2007/01/26 by Meng-Chen Hsieh, Meng‐Chen Hsieh, Clifford M. Hurvich +1 · 9 citations
Computer Science · Economics, Econometrics and Finance · Mathematics · #Applied mathematics #Asymptotic distribution #Bayesian Methods and Mixture Models #Estimator #Financial Risk and Volatility Modeling #Gaussian #Mathematics #Physics #Range (aeronautics) #Sample (material) #Statistical physics #Statistics #Stochastic processes and financial applications #math.ST #msc:60G10 #stat.TH
paper · pdf · doi:10.1016/j.jeconom.2006.12.001
published in Journal of Econometrics 141(2), 913-949 (Elsevier BV)
openalex publication_date 2007/01/26 · arxiv created 2007/05/18 · arxiv updated 2012/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider processes with second order long range dependence resulting from heavy tailed durations. We refer to this phenomenon as duration-driven long range dependence (DDLRD), as opposed to the more widely studied linear long range dependence based on fractional differencing of an iid process. We consider in detail two specific processes having DDLRD, originally presented in Taqqu and Levy (1986), and Parke (1999). For these processes, we obtain the limiting distribution of suitably standardized discrete Fourier transforms (DFTs) and sample autocovariances. At low frequencies, the standardized DFTs converge to a stable law, as do the standardized sample autocovariances at fixed lags. Finite collections of standardized sample autocovariances at a fixed set of lags converge to a degenerate distribution. The standardized DFTs at high frequencies converge to a Gaussian law. Our asymptotic results are strikingly similar for the two DDLRD processes studied. We calibrate our asymptotic results with a simulation study which also investigates the properties of the semiparametric log periodogram regression estimator of the memory parameter.