Consistency of an Estimator for Change Point in Volatility of Financial Returns

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. test statistic unknown abrupt change point takes into consideration heteroskedasticity, dependence, heterogeneity fourth moment of returns, since kurtosis a function considered. The based on L2norm variance squared residuals. non-parametric estimator further obtained. consistency shown theoretically through simulation. An application estimation United States Dollar/Kenya Shilling exchange rate data set made. Through binary segmentation procedure, three points accounted for.