Nonparametric Estimation of Volatility Models with General Autoregressive Innovations

We are interested in modeling a zero mean heteroscedastic time series process with autoregressive error process of finite known order p. The model can be used for testing a martingale difference sequence hypothesis that is often adopted uncritically in financial time series against a fairly general alternative. When the argument is deterministic, we provide an innovative nonparametric estimator of the variance function and establish its consistency and asymptotic normality. We also propose a semiparametric estimator for the vector of autoregressive error process coefficients that is √ T consistent and asymptotically normal for a sample size T . Explicit asymptotic variance covariance matrix is obtained as well.