Contents

Preface

CHAPTER 1: EViews workfile and descriptive data analysis

1.1 What is the EViews workfile?

1.2 Basic options in Eviews

1.3 Creating a workfile

1.4 Illustrative data analysis

1.5 Special notes and comments

1.6 Statistics as a sample space

CHAPTER 2: Continuous growth models

2.1 Introduction

2.2 Classical growth models

2.3 Autoregressive growth models

2.4 Residual tests

2.5 Bounded autoregressive growth models

2.6 Lagged variables or autoregressive growth models

2.7 Polynomial growth model

2.8 Growth models with exogenous variables

2.9 A Taylor series approximation model

2.10 Alternative univariate growth models

2.11 Multivariate growth models

2.12 Multivariate AR(p) GLM with trend

2.13 Generalized multivariate models with trend

2.14 Special notes and comments

2.15 Alternative multivariate models with trend

2.16 Generalized multivariate models with time-related effects

CHAPTER 3: Discontinuous growth models

3.1 Introduction

3.2 Piecewise growth models

3.3 Piecewise S-shape growth models

3.4 Two-piece polynomial bounded growth models

3.5 Discontinuous translog linear AR(1) growth models

3.6 Alternative discontinuous growth models

3.7 Stability test

3.8 Generalized discontinuous models with trend

3.9 General two-piece models with time-related effects

3.10 Multivariate models by states and time periods

CHAPTER 4: Seemingly causal models

4.1 Introduction

4.2 Statistical analysis based on a single time series

4.3 Bivariate seemingly causal models

4.4 Trivariate seemingly causal models

4.5 System equations based on trivariate time series

4.6 General system of equations

4.7 Seemingly causal models with dummy variables

4.8 General discontinuous seemingly causal models

4.9 Additional selected seemingly causal models

4.10 Final notes in developing models

CHAPTER 5: Special cases of regression models

5.1 Introduction

5.2 Specific cases of growth curve models

5.3 Seemingly causal models

5.4 Lagged variable models

5.5 Cases based on the US domestic price of copper

5.6 Return rate models

5.7 Cases based on the BASICS workfile

CHAPTER 6: VAR and system estimation methods

6.1 Introduction

6.2 The VAR models

6.3 The vector error correction models

6.4 Special notes and comments

CHAPTER 7: Instrumental variables models

7.1 Introduction

7.2 Should we apply instrumental models?

7.3 Residual analysis in developing instrumental models

7.4 System equation with instrumental variables

7.5 Selected cases based on the US_DPOC data

7.6 Instrumental models with time-related effects

7.7 Instrumental seemingly causal models

7.8 Multivariate instrumental models based on the US_DPOC

7.9 Further extension of the instrumental models

CHAPTER 8: ARCH models

8.1 Introduction

8.2 Options of ARCH models

8.3 Simple ARCH models

8.4 ARCH models with exogenous variables

8.5 Alternative GARCH variance series

CHAPTER 9: Additional testing hypotheses

9.1 Introduction

9.2 The unit root tests

9.3 The omitted variables tests

9.4 Redundant variables test (RV-test)

9.5 Nonnested test (NN-test)

9.6 The Ramsey RESET test

9.7 Illustrative examples based on the Demo.wf1

CHAPTER 10: Nonlinear least squares models

10.1 Introduction

10.2 Classical growth models

10.3 Generalized Cobb–Douglas models

10.4 Generalized CES models

10.5 Special notes and comments

10.6 Other NLS models

CHAPTER 11: Nonparametric estimation methods

11.1 What is the nonparametric data analysis

11.2 Basic moving average estimates

11.3 Measuring the best fit model

11.4 Advanced moving average models

11.5 Nonparametric regression based on a time series

11.6 The local polynomial Kernel fit regression

11.7 Nonparametric growth models

Appendix A: Models for a single time series

A.1 The simplesst model

A.2 First-order autoregressive models

A.3 Second-order autoregressive model

A.4 First-order moving average model

A.5 Second-order moving average model

A.6 The simplest ARMA model

A.7 General ARMA model

Appendix B: Simple linear models

B.1 The simplest linear model

B.2 Linear model with basic assumptions

B.3 Maximum likelihood estimation method

B.4 First-order autoregressive linear model

B.5 AR(p) linear model

B.6 Alternative models

B.7 Lagged-variable model

B.8 Lagged-variable autoregressive models

B.9 Special notes and comments

Appendix C: General linear models

C.1 General linear model with i.i.d. Gaussian disturbances

