Asymptotic Properties in ARCH(p)-time Serie

Abstract

ARCH(p)-model has found much interest in Financial econometrics. It was introduced by Engle (1982) in order to provide a framework in which so-called volatility clusters may occur, i.e., periods of high and low (conditional) variances depending on past values of the series. The model was later extended into various directions. In most of the work for ARCH(p)-model,? the main focus has been on estimating the unknown parameters. But it is of interest and of practical importance to know the nature of the innovation distribution. Actually, if the distribution of the innovation is unspecified, the parametric component only partly determines the distribution behavior.? It is as important to investigate the distribution of the innovation as estimating the parameters. In this talk, we consider the consistency and asymptotic distribution of the innovation density estimators in ARCH(p)-time series.? We also extend the central limit theorem (CLT) and the strong law of large number (SLLN) to the average of the residuals.?