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Title: Optimal bias-correction in the log periodogram estimation of the fractional parameter: A jackknife approach Authors:  Kanchana Nadarajah - Monash University, Australia (Australia) [presenting]
Gael Martin - Monash University (Australia)
Donald Poskitt - Monash University (Australia)
Abstract: A bias-corrected log-periodogram regression (LPR) estimator based on a jackknife method is proposed for the fractional parameter in a stationary class of fractionally integrated models. The weights of the full sample and the subsamples in the jackknife estimator are chosen such that bias reduction occurs to an order of $n^{-a}$, where $0<a<1$ with $n$ the sample size, without inflating the asymptotic variance. Some statistical properties of the discrete Fourier transform and periodograms related to the full sample and subsamples of a time series, which are exploited in constructing the optimal weights, are also provided. Under some regularity conditions, it is shown that the optimal jackknife estimator is consistent and has a limiting normal distribution with the same asymptotic variance and rate of convergence as the original LPR estimator. These theoretical results are valid under both non-overlapping and moving-block sub-sampling schemes used in the jackknife technique. In a Monte Carlo study the new optimal jackknife estimator outperforms some of the main competing estimators, in terms of bias-reduction and root mean-squared-error. The proposed method is applied to two empirical time series: (i) the annual minimum level of the Nile River, and (ii) realized volatility for the daily returns on the S\&P500 index.