Abstract:
A non parametric Auto-Regressive Conditional Heteroscedastic model for financial returns series is considered in which
the conditional mean and volatility functions are estimated non-parametrically using Nadaraya Watson kernel. A test
statistic for unknown abrupt change point in volatility which takes into consideration conditional heteroskedasticity, dependence, heterogeneity and the fourth moment of financial returns, since kurtosis is a function of the fourth moment is
considered. The test is based on L2 norm of the conditional variance functions of the squared residuals. A non-parametric
change point estimator in volatility of financial returns is further obtained. The consistency of the estimator is shown
theoretically and through simulation. An application of the estimator in change point estimation in volatility of United
States Dollar/Kenya Shilling exchange rate returns data set is made. Through binary segmentation procedure, three change
points in volatility of the exchange rate returns are estimated and further accounted for.
