Multivariate Approach to Time Series Model Identification

ABSTRACT 

This work suggests an exact and systematic model identification approach which is entirely new and addresses most of the challenges of existing methods. We developed quadratic discriminant functions for various orders of autoregressive moving average (ARMA) models. An Algorithm that is to be used alongside our functions was also developed. In achieving this, three hundred sets of time series data were simulated for the development of our functions. Another twenty five sets of simulated time series data were used in testing out the classifiers which correctly classified twenty three out of the twenty five sets. The two cases of misclassification merely imply that our Algorithm will require a second iteration to correctly identify the model in question. The Algorithm was also applied to some real life time series data and it correctly classified it in two iterations.

TABLE OF CONTENT

Title page..................................................................................................................i

Certification……………………………………………………………………….ii

Dedication………………………………………………………………………...iii

Acknowledgement………………………………………………………………...iv

Abstract………………………….………………………………………………..vi

Table of content……….………...………………………………………………..vii

CHAPTER ONE: INTRODUCTION

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

1.2 Statement of Problem………………………………………….......................3

1.3 Significance of the study………………………………………………..…....4

1.4 Objective of the study………………………………………….......................4

1.5 Scope and Limitation………………………………………………………....5

CHAPTER TWO: LITERATURE REVIEW

2.1 Introduction…………………………………………………………………....6

2.2 Review of Literature……………........................................................................6

CHAPTER THREE: METHODOLOGY

3.1 The Bayesian and Fisher’s Classification Rule……………………………..12

3.2 Distributional Assumptions..………………………….……………………....15

3.3 Development of the Proposed Classifier………………………………….......17

3.4 The proposed Algorithm…………………………………………………........18

CHAPTER FOUR: RESULTS

4.1 The Proposed Classifiers….…………………..……………………………20

4.2 Application of the proposed classifiers to simulated Time Series….………26

4.3 Application of our method to real life series………………………………..27

4.4 Brief comparison with other methods………………………………………28

CHAPTER FIVE: SUMMARY AND CONCLUSION

5.1 Summary……………..………………………………………………………29

5.2 Discussion of Results………….………………………………………….…30

5.3 Contributions…………………………………………………………………32

References…………….…………………………………………………………..34