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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.

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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

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