Preliminary Detection for ARCH-Type Heteroscedasticity in a Nonparametric Time Series Regression Model

Abstract

In this paper a nonparametric method is proposed for detecting conditionally heteroscedastic errors in a nonparametric time series regression model where the observation points are equally spaced on [0; 1]. It turns out that the first-order sample autocorrelation of the squared residuals from the kernel regression estimates provides essential information. Illustrative simulation study is presented for diverse errors such as ARCH(1), GARCH(1,1) and threshold-ARCH(1) models.