A stationary unbiased finite sample ARCH-LM test procedure

Abstract

Engle's (1982) Autoregressive Conditional Heteroscedasticity-Lagrange Multiplier (ARCH-LM) test is the undisputed standard test to detect ARCH. In this article, Monte Carlo (MC) simulations are used to demonstrate that the test's statistical size is biased in finite samples. Two complementing remedies to the related problems are proposed. One simple solution is to simulate new unbiased critical values for the ARCH-LM test. A second solution is based on the observation that for econometrics practitioners, detection of ARCH is generally followed by remedial modelling of this time-varying heteroscedasticity by the most general and robust model in the ARCH family; the Generalized ARCH (GARCH(1,1)) model. If the GARCH model's stationarity constraints are violated, as in fact is very often the case, obviously, we can conclude that ARCH-LM's detection of conditional heteroscedasticity has no or limited practical value. Therefore, formulated as a function of whether the GARCH model's stationarity constraints are satisfied or not, an unbiased and more relevant two-stage ARCH-LM test is specified. If the primary objectives of the study are to detect and remedy the problems of conditional heteroscedasticity, or to interpret GARCH parameters, the use of this article's new two-stage procedure, 2-Stage Unbiased ARCH-LM (2S-UARCH-LM), is strongly recommended.