A TIME SERIES ANALYSIS OF DAILY EXCHANGE RATE OF U.S DOLLAR TO NAIRAFROM 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
CHAPTER ONE: INTRODUCTION
1.1 Background of the Study
1.2 Statement of the Problem
1.3 Aim and Objectives of the Study
1.4 Justification for the Study.
1.5 The Scope of the Study
1.6 Limitations:
1.7 Definition of Key Concept Terms
CHAPTER TWO: LITERATURE REVIEW
CHAPTER THREE: METHODOLOGY
3.1 Data and Source
3.2 Time Series Analysis
3.3 Component Analysis
3.4 Box and Jenkins Time Series Methodology
3.5 Test for Stationarity:
3.5.1. The graphical approach includes
3.5.2. Quantitative methods includes:
3.5.3 Augmented Dickey-Fuller (ADF) Test
3.5.4 Phillips – Perron test
3.6 Differencing to achieve the stationarity
3.6.1 Differencing operations
3.7 Box and Jenkins Modelling Approach
3.7.1 Autoregressive (AR) models
3.7.2 Moving – Average MA(q) Model
3.7.3 ARMA (p, q) Model
3.8 Model Identification
3.8.1 Autocorrelation Function:
3.8.2 Partial Autocorrelation Function
3.8.3 Summarizes the behavior of the theoretical
3.9 Best Model Selection Criteria
3.10 Estimation of Model parameters:
3.11 Model Diagnostics check
3.11.1 Test for Heteroscedasticity
3.11.2Ljung-Box test
3.12 Forecasting
3.12.1 ARIMA Model Forecast Performance
CHAPTER FOUR : ANALYSIS OF DATA
4.1 Graphical presentation of the exchange rate time series data
4.2 Component of the series
4.3 Test for Stationarity of Exchange Rate of Naira/USD
4.3.1 Unit Root Test (Buying Rate Series) of Naira/USD
4.3.3 Unit Root Test (Selling Rate Series) of Naira/USD
4.4 ACF and PACF for the Non-Stationary Exchange Rate Series are Reported in the following Autocorrelation and Partial-autocorrelation Correlogram.
4.5 Next we take the first differencing of each of the series and repeat
the test for Stationarity
4.5.1 Unit Root Test for (difference buying rate series) of Naira/USD
4.5.2 Unit Root Test (Difference Central Rate Series) of Naira/USD
4.5.3 Unit Root Test (Difference Selling Rate Series)
4.6 Model identification
4.6.1 ACF and PACF for the Stationary Exchange Rate Series are Reported
in the following Autocorrelation and Partial-autocorrelation Correlogram.
4.6.2 Best Model Selection
4.7 ARIMA Model Estimation
4.8 Model Diagnostic Check
4.8.1 Test for Heteroscedasticity
4.9 Forecasting
CHAPTER FIVE: SUMMARY, CONCLUSION AND RECOMMENDATION
5.1 Summary
5.2 Conclusion
5.3 Recommendation
REFERENCE
ABBREVIATION WORDS
APPENDIX
LIST OF TABLES
Table 4.1: Dickey-Fuller test (ADF(stationary) / k: 6 / Buying Rate):
Table 4.2 Philips –perron test result (Buying rate)
Table 4.3 Dickey- fuller test result (Central Rate)
Table 4.4 philips perron test result (Central Rate)
Table 4.5 Dickey- fuller test result (selling Rate)
Table 4.6 philips perron test result (Selling Rate)
Table 4.7 Dickey- fuller test result (Stationary) (Buying Rate)
Table 4.8 philips perron test result (Stationary) (Buying Rate)
Table 4.9 Dickey- fuller test result (Stationary) (Central Rate)
Table 4.10 philips perron test result (Stationary) (Central Rate)
Table 4.11 Dickey- fuller test result (Stationary) (Selling Rate)
Table 4.12 philips perron test result (Stationary) (Selling Rate
Table 4.13: Results of ARIMA modeling of the Buying Rate series
Table 4.14: Results of ARIMA modeling of the Central Rate series:
Table 4.15: Results of ARIMA modeling of the Selling Rate series:
Table 4.16: Final Estimates of Parameters for Buying Rate model
Table 4.17: Final Estimates of Parameters for Central Rate model
Table 4.18: Final Estimates of Parameters for Selling Rate model
Table 4.19 ARCH-LM test result for buying rate
Table 4.20 ARCH-LM test result for Central rate
Table 4.21 ARCH-LM test result for Selling rate
Table 4.22: Ljung-Box Q-test Residual autocorrelation
test results for Buying rate series
Table 4.23: Ljung-Box Q-test Residual autocorrelation
test results for central rate series
Table 4.24: Ljung-Box Q-test Residual autocorrelation
test results for selling rate series
Table 4.25 Daily Exchange Rate Forecast on Selling
Rate of Naira/ US dollar
Table 4.26: Daily Exchange Rate Forecast on Central
Rate of Naira/ US dollar
Table 4.27: Daily Exchange Rate Forecast on Selling
Rate of Naira/US-Dollar
Table 4.28: In-sample forecast error performance of
ARIMA (0, 1, 1) model
LIST OF FIGURES
Figure 3.1: Diagrammatic representation of Box -Jenkins process
Figure 4.1: Time plot of (Buying Rate) of Daily exchange
rate of naira to us dollar from January 2016 to May 2017
Figure 4.2: Time plot of (Central Rate) of Daily exchange
rate of naira to us dollar from January 2016 to May 2017
CHAPTER ONE
INTRODUCTION
The Exchange rate reflects the ratio at which one currency can be exchange with another currency (Jhingan, 2005). It is the value of a foreign nation’s currency in terms of the home nation’s currency. An accurate or stable exchange rate has been one of the most important factor for the economic growth in the economies of most developed countries, whereas a high or unstable exchange rate has been a major obstacle to economic growth of many African countries of which Nigeria is inclusive. Furthermore, consequences of substantial misalignments of exchange rate can lead to extensive economic hardship. Moreover, there is reasonable strong evidence that the alignment of exchange rates has a critical influence on the rate of growth of per capital output of low income countries (Isard, 2007). Therefore, analysis of the statistical properties of daily exchange rates and accurate forecast of future exchange rate of financial asset returns is essential to derivative pricing.
