Application of a GARCH, TGARCH, and EGARCH, Models to Test the Spot GBP/USD Exchange Rate Volatility.

Abstract

In this article, we have tested the volatility of the returns of the spot exchange rate of GBP/USD for changing conditional variances. Generalized autoregressive conditional heteroskedastic models, GARCH, threshold generalized autoregressive conditional heteroskedastic models, (TGARCH), and exponential generalized autoregressive conditional heteroskedastic models, (EGARCH) models take into account the non- linearity that arises in financial time series. We have checked the volatility clusters for a long period of time that arises in the financial times series of returns or the fact that large and small values occur persistently in clusters. By applying a GARCH (1,1) model, we have found that the variance equation of the natural logarithmic returns of the GBP/USD spot rate are very significant. The coefficients of the ARCH and GARCH effects are statistically significant, which is a sign that the conditional variance and volatility clusters are persistent. By applying a TGARCH (1,1) model, we have found that there is no leverage effect. By applying an EGARCH (1,1) model, we have found that the asymmetry term is not statistically significant at the 5% significance level. Negative shocks do not imply a higher next period conditional variance than positive shocks of the same sign. There is no serial correlation in the residuals of the GARCH (1,1), TGARCH (1,1), and EGARCH (1,1), models. The residuals of the GARCH (1,1), TGARCH (1,1), and EGARCH (1,1) are homoskedastic and there is no additional ARCH effect. Finally, there are negative and positive shocks that are driving the GBP/USD exchange spot rate away from normality. The data that we have used are monthly returns starting from 01/01/1990 to 01/01/2013, which total to 276 observations. The data was obtained from the Federal Reserve Statistical Release Department and the symbol of the series is H.10.