NAME: NANGAY ANDARAY EMMANUEL
REG NO: 2016-06-00571
MA.STATISTICS.
DEPARTMENT: STATISTICS
COLLEGE: COSS
PROPOSAL
NOVEMBER 2017
TITLE: FORECASTING EXCHANGE RATES IN TANZANIA
USING TIME SERIES ANALYSIS.
1. INTRODUCTION
Exchange rate is the currency rate of one country
expressed in terms of the currency of another country. Exchange rate fluctuates
from time to time. For example we can see that the exchange rates has traded
with a range of 798.78-2232.8 per USD, 1713.02-2439.99 per EURO,
1155.35-2820.60 per GBP from the year 2000-2017.( (https://www.ofx.com/en-us/forex-news/historical-exchange-rates/,
2017).
There is a lot of uncertainty in the exchange rate in the sense that it’s
difficult to tell when the currency will depreciate or appreciate against other
currencies. This system is set by the foreign exchange market over supply and
demand for that particular currency in relation to other currencies. In
addition, the exchange rate is guided by significant impact of the activities
of central banks and other financial institutions. Rising and falling of the
exchange rates has a great impact on the economy (Lugaiyamu, 2015). Developing countries
like Tanzania need to achieve higher growth rate in order to have a strong
economy. One of the most important sources of this growth rate is the external sector.
A well functioning external sector can help
Tanzania to have competitive exports and favorable domestic atmosphere to
attract foreign capital and technology (Madani, 1999). Now the achievement
of these conditions depends on the dynamic prices of Tanzania relative to its
trading partners. Higher exchange rates tend to inhibit most of investments and
other trading partners. Therefore, it is very crucial that
policy makers in Tanzania are equipped with knowledge of how and why the real
exchange rate would move in particular direction overtime. Therefore the
fluctuations in the exchange rates are the basis for my study, i.e. to analyze
the fluctuations and later on forecast the exchange rates so as to have
awareness and knowledge of the future exchange rate.
1.2 STATEMENT OF THE PROBLEM
From the
introduction part we have seen that the variation in exchange rate poses a
great challenge in the country’s economy. We cannot eradicate that problem but
we can at least reduce the impact by having the awareness and knowledge of the
future exchange rates. Tanzania introduced financial sector
reforms in early 1990s. As part of the reforms, efforts were made to develop,
broaden and deepen the financial sector. This included liberalization of
foreign currency whereby private companies and individuals were allowed to
hold, buy or sell foreign currencies to authorized dealer or a Bureau de
Change. When foreign currency started to circulate in the market, its exchange
rate also started to move up and down. Exchange rate is one of the key measures
of economic performance which shows growth (output), demand conditions, and the
levels and trends in monetary and fiscal policy stance. The exchange rate is
one of the most important determinants of a country’s relative level of
economic health.
Exchange rate
plays a vital role in a country’s level of trade, which is critical to most
every free market economy in the world. For this reason exchange rates are
among the most watched analyzed and governmentally manipulated economic
measures. But exchange rates matter on a smaller scale as well, they impact the
real return of an investor’s portfolio. In fact it is worth noting that
exchange rate movements affect the nations trading relationships with other
nations. A higher currency exchange rate makes a country’s exports more
expensive and imports cheaper in foreign markets, while a lower exchange rate makes
a country’s export cheaper and imports more expensive in foreign markets. A
higher exchange rate can be expected to lower the country’s balance of trade,
while a lower exchange rate would increase it.
In Tanzania
and precise in this topic “forecasting
of exchange rates using box Jenkins”
has not been researched enough. For that reason I want to undertake a proper
study on this area. This will assist to bring awareness of the expected future
exchange rates. It will also help Institutions that are affected by the
exchange rates to have a proper knowledge of the future and have a proper
planning in time.
1.3 OBJECTIVES
1.3.1 MAIN OBJECTIVE
The
main objective of this study is to determine the trend and forecast the exchange
rates using the Box Jenkin’s method.
1.3.2 SPECIFIC OBJECTIVES
1.
