Conditional variance estimation in regression models with long memory - Kulik, Rafal; Wichelhaus, Cornelia (Journal of time series analysis, 2012)
In this article we study asymptotic properties of a non-parametric kernel estimator of the conditional variance in a random design model with parametric mean and heteroscedastic errors, for a class of long-memory errors and predictors. We establish small and large bandwidths asymptotics, which show a different behaviour compared with that of kernel estimators of the conditional mean. We distinguish between an oracle case (i.e. where the errors are directly observed) and a non-oracle case (where the errors are replaced with residuals) and show non-equivalence between the oracle and non-oracle case. We also discuss a practical problem of bandwidth choice. Theoretical results are justified by simulation studies. We apply our theory to DJA and FTSE indices.