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 L2norm 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.
Highlights
A change point is a situation where an entire data set is no longer characterized by the same underlying process
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
Since the interest is on the future volatility, by representing the innovations as ut = σ(Xt−1, Xt−2, ..., Xt−d)zt, Equation (1) is extended to a Non Parametric Auto-Regressive Conditional Heteroscedastic (NP-ARCH) model of the form
Summary
A change point is a situation where an entire data set is no longer characterized by the same underlying process. The observations have two or more distinct segments and each segment has a unique underlying process. The segments could have different variances or different mean. Change points are as a result of an observed event or an unobserved combination of factors. These include among others financial liberalization of emerging markets and integration of world equity markets, changes in exchange rate regimes from a fixed exchange rate regime to a floating exchange rate regime and introduction of a single currency like the Euro in Europe. Synonyms for change point include probabilistic diagnostics and disorder problems
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