https://www.centralbank.go.ke/index.php/rate-and-statistics/exchange-rates-2 . Mean values of daily exchange rate is the variable used to model volatility.
3.2 THE GARCH MODEL
The standard GARCH model allows the conditional variance to be dependent upon previous own lags. The basic structure of the symmetric normal GARCH model is GARCH (1, 1) given by Chris Brooks (2008)
,
Where denote the conditional variances.
The GARCH model above cannot account for leverage effect, does not allow for any feedback between the conditional Variance and mean and violates the non-negativity conditions. For these reason I opted to model the problem using asymmetric GARCH model called EGARCH.
EGARCH MODEL
The exponential generalized autoregressive conditional heteroskedasticity model (EGARCH) is one of the many forms of GARCH model by nelson (1991).We shall use EGARCH which has added benefit because it is expressed in terms of the log of conditional variance so that even if the parameters are negative, the conditional variance will always be positive thus we do not therefore have to artificially impose non-negativity constraints
Let be an identically and indeed sequence such that and
Then the conventional EGARCH model become
where are the coefficients to be estimate
Furthermore parameter represent a magnitude effect or the symmetric effect of the model. Measures the persistence in conditional volatility. The parameter measures the leverage effect. This parameter is important as it allows the EGARCH model to test for Asymmetrics.If then the model is symmetric when is greater than zero the positive shocks (good news) generate less volatility than negative shocks (bad news). When it implies that good news is more destabilizing than bad news. The EGARCH model used got a distinctive feature, i.e., conditional variance was modeled to capture the leverage effect of volatility.
The parameter measures the asymmetry or the leverage effect, the parameter of
importance so that the EGARCH model allows for testing of asymmetries. If , then the mo
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