Abstract:
Volatility modeling and forecasts are essential tools to all financial sectors. This work
focuses on weekly exchange rate data of the Rwf referred to the USD for a period of seven
years spanning from 2012 to 2018. Through transformation of data from daily to weekly,
we intended to reduce the size and adjust the outliers in data. Data obtained from the
National Bank of Rwanda is analyzed using a non linear time series model. The aim of
this Thesis is to apply a GARCH(1,1) model to describe the volatility of the data using
visual inspections and statistic results comparison. Diagnostic check ensured the model
accuracy. The main approach was to apply a Bayesian inference that uses MCMC method
in unknown parameters estimation. Both visual inspection and basic statistics illustrate a
good compatibility between simulated and observed data. The results obtained from the
LSQ and MCMC methods are compared and found to be almost similar. An agreement
between the model and actual data is obtained since the estimated model matched the real
data . The estimated model is trusted for forecasting and is recommended to be applied
by researchers and financial institutions. The model is used to predict exchange rate for
the next 52 weeks. To find the results through data treatment software like MATLAB,
R, Eviews and SPSS were used.