C.2 AR(1) general linear model

C.3 AR(p) general linear model

C.4 General lagged-variable autoregressive model

C.5 General models with Gaussian errors

Appendix D: Multivariate general linear models

D.1 Multivariate general linear models

D.2 Moments of an endogenous multivariate

D.3 Vector autoregressive model

D.4 Vector moving average model

D.5 Vector autoregressive moving average model

D.6 Simple multivariate models with exogenous variables

D.8 Maximum likelihood estimation for an MGLM

D.9 MGLM with autoregressive errors

References

Index

STATISTICS IN PRACTICE

*Series Advisory Editors*

Marian Scott

*University of Glasgow, UK*

Stephen Senn

*University of Glasgow, UK*

*Founding Editor*

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*Nottingham Trent University, UK*

Statistics in Practice is an important international series of texts which provide detailed coverage of statistical concepts, methods and worked case studies in specific fields of investigation and study.

With sound motivation and many worked practical examples, the books show in down-to-earth terms how to select and use an appropriate range of statistical techniques in a particular practical field within each title’s special topic area.

The books provide statistical support for professionals and research workers across a range of employment fields and research environments. Subject areas covered include medicine and pharmaceutics; industry, finance and commerce; public services; the earth and environmental sciences, and so on.

The books also provide support to students studying statistical courses applied to the above areas. The demand for graduates to be equipped for the work environment has led to such courses becoming increasingly prevalent at universities and colleges.

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*Library of Congress Cataloging-in-Publication Data*

Agung, Ign.

Time series data analysis using EViews / Ign Agung.

p. cm.

Includes bibliographical references and index.

ISBN 978-0-470-82367-5 (cloth)

1. Time-series analysis. 2. Econometric models. I. Title.

QA280.A265 2009

519.5’5–dc22 2008035077

ISBN 978-0-470-82367-5 (HB)

Dedicated to my wife

Anak Agung Alit Mas,

children

Ningsih A. Chandra, Ratna E. Lefort, and Dharma Putra,

sons in law

Aditiawan Chandra, and Eric Lefort,

daughter in law

Refiana Andries, and

all grand children

Indra, Rama, Luana, Leonard, and Natasya

Preface

Time series data, growth, or change over time can be observed and recorded in all their biological and nonbiological aspects. Therefore, the method of time series data analysis should be applicable not only for financial economics but also for solving all biological and nonbiological growth problems. Today, the availability of statistical package programs has made it easier for each researcher to easily apply any statistical model, based on all types of data sets, such as cross-section, time series, cross-section over time and panel data. This book introduces and discusses time series data analysis, and represents the first book of a series dealing with data analysis using EViews.

After more than 25 years of teaching applied statistical methods and advising graduate students on their theses and dissertations, I have found that many students still have difficulties in doing data analysis, specifically in defining and evaluating alternative acceptable models, in theoretical or substantial and statistical senses. Using time series data, this book presents many types of linear models from a large or perhaps an infinite number of possible models (see Agung, 1999a, 2007). This book also offers notes on how to modify and extend each model. Hence, all illustrative models and examples presented in this book will provide a useful additional guide and basic knowledge to the users, specifically to students, in doing data analysis for their scientific research papers.

It has been recognized that EViews is an excellent interactive program, which provides an excellent tool for us to use to do the best detailed data analyses, particularly in developing and evaluating models, in doing residual analysis and in testing various hypothesis, either univariate or multivariate hypotheses. However, it has also been recognized that for selected statistical data analyses, other statistical package programs should be used, such as SPSS, SAS, STATA, AMOS, LISREL and DEA.