1.1 Background of the Study
There are different types of exchange rate regimes practiced all over the world, from the extreme case of fixed exchange rate system to a freely floating regime. Practically, countries tends to adopt a combination of different regimes such as adjustable peg, crawling peg, target zone/crawling bands, and managed float,
hi h th t it th i li i diti F i t h
whichever that suits their peculiar economic conditions. For instance, exchange rate managements in Nigeria has witness different significant changes over the past
four decades. Nigeria maintained fixed exchange rates from 1960 till the breakdown of the Bretton Woods Monetary System in the early 1970s (Sanusi, 2004). Between 1970 and mid 1980 Nigeria exchange rate policy shifted from fixed exchange rate to a pegged arrangement and finally to the various types of the floating regime, following the adoption of the Structural Adjustment Program (SAP) in 1986, the key element of structural adjustment program (SAP) was the free market determination of the naira exchange rate through an auction system (Sanusi, 2004). Before the adoption of structural adjustment program (SAP), the Nigerian pounds and its external value was fixed at par with the British Pound Sterling in 1959 which in turn defined its United States Dollar (USD) value as $2.80.
In early 1973 naira replaced the Nigerian pound as Nigeria’s currency in January 1973 and it’s per value was set at half that of the pounds. Hence the exchange rate became $1.52 to the naira. Finally, as at April 1974 the rigid relationship between the USD and the Naira was terminated. In February 1978, the system of determining the Naira exchange rate against a basket of currencies of Nigeria’s main trading partners was finally adopted. (Ewa, 2011) agreed that the exchange rate of the naira was relatively stable between 1973 and 1979 during the oil boom era and when agricultural products forms more than 70% of
th ti ’ d ti d t (GDP)
the nation’s gross domestic products (GDP).
Between 1986 and 2003, following the adoption of the Structural Adjustment Program (SAP) the federal Government experimented with different exchange rate policies without allowing any of them to make a remarkable impact in the economy before its change. This inconsistency in policies and lack of continuity in exchange rate policies aggravated unstable nature of the naira rate (Gbosi, 1994), the government had to establish the foreign exchange market (FEM) to stabilize the exchange rate depending on the state of balance of payments, the rate of inflation, Domestic liquidity and employment. Benson and Victor, (2012) and Aliyu, (2011) noted that despite various efforts by the government to
maintain a stable exchange rate, the naira has depreciated throughout the 80’s to
date. Hence, forecasting a variable in the financial markets is a matter of imperative importance, especially in a country like Nigeria. Moreover, there is reasonable evidence that the alignment of exchange rates has a critical influence on the rate of growth of per capital output of low income countries (Isard, 2007). Therefore, analysis of the statistical properties of daily exchange rates and accurate forecast of future exchange rate of financial asset returns is very much important especially in a developing country like Nigeria.
1.2 Statement of the Problem
There are some factors or variables which definitely affect or influences exchange rate like interest rate, inflation rate, concurrent oil boom, high yield of agricultural products, GDP (gross domestic product), amount of money in
i l ti d th i il i i t ’ i bl M
circulation and other similar macro – economic giants’ variables. Many researchers have used multi-variant regression approach and time series statistical analysis to study and to predict the exchange rate base on some of these above listed variables, but this has a limitation in the sense that macro-economic variables are readily available at most monthly and yearly data. As a result, most research works on exchange rate forecast and analysis are mainly based on monthly and yearly bases. Whereas in the market system, it is observable that the distribution of exchange rate changes varies within weekdays and also a close look at the movement of exchange rates in the parallel market in Nigeria for instance, shows that there is a tendency for the naira exchange rates to appreciate on Fridays but depreciate on Mondays and Tuesdays (AERC Research, Paper 49, 1996). Consequently, the analysis of the statistical properties and forecast on daily exchange rates is very important for possible and effective management system.
