Filtering and forecasting with misspecified ARCH models I. Getting the right variance with the wrong model (Q1185106)

For modelling time-varying conditional variances the financial economists have recently used ARCH (autoregressive conditional heteroscedastic) models to specify market volatility. This paper develops conditions under which a misspecified ARCH model may provide a consistent estimate of the conditional covariance matrix of a stochastic process. For example, if the stochastic process generating prices is approximately a diffusion process, then the paper shows that there may still be so much information on the conditional second moments at high frequencies, that even a misspecified ARCH model can be a consistent filter with a high degree of forecasting power. The paper also shows other cases of ARCH models where consistency properties and robustness fail altogether.