To study and extract
the trend of exchange rates of TZS against US Dollar, Euro and Pounds from June
2007 to 2017.
2.
To develop a
suitable forecasting model to forecast the exchange rates of TZS against US
Dollar, Euro and Pound.
1.4 RESEARCH
QUESTIONS
My
study will be guided by the following research questions
1.
Is there existence
of any trend in exchange rate between TZS and US Dollar, Euro and Pound and if
yes which trend?
2.
What is the
best/optimum forecasting model for the exchange rate of TZS against US Dollar,
Euro and Pound using the Box Jenkin’s approach?
1.5 SIGNIFICANCE OF THE STUDY
The
significance of my study is that having a model that will be able to forecast
the exchange rates for the above currency it will first assist the government to make proper policy that will
accommodate the impact of the exchange rates in the economy at that specific
time.
It will also bring
awareness to the business people whose business’ involves transactions of the
above currency. Levels and fluctuations in the exchange rate exert a powerful
impact on exports, imports and the trade
balance.
A high and rising exchange
rate tends to depress exports, to boost import and to deteriorate the trade balance, as far
as these variables respond to price stimuli. Consumers find foreign
goods cheaper, so the consumption composition
will change. Similarly, firms will reduce their costs by purchasing
intermediate goods abroad (Lugaiyamu, 2015). Therefore having a
proper knowledge of the expected future trend of the exchange rates will in one
way or another harmonize the effects posed by the fluctuation of the exchange
rates to the economy.
1.5 SCOPE OF THE STUDY.
This study
involves only Tanzanian currency against the US Dollar, Sterling Pound, and the
Euro. Most of the data will be obtained from the Bank of Tanzania (BOT). In my
research I am planning to model monthly
exchange rates between USD/TZS, EUR/TZS and GBP/TZS, and compare the actual
data with developed forecasts using time series analysis over the period from June
2007 to June 2017. The official monthly data of Bank of the United Republic of
Tanzania will be used for my study. The main goal of my research is to apply
the Box Jenkins method for forecasting of monthly exchange rates of USD/TZS,
EUR/TZS and GBP/TZS as stated above.
1.6 LITERATURE REVIEW
Most
researchers have done a great research on forecasting of exchange rate for
developed and developing countries using different approaches. The approach
might vary in either fundamental or technical approach. Like the work of Ette (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. His good work expatiate on that seasonal difference once produced a
series with slightly positive trend but still within discernible Stationarity.
Newaz (2008) made a comparison on the performance of time series models for
Shittu (2008) used an intervention analysis to model Nigeria exchange rate in
the presence of financial and political instability from the period (1970 –
2004). He explains that modeling of such series using the technique was
misleading and forecast from such model will be unrealistic, he continued in
his findings that the intervention are pulse function with gradual and linear
but significant impact in the naira – dollar exchange rates. Appiah and
Adetunde (2011) conducted a research on forecasting exchange rate between the
Ghana cedi’s and the US dollar using time series analysis for the period
January 1994 to December 2010. Their findings reveal that predicted rates were
consistent with the depreciating trend of the observed series and ARIMA (1, 1,
1) was found to be the best model to such series and a forecast for two years
were made from January 2011 to December 2012 and reveals that a depreciation of
Ghana cedi’s against the US dollar was found. As it can be seen from the
literature review most of the research that has been done is from the developed
countries and other few from other African countries but not Tanzania.
Therefore due to this gap that has been spotted it therefore forms a strong
basis for my research.
1.7 METHODOLOGY
The
methodology that I will employ in this research is the use of Box Jenkins
Methodology. Box
– Jenkins Analysis refers to a systematic method of identifying, fitting,
checking, and using integrated autoregressive moving average (ARIMA) time
series models. The ARIMA model is for non-seasonal non-stationary data.
The Box-Jenkins
methodology requires that the model to be used in describing and forecasting a
time series to be both stationary and invertible.
The series may be denoted by
where t refers to the time period and x refers to the
value. For our case the
will represent
the exchange rates and t represent time in months. Thus, in
order to identify a Box-Jenkins model, we must first determine whether the time
series we wish to forecast is stationary. If it is not, we must transform the
time series into a series of stationary time series values through the process
of differencing.
