A TIME SERIES ANALYSIS OF DAILY EXCHANGE RATE OF U.S DOLLAR TO NAIRA FROM 2016-2017 (RECESSION PERIOD)

ABSTRACT

 This project presents an empirical study of time series modeling and forecasting of the official daily Exchange rate of Nigeria Naira for US Dollar in terms of buying rate, central rate and selling rate, from the period of 1st January 2016 to 19th of May 2017 (recession period). In this view, Box Jenkins approach was applied for the modelling of naira/dollar daily exchange rate using ARIMA model. The results of the analysis show that the series became stationary after first differencing. Based on AIC and BIC selection criteria, the best model that explains the series was found to be ARIMA (0, 1, 1). The diagnosis checking on such model was confirmed, the error was white noise, and the presence of no serial correlation. The performance of the three ARIMA (0, 1, 1) models for buying rate, central rate and selling rate shows that the selling rate model had the Minimum ME, MSE, RMSE and MAPE. 

 

 

 

 

 

 

 

 

TABLE OF CONTENT

Abstract                                                                                                                  vi

Table of Content                                                                                    vii

LIST OF TABLES                                                                                                 xi

LIST OF FIGURES                                                                                              xiii

CHAPTER ONE: INTRODUCTION                                                            1

1.1 Background of the Study                                                                                  1

1.2 Statement of the Problem                                                                      3

1.3 Aim and Objectives of the Study                                                            5

1.4 Justification for the Study.                                                                                         6

1.5 The Scope of the Study                                                                          7

1.6 Limitations:                                                                                             7

1.7 Definition of Key Concept Terms                                                           8

CHAPTER TWO: LITERATURE REVIEW                                                        10

CHAPTER THREE: METHODOLOGY                                                              14

3.1 Data and Source                                                                                               14

3.2 Time Series Analysis                                                                                       14

3.3 Component Analysis                                                                                        15

3.4 Box and Jenkins Time Series Methodology                                                    16

3.5 Test for Stationarity:                                                                                        16

3.5.1. The graphical approach includes                                                                 19

3.5.2. Quantitative methods includes:                                                                    19

3.5.3 Augmented Dickey-Fuller (ADF) Test                                                         19

3.5.4 Phillips – Perron test:                                                                                    20

3.6 Differencing to achieve the stationarity:                                                         21

3.6.1 Differencing operations                                                                               22

3.7 Box and Jenkins Modelling Approach                                                           23

3.7.1 Autoregressive (AR) models                                                              23

3.7.2 Moving – Average MA(q) Model                                                                24

 3.7.3 ARMA (p, q) Model                                                                            25

3.8 Model Identification                                                                              25

3.8.1 Autocorrelation Function:                                                                             25

3.8.2 Partial Autocorrelation Function                                                                   27

3.8.3 Summarizes the behavior of the theoretical                                                 28

3.9 Best Model Selection Criteria                                                                         29

3.10 Estimation of Model parameters:                                                                 30

3.11 Model Diagnostics check                                                                               30

3.11.1 Test for Heteroscedasticity                                                                          30

3.11.2Ljung-Box test                                                                                              31

3.12 Forecasting                                                                                                      33

3.12.1 ARIMA Model Forecast Performance                                                         34

CHAPTER FOUR         : ANALYSIS OF DATA                                                   36

4.1 Graphical presentation of the exchange rate time series data                           36

4.2 Component of the series                                                                                    38

4.3 Test for Stationarity of Exchange Rate of Naira/USD                                       38

4.3.1 Unit Root Test (Buying Rate Series) of Naira/USD                                        38

4.3.3 Unit Root Test (Selling Rate Series) of Naira/USD                                         40

4.4 ACF and PACF for the Non-Stationary Exchange Rate Series are Reported in the following Autocorrelation and Partial-autocorrelation Correlogram.                                        41

4.5 Next we take the first differencing of each of the series and repeat

     the test for Stationarity.                                                                          44

4.5.1 Unit Root Test for (difference buying rate series) of Naira/USD                      44

4.5.2 Unit Root Test (Difference Central Rate Series) of Naira/USD                       46

4.5.3 Unit Root Test (Difference Selling Rate Series)                                               47

4.6 Model identification                                                                                             48

4.6.1 ACF and PACF for the Stationary Exchange Rate Series are Reported

in the following Autocorrelation and Partial-autocorrelation Correlogram.             48

4.6.2 Best Model Selection                                                                             52

4.7 ARIMA Model Estimation                                                                                   54

4.8 Model Diagnostic Check                                                                                      55

4.8.1 Test for Heteroscedasticity                                                                                55

4.9 Forecasting                                                                                                           60

CHAPTER FIVE: SUMMARY, CONCLUSION AND RECOMMENDATION 68

5.1 Summary                                                                                                               68

5.2 Conclusion                                                                                                             69

5.3 Recommendation                                                                                                   70

REFERENCE                                                                                                       71

ABBREVIATION WORDS                                                                                          75

APPENDIX                                                                                                                   76

LIST OF TABLES

Table 4.1: Dickey-Fuller test (ADF(stationary) / k: 6 / Buying Rate):                          38

Table 4.2 Philips –perron test result (Buying rate)                                                         38

Table 4.3 Dickey- fuller test result (Central Rate)                                                          39

