One‐sided testing for conditional heteroskedasticity in time series models

Engle’s autoregressive conditional heteroskedasticity (ARCH) model and its various generalizations have been widely used to model the volatility of economic and financial time series. Most existing ARCH tests fail to exploit the one‐sided nature of the alternative hypothesis. Lee and King (A locally most mean powerful based score test for ARCH and GARCH regression disturbances. J. Bus. Econ. Stat. 11 (1993), 17–27) recently proposed a locally most mean powerful score‐based one‐ sided test for ARCH effects. In this paper a new one‐sided test for ARCH effects of the disturbance of a dynamic regression model is proposed. The test is based on a weighted sum of sample autocorrelations of squared regression residuals, with the weighting function typically giving more weight to lower orders of lags and less weight to higher orders of lags. Lee and King’s (1993) test can be viewed as a special case of the present approach with the use of uniform weighting. Many non‐uniform weighting schemes deliver better power than uniform weighting; the efficiency gain is substantial when a relatively long lag is used. A simulation experiment confirms the gains from exploiting the one‐sided nature of the alternative hypothesis and from using non‐uniform weighting.