Robust automatic bandwidth for long memory (Q2740037)

This paper is concerned with the optimal choice of bandwidth, or number of periodogram ordinates, used in the estimation of long memory time series. The considered semiparametric estimates are those for which asymptotic theory was provided. Namely, this paper is concerned with bandwidth choice in local Whittle (LW), \(\log\) periodogram (LP) and averaged periodogram (AP) estimation. Here, interest is on theoretical optimal bandwidth for LW, LP and AP, and feasible approximations. The paper focuses on the robustness of these procedures for time series with (possibly long-memory) conditionally heteroscedastic errors. Such considerations are motivated by the recognition that semiparametric estimation procedures seem particularly well suited for time series of financial measurements sampled at high frequencies.NEWLINENEWLINENEWLINEThe study of the robustness of automatic bandwidth selection procedures for semiparametric estimation of long memory is organized along two major lines. First, the optimal bandwidth formulas for the AP and for the LW are shown to remain valid under a very wide range of conditional heteroscedasticity specifications, including long memory in the error variances. The theoretical results then serve as a basis for an extensive Monte Carlo investigation of the robustness of infeasible and feasible approximations to the optimal bandwidth formulas for the LW, LP and AP procedures.