Even though it is easy to obtain the statistical output from a data set, we should always be aware that we never know exactly the true value of any parameter of the corresponding population or even the true population model. A population model is defined as the model that is assumed or defined by a researcher to be valid for the corresponding population. It should be remembered that it is not possible to represent what really happens in the population, even though a large number of variables are used. Furthermore, it is suggested that a person’s best knowledge and experience should be used in defining several alternative models, not only one model, because we can never obtain the best model out of all possible models, in a statistical sense. To obtain the truth about a model or the best population model, read the following statements:

Often in statistics one is using parametric models…. Classical (parametric) statistics derives results under the assumption that these models are strictly true. However, apart from simple discrete models perhaps, such models are never exactly true (Hample, 1973, quoted by Gifi, 1990, p. 27).

Corresponding to this statement, Agung (2004, 2006) has presented the application of linear models, either univariate or multivariate, starting from the simplest linear model, i.e. the cell-means models, based on either a single factor or multifactors. Even though this cell-means model could easily be justified to represent the true population model, the corresponding estimated regression function or the sample means greatly depends on the sampled data.

In data analysis we must look on a very heavy emphasis on judgment (Tukey, 1962, quoted by Gifi, 1990, p. 23).

Corresponding to this statement, there should be a good or strong theoretical and substantial base for any proposed model specification. In addition, the conclusion of a testing hypothesis cannot be taken absolutely or for granted in order to omit or delete an exogenous variable from a model. Furthermore, the exogenous variables of a growth or time series model could include the basic or original independent variables, the time *t*-variable, the lagged of dependent or independent variables and their interaction factors, with or without taking into account the autocorrelation or serial correlation and heterogeneity of the error terms. Hence, there is a very large number of choices in developing models. It has also been known that based on a time series data set, many alternative models could be applied, starting with the simplest growth models, such as the geometric and exponential growth models up to the VAR (*Vector Autoregression*), VEC (*Vector Error Correction*), System Equation in general and GARCH (*Generalized Conditional Heteroskedasticity*) models.

The main objective of this book is to present many types of time series models, which could be defined or developed based on only a set of three or five variables. The book also presents several examples and notes on unestimable models, especially the nonlinear models, because of the *overflow* of the iteration estimation methods. To help the readers to understand the advantages and disadvantages of each of the models better, notes, conclusions and comments are also provided. These illustrative models could be used as good basic guides in defining and evaluatingmore advanced time series models, either univariate or multivariate models, with a larger number of variables.

This book contains eleven chapters as follows.

Chapter 1 presents the very basic method in EViews on how to construct an EViews workfile, and also a descriptive statistical analysis, in the form of summary tables and graphs. This chapter also offers some remarks and recommendations on how to use scatter plots for preliminary analysis in studying relationships between numerical variables.

Chapter 2 discusses continuous growth models with the numerical time *t* as an independent variable, starting with the two simplest growth models, such as the geometric and exponential growth models and the more advanced growth models, such as a group of the general univariate and multivariate models, and the S-shape *vector autoregressive* (VAR) growth models, together with their residual analyses. This chapter also presents growth models, which could be considered as an extension or modification of the Cobb–Douglas and the CES (Constant Elasticity of Substitution) production functions, models with interaction factors and trigonometric growth models. For alternative estimation methods, this chapter offers examples using the White and the Newey–West HAC estimation methods.

Chapter 3 presents examples and discussions on discontinuous growth models with the numerical time *t* and its defined or certain dummy variable(s) as independent variables of the models. This chapter provides alternative growth models having an interaction factor(s) between their exogenous variable(s) with the time *t* as an independent variable(s). Corresponding to the discontinued growth models, this chapter also presents examples on how to identify breakpoints, by using Chow’s Breakpoint Test.

