Abstract
Long-memory parameter estimation using log-periodogram regression relies largely on the frequency bandwidth and the order of estimation. Literature shows that a data-dependent plug-in method for the bandwidth significantly increases the MSE’s. In a long memory time series with mild short range effect, a simple approach to determine the bandwidth size is suggested based on the spectral analysis. Monte Carlo simulation results and empirical applications show that the proposed bandwidth selection performs satisfactorily.
Highlights
There has been research on estimation of long memory parameter in time series using periodogram-based semi-parametric estimate, namely the local Whittle (Kunsch, 1987; Robinson, 1995a), average periodogram (Robinson, 1994) and log-periodogram (Geweke & Porter-Hudak, 1983; Robinson, 1995b)
To balance the squared bias and variance, optimal bandwidth selection is usually proposed to minimize the approximation of the MSE or the root mean-squared error (RMSE)
Even in the case without long memory effect, the proposed method suggests the bandwidths that are closer to the one that gives the minimum RMSE in the Monte Carlo simulations, giving the smaller average RMSE compared to the plug-in AG method
Summary
There has been research on estimation of long memory parameter in time series using periodogram-based semi-parametric estimate, namely the local Whittle (Kunsch, 1987; Robinson, 1995a), average periodogram (Robinson, 1994) and log-periodogram (Geweke & Porter-Hudak, 1983; Robinson, 1995b). Semi-parametric estimation procedures are desired in the time series analysis of financial measurements sampled at high frequencies (Barros, Gil-Alana & Payne 2014; Bollerslev et al, 2013; Garvey & Gallagher, 2013) as they allow the estimation of the long-run characteristics (low frequency behaviour) of the time series without the knowledge of the short-run (high frequency) structure Amongst these methods, log-periodogram (LP) regression proposed by Geweke and Porter-Hudak (1983) (GPH) has become a popular tool for statistical inference in empirical research due to its simple implementation, pivotal asymptotic normality and robustness as a result of the local condition (Arteche & Orbe, 2009).
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