Also in past years, Nigeria solely depends on concurrent oil boom because of the huge earnings from crude petroleum exports, which supported the appreciation of the naira against foreign currencies, currently Nigeria is undergoing economic recession which has affected its financial markets and GDP(gross domestic product) as a result of economic crisis, social vises, ethnic differences and its present government economic reform structure in reduction of over-dependency on imports of goods and petroleum exports, which has affected its major micro-economic variables which in large extent has devalued the naira.
In past years, most researchers have done a great research on forecasting of exchange rate of Nigeria (naira) against the US (dollar) using different approaches especially time modeling techniques ARIMA which is the fundamental approach Like the work of (Ette Harrison 1998), used a technical approach to forecast Nigeria naira – US dollar using seasonal ARIMA model for the period of 2004 to 2011. He reveals that the series (exchange rate) has a negative trend between 2004 and 2007 and was stable in 2008. Further work by (Shittu O. I 2008) used an intervention analysis to model Nigeria exchange rate in the presence of financial and political instability from the period (1970 - 2004). Consequently, it evidently shows that no work has been carried out during the Nigeria period of economic recession which has affected all its global financial markets.
1.5 Aim and Objectives of the Study
The analysis of the statistical properties of daily exchange rates is important for understanding the possible causes of instability in a developing country like Nigeria market system. Specifically, the purpose of this study is to find out:
1. To isolate the components of the time series for the buying rate, selling rate and central rate.
2. To understand the nature of the relationship in the exchange rate of U.S dollar to naira for the buying rate, selling rate and central rate.
3. To estimate the parameters of the models.
4. To predict the future daily exchange rate of U.S dollar to naira using the models.
1.4 Justification for the Study.
The analysis of the statistical properties of daily exchange rates is important for understanding the possible causes of instability or otherwise in a country's market determined exchange rate management system. This study would help the government and the central bank of Nigeria (CBN) to identify the strength and weakness of naira to dollar exchange system and hence adopt the policy that suits the economy best. This will definitely enhance growth and development of the economy. Importantly, the justification of this research work lies in the fact that if the unstable exchange rate of the naira per US dollar can be accurately predicted, identify and corrected, the economy will rapidly grow and government will make good policies that will re-strategize the nation financial market. This is because exchange rate are gauge for the measurement of growth and development of any economy. Moreover, if the unstable exchange rate of naira is proved to be affecting the macro-economy major variables, including Real exchange rate, Real interest rate, inflation rate, gross domestic product and trade openness of the country, attempts should be made to stabilize the exchange rate, and this can be achieved by having a prior knowledge of the structure of exchange rate in near future, the study will also serve as a guide to
f t h thi bj t
future researchers on this subject.
1.5 The Scope of the Study
The data was obtained from the Central Bank of Nigeria (CBN), Which cover the daily exchange rate of naira to US dollar (US$) for a period of January 2016 to May 2017 (343 days). It is a period of Nigeria economic recession which affected all its global financial markets.
1.6 Limitations:
The only major problem encountered is the process of collecting the data of exchange rate of Nigerian naira against U.S. Dollars used in the study, by the grace of God, was later obtain hitch free from the central bank of Nigeria (CBN) website and world bank database website.
Finance was also major challenge as it was very difficult to obtain any piece of information without cost. But, all were taking care of due to the support I got from my parent and sponsors.
Also, the problem of electric power failure causes delay in typesetting the work, but I was able to use the assistance of FUTO (Federal university of technology) e-library and a neighboring business center.
Time constraint- the researcher will simultaneously engage in this study with other academic work. This consequently will cut down on the time devoted for the research work.
1.7 Definition of Key Concept Terms
Auction system: A system where potential buyers place a competitive bid on assets and services.
Financial markets: a financial market is a market in which people trade financial securities, commodities, and value at low transaction costs and at prices that reflect supply and demand. Securities include stocks and bonds, and commodities include precious metals or agricultural products. Macro-economic variables: Macro-economic variables, includes national output, employment, interest rate, inflation rate, stock prices, and the exchange rate.
Gross domestic product: the gross domestic product (GDP) is one of the
primary indicators used to gauge the health of a country’s economy. It
represents the total dollar value of all goods and services produced within the geographic boundaries of a country during a specific period of time, normally a year.
Appreciate: Currency appreciate in the same context is an increase in the value of the currency.
Depreciate: Currency depreciate is the loss of value of a country’s currency
with respect to one or more foreign reference currencies, typically in a floating exchange rate system in which no official currency value is maintained.
Naïve forecasting: estimating technique in which the last periods actuals are
d thi i d’ f t ith t dj ti th tt ti t t bli h
used as this period’s forecast without adjusting them or attempting to establish
casual factors. It is used only for comparison with the forecasts generated by the better techniques.