Table 4.4 philips perron test result (Central Rate)                                                           39

Table 4.5 Dickey- fuller test result (selling Rate)                                                            40

Table 4.6  philips perron test result (Selling  Rate)                                                          40

Table 4.7 Dickey- fuller test result  (Stationary)  (Buying Rate)                                    44

Table 4.8  philips perron test result (Stationary) (Buying Rate)                                      44

Table 4.9 Dickey- fuller test result  (Stationary)  (Central Rate)                                    46

Table 4.10 philips perron test result (Stationary) (Central  Rate)                                     46

Table 4.11 Dickey- fuller test result  (Stationary)  (Selling Rate)                                    47

Table 4.12 philips perron test result (Stationary) (Selling Rate)                                       47

Table 4.13: Results of ARIMA modeling of the Buying Rate series:                       52

Table 4.14: Results of ARIMA modeling of the Central Rate series:                               53

Table 4.15: Results of ARIMA modeling of the Selling Rate series:                       53

Table 4.16: Final Estimates of Parameters for Buying Rate model                                  54

Table 4.17: FinalEstimates of Parameters for Central Rate model                                  54

Table 4.18: Final Estimates of Parameters for Selling Rate model                                  55

Table 4.19 ARCH-LM test result for buying rate                                                             56

Table 4.20 ARCH-LM test result for Central rate                                                            57

Table 4.21 ARCH-LM test result for Selling  rate                                                           58

Table 4.22: Ljung-Box Q-test Residual autocorrelation                                                  59

          test results for Buying rate series

Table 4.23: Ljung-Box Q-test Residual autocorrelation

          test results for central    rate series                                                                         59

Table 4.24: Ljung-Box Q-test Residual autocorrelation

          test results for selling     rate series                                                                         60

Table 4.25 Daily Exchange Rate Forecast on Selling

          Rate of Naira/ US dollar                                                                                         61

Table 4.26: Daily Exchange Rate Forecast on Central

          Rate of Naira/ US dollar                                                                                         63

Table 4.27: Daily Exchange Rate Forecast on Selling

           Rate of Naira/US-Dollar                                                                                         64

Table 4.28: In-sample forecast error performance of

          ARIMA (0, 1, 1) model.                                                                                           66

 

 

 

 

LIST OF FIGURES

Figure 3.1: Diagrammatic representation of Box -Jenkins process.                   18

Figure 4.1: Time plot of (Buying Rate) of Daily exchange

          rate of naira to us dollar from January 2016 to May 2017.                       36

Figure 4.2: Time plot of (Central Rate) of Daily exchange

          rate of naira to us dollar from January 2016 to May 2017.                       37

Figure 4.3: Time plot of (Selling Rate) of Daily exchange rate

          of naira to US dollar (US$) from January 2016 to May 2017.                   37

Figure 4.4: ACF plot of (Buying Rate) of Daily exchange

          rate of naira to US dollar from January 2016 to May 2017                       41

Figure 4.5: PACF plot of (Buying Rate) of Daily exchange rate                         

          of naira to US dollar from January 2016 to May 2017                              41

Figure 4.6: ACF plot of (Central Rate) of Daily exchange

          rate of naira to US dollar from January 2016 to May 2017.                      42

Figure 4.7: PACF plot of (Central Rate) of Daily exchange

          rate of naira to US dollar from January 2016 to May 2017.                       42

Figure 4.8: ACF plot of (Selling Rate) of Daily exchange

          rate of naira to US dollar from January 2016 to May 2017.                       43

Figure 4.9: PACF plot of (Selling Rate) of Daily exchange

          rate of naira to US dollar from January 2016 to May 2017.                       44

Figure 4.10: Difference plot of (Buying Rate) of Daily exchange rate

          of naira to US dollar from January 2016 to May 2017                                     44

Figure 4.11: Differencing plot of (Central Rate) of Daily exchange

          rate of naira to US dollar from January 2016 to May 2017                         45

 Figure 4.12: Differencing plot of (Selling Rate) of Daily exchange

          rate of naira to US dollar from January 2016 to May 2017                          47

Figure 4.13: ACF of (Buying Rate) of Daily exchange

          rate of naira to US dollar from January 2016 to May 2017.                        48

Figure 4.14: PACF plot of (Buying Rate) of Daily exchange

          rate of naira to US dollar from January 2016 to May 2017.                         49

Figure 4.15: ACF plot of (Central Rate) of Daily exchange

          rate of naira to US dollar from January 2016 to May 2017.                          49

Figure 4.16: PACF plot of (Central Rate) of  Daily exchange

          rate of naira to US dollar from January 2016 to May 2017.                         50

Figure 4.17: PACF plot of (Selling Rate) of Daily exchange

          rate of naira to US dollar from January 2016 to May 2017.                         50

Figure 4.18: PACF plot of (Selling Rate) of Daily exchange

          rate of naira to US dollar from January 2016 to May 2017.                          51

Figure 4.19: Residuals QQ-Plot of (Buying Rate) of Daily exchange

          rate of naira to US dollar from January 2016 to May 2017.                          56

Figure 4.20: QQ-Plot of the (Central Rate) of Daily exchange rate of naira to

          US dollar from January 2016 to May 2017.                                                   57