involvement consumers This group of consumers mostly has low income and usually buy cheaper things without extra attention before buying a product. To selling goods for low-involvement consumers there are few main important factors of consumer needs and wants from the product. First of all low involvement consumers don’t spend a lot of time thinking about which windscreen wiper has the best quality and which one has to choose - because of habitual decisions. Their primary priority is price. For that reason “50% discount” or “buy 1 and other get for free” can really attract low-involvement consumers. Other important priority is product convenience. Mostly consumers choose those products which attractively displayed and easy to find. The windscreen wipers should be in the center of the store shelves. For consumers it would be eye-catching product. Also accurate information – consumers place a high value. They have to quick and easy understand what written about the product, how can use it (simple instruction) and why this product is better than others. For that reason on product should not be too much text. Main characteristics of......

Words: 750 - Pages: 3

Free Essay

...Products Liability Research Paper Select a company that has been the subject of a product liability lawsuit in the last ten (10) years. The Plaintiffs vs. Bayer Pharmaceuticals, the German manufacturer of the birth controls Yaz and Yasmin has landed themselves in hot water and is headed to the courts. Bayer Pharmaceuticals net worth is over a billion dollars and is still climbing. The use of the birth controls Yaz and Yasmin has sparked a lot of attention with claims of a number of dangerous side effects. This case has become very popular, with over 11,300 claims pending and the possibility of more to come, Bayer is expected to pay out about $110 Million in the Yaz case in an attempt to avoid being tried before a jury but that is only the beginning of a long list of active claims. The use of these birth controls are causing an increased number of blood clots in women as well as complications of blood disorders, problems of the heart, strokes, and in some cases even death. www.drugwatch.com the problem appears to be stemming from drospirenone (a progestin) that is found in the birth control pills. In the case of Shannon Landry of Louisiana she filed a complaint with the U.S. district Court for the Southern District of Illinois. In 2000 Landry began taking Yaz and continued until 2010, and shortly thereafter she began having severe side effects. She was later diagnosed with a gallbladder disease called biliary dyskinesia that resulted in surgery to have her gallbladder......

Words: 2128 - Pages: 9

Premium Essay

...Market Research and Product Development By Kevin Ofor Abugu PhD Student – Cardiff Metropolitan University Introduction Organisations invest in new product development to ensure their future success in the market. Nevertheless most of the new products introduce into the market are more likely to fail than succeed (Viaene, 1999). Hoban (2002) posits that only one-third of the new products launched survive. Young (Ibid) states that the rate of new product failure is as high as 90 to 95 percent. The failures of the new products in mobile industry, automobile industry, beverage industry, etc. are few examples. Hence a thorough market research should be employed to precede new product development (Cooper & Klienschmidts, 2000). This elucidates the importance of market research in new product development (NPD). Companies must continuously acquire market information to be able to adapt a new product into the market (Cooper & Klienschmidts, Ibid). Such effort is expected to bring the customers’ need, wants and perception into the new product development process. For example, Cisco introduced a system through which her B2B customers share their ideas, design and order products online. Similarly, IBM introduced a forum through which her customers exchange information concerning the development of a new product. The information gathered through the various means is transmitted to the R&D through the communication with marketing. Marketing research acquires customer......

Words: 3400 - Pages: 14

Premium Essay

...Kevin Dunn MGT 364- Section 01 Research Paper: Product Development Dr. Denton November 21, 2013 Table of Contents: I. Introduction……………………………………………………………………3 II. Developing Products………………………………………………………….4 III. Product Differentiation……………………………………………………..10 IV. Conclusion and Recommendations ………………………………………..13 V. Works Cited…………………………………………………………………..15 Introduction Product development is one of the most important aspects to any business. New and innovative products have placed companies like Apple, Google and Samsung on the map. Companies like General Motors have been able to rebound from bankruptcy thanks to product development. On the other hand, companies like Eastman Kodak have fallen by the wayside due to their inability to keep up with new products. According to an article in the European Journal of Engineering Education, “Product development is the set of activities starting with the perception of a market need and ending in the production and sale of a new product satisfying that need” (Silva, Arlindo, Elsa Henriques, Aldina Carvalho). By successfully developing a product firms can see increased profits as well as an increased market share. To the helicopter game players, proper product development can set one team apart and earn them more profits. The purpose of this research paper is to explain how to successfully build a product through the phases of product development and product differentiation. As well as to give......

Words: 3881 - Pages: 16

Free Essay

...Secondary Market Research to Support a New Product Innovation The Product The Energy Bar is a mountable wall unit for households that enables them to track their energy usage by providing numbers for electric, heat, and water consumption. The Energy Bar provides a visual to let you know how much you are using, how much you should be using, and how much you could be saving! It also compares your usage for the current month to that of the month prior to help homeowners improve the energy efficiency of their homes, while also saving money. As you see the numbers go up and down, you will intuitively know where you can reduce your consumption and utilities costs, and act on it immediately. Place it near your alarm system and it becomes easy to check before you, and the rest of your family, leave the house. This way, no unnecessary lights will be left on, heat will be kept to a minimum when you are away from the home, and no faucets will be left running by accident. This unique device addresses the energy shortages and water management problems that we should all be concerned about. Install an Energy Bar to ensure your future and your wallet! The Evidence In a poll conducted by Ipsos for Procter and Gamble, respondents chose “saving money” (64%) and “preserving resources” (56%) as the most important reasons for taking environmentally-friendly measures. When reporting the reasons that prevented people from leading a more environmentally-friendly......

