Modeling And Forecasting CAD to Naira Exchange Rate

ABSTRACT

The economy of any nation is greatly dependent on the level and stability of its exchange rate, with our nation’s (Nigeria) dwindling exchange rate, exploring the trend and pattern of our exchange rate is very needful. A secondary data on monthly exchange rates from 2010 to 2020 was obtained from ExchangeRate UK was analyzed using the Box-Jenkins (ARIMA) methodology. The series was first-order differenced in order to achieve series stationarity. The results showed that ARIMA(0,1,1)  model which had the least information criteria with AIC of  906.6, AICC of  906.66 and BIC of  912.32, described the patterns observed in the exchange rate series . The diagnostic tests on the model residuals using Ljung-Box test, Shapiro-Wilk Normality test and ARCH-LM test revealed that the selected model is free from autocorrelation effect, heteroscedasticity and found to be normally distributed. The model was used to forecast the monthly exchange rates for the next two year (2021-2022) with 95% confidence interval. This model is recommended for use until further analysis proves otherwise.

 

TABLE OF CONTENTS

CONTENT                                                                                                                            PAGE

Title Page                                                                                                                                i

Declaration                                                                                                                              ii

Certification                                                                                                                            iii

Dedication                                                                                                                              iv

Acknowledgement                                                                                                                  v

Table of Contents                                                                                                                   vii

List of Tables                                                                                                                          x

List of Figures                                                                                                                         xi

List of Appendices                                                                                                                  xii

List of Abbreviations                                                                                                              xiii

Abstracts                                                                                                                                 xiv

CHAPTER ONE:                 INTRODUCTION

1.1.Background of the study                                                                                                  1-3      

1.2.Statement of Problems                                                                                                      3

1.3.Aim and Objectives                                                                                                          3

1.4.Significance of the study                                                                                                  3

1.5.Scope and limitations of the study                                                                                   4

1.6.Definition of Basic Terms                                                                                                 4-5

1.7.Organization of the study                                                                                                 5

CHAPTER TWO:                LITERATURE REVIEW

2.1. Introduction                                                                                                                      6

2.2. Empirical Research with Time Series Methods                                                              6-14

CHAPTER THREE:            RESEARCH METHODOLOGY

3.1. Basic Definitions and Concepts of Time Series                                                              15

 3.1.1. Basic Definitions                                                                                                         15

3.1.2. Stationary and Non-stationary Time Series                                                                  16   

 3.1.3. Univariate Time Series and Multivariate Time Series                                                 16

3.1.4.continuous time series discrete and time series                                                            17

3.1.5. Time and frequency Domain                                                                                        17

3.2.   Components of Time Series                                                                                           17

3.2.1. Trend Component                                                                                                         17-18

3.2.2. Seasonal Component                                                                                                    18

3.2.3. Cyclical Component                                                                                                     18

3.2.4. Irregular Component                                                                                                    18

3.3.   Common Assumptions in Time Series                                                                          19

3.4.   Univariate Time Series                                                                                                  19

3.5. Common Univariate Time Series Approach                                                                   19

3.5.1. Decomposition                                                                                                              19-20

3.5.2. Autoregressive (AR) Models                                                                                        20

3.5.3. Moving Average (Ma) Models                                                                                     20-21

3.5.4. Auto regress Moving Average (ARMA) Models                                                         21-22

3.6. The Differencing Operator                                                                                              22

3.7. Unit Root and Stationary                                                                                                 22

3.7.1. Augmented Dickey-Fuller (ADF) Unit Root Tests                                                      23                     

3.7.2. KPSS Unit Root Test                                                                                                    23-24                        

3.8. The Principle of Parsimony                                                                                             24                       

3.9. Box-Jenkins ARIMA Process                                                                                     24                        

3.10. Box-Jenkins Modeling Approach                                                                                 25

3.10.1. Model Identification Stage                                                                                        25-26      

3.10.2.        Model Estimation Stage                                                                                            26-28    

3.10.3. Diagnostic Checking                                                                                                        28-30

CHAPTER FOUR:               DATA ANALYSIS AND DISCUSSION OF RESULTS

4.1. Descriptive Analysis                                                                                                        31

4.2. Graphical Presentation of the Data                                                                                  31-32

4.3. Model Identification Process                                                                                           32-33

4.4. Unit Root Test for the exchange rate Series                                                                    33-34

4.5. Differenced exchange rate Series                                                                                    34-36

4.6. Estimation of Model Parameters                                                                                     36-38

4.7. Diagnostic Checking for the Fitted Model                                                                      38-39

4.8. Model Forecast                                                                                                                40-42

CHAPTER FIVE: DISCUSSION OF FINDINGS, CONCLUSION AND

RECOMMENDATIONS

5.1. Discussion of Findings                                                                                                    43-44

5.2. Conclusion                                                                                                                       44

5.3. Recommendations                                                                                                           44

References                                                                                                                              45-46

Appendix A                                                                                                                            47       

 

 

 

LIST OF TABLES

TABLE NUMBER                              TITLE                                                         PAGES

4.1       Descriptive analysis of exchange rate series                                                   31

4.2       Unit root test and stationarity test for the series                                             33

4.3       Unit root test and stationarity test for the differenced series                          36

4.4       Comparison for ARIMA (p,d,q) models                                                        37

4.5       Parameter for ARIMA (0,1,1) model                                                             37

 4.6       ARIMA(0,1,1) model residuals diagnostic test                                             39-40

 4.7       ARIMA(0,1,1) model residuals diagnostic test                                             40

 4.8       The model forecast values                                                                             40-41

 4.9       The forecast plot                                                                                            43