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