Words: 790 - Pages: 4

Premium Essay

...Marketing Mix impending * Product * Price * Place * Promotion Outrageous crave Product life cycle (4 stages) * Intro * Growth * Maturity * Decline thrill Perceptional Map Maserati nuclelyptus New Product Launch Marketing Plan The purpose of this assignment is to create a marketing plan to launch a new product for both the domestic and international marketplace. Kotler & Keller define the marketing plan as “the central instrument for directing and coordinating the marketing effort” (Kotler & Keller, 2012, p36). This plan will include the following components: market need, market growth, SWOT analysis, potential competition, product offering and product definition, product identification, justification for choosing this product, and a 10-question survey. Market Needs According to research, young adults are the most attractive segment among marketing consumers both in terms of its size and its multibillion dollar purchasing power (Awan, M. 2014). The youth culture has been held up as the prototypical example of a global segment. They are reported to be the world biggest adopters of mobile technology, but limited research is available regarding segmentation. Therefore, there is a strong need for more segmentation research in the cell phone market, especially among the young adults since this age group is driving the market to new directions and uses. Market Growth According to the Cellular Telephone Industries......

Words: 325 - Pages: 2

Premium Essay

...New products from market research Curriculum Topics • Market research • Types of research • Quantitative and qualitative • Product development Kellogg’s with a sales value of £68 million*. In 2003 the Crunchy Introduction Nut brand created a brand extension. This involved using the The Kellogg Company is the world’s leading producer of cereals. Crunchy Nut name to launch a new product called Crunchy Nut Its products are manufactured in 18 countries and sold in more Clusters. This variant has two varieties, Milk Chocolate Curls and than 180 countries. For more than 100 years, Kellogg’s has been a Honey and Nut. Both of them have enabled the brand to reach a leader in health and nutrition through providing consumers with a wider group of consumers. This brand extension is now worth wide variety of food products. These are designed to be part of a £21 million in annual value sales.* balanced diet and meet the different tastes of consumers. Kellogg’s focuses on sustainable growth. This involves constantly looking This case study focuses on the importance of market research for ways to meet consumer needs by growing the cereal business during the development and launch of Crunchy Nut Bites, a more and expanding its product portfolio. recent extension to the Crunchy Nut brand. The objective of this innovation was to provide a new flavour and texture for consumers, Market research is a specific area of marketing that...

Words: 2461 - Pages: 10

Premium Essay

...A project on “The study on market research for the product of S.B. Beverages Pvt., Ltd, products.” (oxygem) A Project Report Submitted in partial fulfillment Of MBA (Batch 2014-2016) Submitted By: Kishor Dahare Submitted To: Director Academics: Prof. L.C Jamb Dr. Parag Kalkar SINHGAD INSTITUTES OF MANAGEMENT STUDIES, PUNE-411041 2014-2016 Declaration I kishor Dahare here by declare that the project titled {“The study on Market research for the product of S.B. Beverages Pvt. ,Ltd,products.” (oxygem)}is an original work carried out under the guidance of Prof. L.C Jamb.The report submitted is a bonafide work of my own efforts and has not been submitted to any institute or published before. Signature of the student (Kishor Dahare) Date: Place: ACKNOWLEDGEMENT It is with a sage sense of gratitude, I acknowledge the efforts of whole hosts of well-wishers who have in some way or other contributed in their own special ways to the success and completion of this summer internship project. First of all, I express my sage sense of gratitude and indebtedness to the Director of “Sinhgad Institute of Management”, Dr. Parag Kalkar, from the bottom of my heart, for his unprecedented support and faith that I do the best and his valuable recommendation and for accepting this......

Words: 7160 - Pages: 29

Premium Essay

...Marketing research plan product for Edible Arrangements® Problem definition Unfortunately over the last three years the sales and market share have declined 5% each year in the consumer segment and the business segment in several of our top franchises in New York, NY. Information Needs To conduct an examination to identify the problem and understand what events led to these results. I’ll visit all franchises and talk to managers, employees and customers in order to find out what they needs and real problems that are causing the decline. Research Objectives Achieve an increase of the sales and market shares within 12 months. Type of Study - Primary Research Finding out answers for specific questions in order to solve the causing problems, this will be done by conducting the following: - Face to face surveys - Online questionnaires - Phone calls This type of personal surveys provides a better feedback because people can express their own opinion. The researchers need to be trained to ensure that the answers won´t be influenced so we can have more accurate results. - Secondary Research - Using existing data - Observation - Focusing in specific groups - Qualitative and Quantitative Research Qualitative Research will give us the information about what are the customers’ preferences, what do they like, and why they won’t buy the products. Are the standards being......

Words: 486 - Pages: 2

Premium Essay

...MARKETING MANAGEMENT ASSIGNMENT Product a breakdown of the principles and processes involved in formulating a marketing strategy including those of market research. MBA ID: Word Count: 1901 A marketing strategy is composed of several interrelated elements. According the definition of marketing strategy by Study Market (2011), it outlines the manner in which the marketing mix is used to attract and satisfy the target market(s) and accomplish organization's objectives. This is quite an encompassing definition of marketing strategy as it touches all the elements. It shows that marketing strategy gives a direction on how the marketing mix (product, price, promotion & place) are utilized in such a way to satisfy consumer target markets to achieve organizational goals and objectives. The marketing mix, segmentation, branding, promotion and market research all serve as parts of the interrelated elements that make up a good marketing strategy. Marketing mix has its origins in the 6O's: Jerome McCarthy (1964) deduced the four-element framework: Product, Price, Promotion and Place. The marketing mix elements redefined by McCarthy became the most widely used and accepted element of marketing theory. Many writers have expressed serious doubts on the role of marketing mix as a management tool in its original form and proposing alternatives approaches. Some of the weaknesses of the 4Ps are domain-specific: which ignored the human factor, lack of strategic dimensions,......

Words: 2299 - Pages: 10