Box
Jenkins have generalized this model to deal with seasonality. Since my data is
seasonal i.e. monthly data from June 2007 to June 2017 then the proposed model
is known as seasonal ARIMA (SARIMA) model. In this seasonal autoregressive integrated
moving average (SARIMA) model seasonal differencing of appropriate order is
used to remove non stationarity from the series.
A
first order differencing is the difference between an observation and the
corresponding observation from the previous month and is calculated as
.Order of seasonality is denoted by s.Non-seasonal and seasonal difference
orders are denoted by d and D respectively. The seasonal part of
the model also has its own autoregressive and moving average parameters with
order P and Q, while the non seasonal part
are order p and q
. Note seasonal parameters are the uppercase version of the non seasonal
parameters. To determine P
and Q, the ACF and
PACF are examined but only at the seasonal lags.
For
monthly time series
,p .This
model is generally termed as the SARIMA
model. The
method is appropriate for time series of medium to long length (at least 50
observations) with seasonal data.. A stationary time series has the following
features;
ü A
constant mean.
ü A
constant variance.
ü A
constant autocorrelation structure. The autocorrelation function does not change over time OR the
autocorrelation function is independent of time.
In box
Jenkins approach there are basically four iterative major steps. These steps
are;
Step1.Model identification
Involves
tentatively identifying a model by looking at the behavior of the autocorrelation
function and partial autocorrelation for values of stationary time series. I
will display the autocorrelation function
as a sample of autocorrelation coefficients evaluated at lag 1,lag
2….lag u and graph vs. u.Once the ACF and PACF have been calculated and their
behavior studied to determine the number of parameters i.e. AR(p) or MA(q) parameters
an appropriate model is selected.
The time
series
is AR (p) if:
ACF will decline steadily or follow a damped cycle and PACF will cut off
suddenly after p lags.
On the other
hand the time series
is MA (q) if: ACF will cut off suddenly after
q lags and PACF will decline steadily, or follow a damped cycle.
Step 2.Model estimation
Thereafter
historical data is used to estimate the parameters of the identified model. Often
the maximum likelihood estimator (MLE) method is used to estimate the parameters.
Step 3 Model validation/diagnostic check
The next procedure
in the Box Jenkins approach is to perform a diagnostic check. A diagnostic
check is carried out to validate the model. For the model to be good it should
have the following properties.
ü Residuals
should be approximately normal.
ü All
the parameters should have significantly P-values.
ü The
model should contain as few parameters as possible.
Step 4. Forecast
future time series values.
Eventually
now the model can be used to forecast the future time series values. The
statistical software that will be used which is in line with my methodology is
the R statistical software. These steps are applied iteratively until step
three does not produce any improvement in the model.
1.8
REFERENCES.
1)
https://www.ofx.com/en-us/forex-news/historical-exchange-rates/
2) Shakira
Green (2011)”Time series analysis of
exchange rates using the Box-Jenkins approach”. Georgia Southern University.
3)
Daniya Tlegenova
(2014) Forecasting Exchange Rates Using Time Series Analysis: The sample of the
currency of Kazakhstan.
4)
Nwankwo, S. C. (2014). Autoregressive Integrated Moving
Average (ARIMA) Model for Exchange Rate (Naira to Dollar). Academic Journal
of Interdisciplinary Studies, 3(4), 429.
5)
Ayekple, Y. E., Harris, E., Frempong, N. K., & Amevialor,
J. (2015). Time Series Analysis of the Exchange Rate of the Ghanaian Cedi to
the American Dollar. Journal of Mathematics Research, 7(3), p46.
6)
Godfrey Nyamrunda and Cosmas Mbogela (2014) impacts
of lower exchange rates on exports,imports and national output of Tanzania. ACRN
Journal of Finance and Risk Perspectives. Vol. 3, Issue 2,
7)
An
Introductory Study on Time Series Modeling and Forecasting
