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