Chapter 4 discusses the time series models without the numerical time *t* as an independent variable, which are considered as *seemingly causal models* (*SCM*) for time series. For illustrative purposes, alternative representation of a model using dummy time variables and three-piece autoregressive SCMs are discussed based on a hypothetical data set, with their residual plots. This chapter also provides examples of the discontinued growth models, as well as models having an interaction factor(s).

Chapter 5 covers special cases of regression models based on selected data sets, such as the POOL1 and BASIC workfiles of the EViews/Examples Files, and the US Domestic Price of Copper, 1951–1980, which is presented as one of the exercises in Gujarati (2003, Table 12.7, p. 499). The BASIC workfile is discussed specifically to present good illustrative examples of nonparametric growth models.

Chapter 6 describes illustrative examples of multivariate linear models, including the VAR and SUR models, and the structural equation model (SEM), by using the symbol *Y* for the set of endogenous variables and the symbol *X* for the set of exogenous variables. The main idea for using these symbols is to provide illustrative general models that could be applied on any time series in all biological and nonbiological aspects or growth. As examples to illustrate, three *X* and two *Y* variables are selected or derived from the US Domestic Price of Copper data, which were used for linear model presentation in the previous chapters. All models presented there as examples could be used for any time series data. Analysts or researchers could replace the *X* and *Y* variables by the variables that are relevant to their field of studies in order to develop similar models.

Chapter 7 covers basic illustrative instrumental variables models, which could be easily extended using all types of models presented in the previous chapters, either with or without the time *t*-variable as an independent variable. Chapter 8 presents the autoregressive conditional heteroskedasticity (ARCH) models, generalized ARCH (GARCH), threshold ARCH (TARCH) and exponential ARCH (E_GARCH) models, either additive or interaction factor models.

In addition to the Wald tests, which have been applied in the previous chapters for various testing hypotheses, Chapter 9 explores some additional testing hypotheses, such as the unit root test, the omitted and redundant variables tests, the nonnested test and Ramsy’s RESET tests, with special comments on the conclusion of a testing hypothesis.

Chapter 10 introduced a general form of nonlinear time series model, which could also represent all time series models presented in the previous chapters. For illustrative examples, this chapter discusses models that should be considered, such as the *Generalized Cobb-Douglas* (G_CD) model and the *Generalized Constant Elasticity of Substitution* (G_CES) model.

Finally, Chapter 11 presents nonparametric estimation methods, which cover the classical or basic moving average estimation method and the *k-Nearest Forecast* (*k*-NF), which can easily be calculated manually or by using Microsoft Excel, and the smoothing techniques (Hardle, 1999), such as the Nearest Neighbor and Kernel Fit Models, which should be done using EViews.

In addition to these chapters, the theoretical aspects of the basic estimation methods based on the time series data are presented in four appendices. In writing these appendices I am indebted to Haidy A. Pasay, Ph.D, lecturer in Microeconomics and Econometrics at the Graduate Program of Economics, the Faculty of Economics, University of Indonesia, who are the coauthors of my book on Applied Microeconomics (Agung, Pasay and Sugiharso, 1994). They spent precious time reading and making detailed corrections on mathematical formulas and econometric comprehension.

I express my gratitude to the Graduate School of Management, Faculty of Economics, University of Indonesia, for providing a rich intellectual environment and facilities indispensable for the writing of this text, as well as other published books in Indonesian.

In the process of writing this applied statistical book in English, I am indebted to Dr Anh Dung Do, the President of PT Kusuma Raya (Management, Financing and Investment Advisory Services) and Lecturer in Strategic Management at the Master Program of the Faculty of Economics, University of Indonesia. Dr Do motivated and supported me in the completion of this book. He spent a lot of his precious time in reading and making various corrections to my drafts.

I am also deeply indebted to my daughter, Martingsih Agung Chandra, BSPh, MSi, The Founder and Director of NAC Consultant Public Relations, and my son, Dharma Putra, MBA, Director of the PURE Technology, PT. Teknologi Multimedia Indonesia, for all their help in reading and making corrections to my drafts.

Puri AGUNG

Jimbaran, Bali