Abstract Several authors have developed statistical procedures for testing whether two models are similar. In this work, we not only present the notion of equivalence but also extend this to a measure of predictive ability of a time series following a stationary self-exciting threshold autoregressive (SETAR) process. A proposition and a lemma were used to join the structure of the predictability measure to the coefficients and sample autocorrelation of the SETAR process. Illustrative examples are given to show how to conduct the test which can help practitioners avoid mistakes in decision making.

Table of Contents

Certification ........................................................................................................ii

Dedication ...........................................................................................................iii

Acknowledgements .............................................................................................iv

Abstract ...............................................................................................................vi

Chapter One: INTRODUCTION

1.1 Introduction ...................................................................................................1

1.2 Statement of Problem.....................................................................................4

1.3 Research Objectives...................................................................................4

1.4 Significance of the Study................................................................................5

1.5 Scope of the Study..........................................................................................5

Chapter Two: LITERATURE REVIEW

2.1 Review of Related Literatures........................................................................7

Chapter Three: METHODOLOGY

3.1 Method..........................................................................................................14

3.2 Definition of Basic Concepts.........................................................................15

3.3 R2 Defined for SETAR Time Series Models..................................................17

3.3.1 Parallelism and Equal Predictive Ability.....................................................20

3.3.2 Testing for Equal Predictive Ability............................................................23

Chapter Four: SOME APPLICATIONS

4.1 Numerical Examples......................................................................................25

vii

4.1.1 Example 1...................................................................................................25

4.1.2 Example 2...................................................................................................34

4.1.3 Example 3...................................................................................................42

Chapter Five: SUMMARY, CONCLUSION AND RECOMMENDATIONS

5.1 Summary........................................................................................................51

5.2 Conclusion.....................................................................................................52

5.3 Recommendations.........................................................................................52

REFERENCES