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Memory Parameter (memory + parameter)
Selected AbstractsOn the properties of the periodogram of a stationary long-memory process over different epochs with applicationsJOURNAL OF TIME SERIES ANALYSIS, Issue 1 2010Valdério A. Reisen Primary 60G10; 60K35; Secondary 60G18 This article studies the asymptotic properties of the discrete Fourier transforms (DFT) and the periodogram of a stationary long-memory time series over different epochs. The main theoretical result is a novel bound for the covariance of the DFT ordinates evaluated on two distinct epochs, which depends explicitly on the Fourier frequencies and the gap between the epochs. This result is then applied to obtain the limiting distribution of some nonlinear functions of the periodogram over different epochs, under the additional assumption of gaussianity. We then apply this result to construct an estimator of the memory parameter based on the regression in a neighbourhood of the zero-frequency of the logarithm of the averaged periodogram, obtained by computing the empirical mean of the periodogram over adjacent epochs. It is shown that replacing the periodogram by its average has an effect similar to the frequency domain pooling to reduce the variance of the estimate. We also propose a simple procedure to test the stationarity of the memory coefficient. A limited Monte Carlo experiment is presented to support our findings. [source] Bootstrap-based bandwidth choice for log-periodogram regressionJOURNAL OF TIME SERIES ANALYSIS, Issue 6 2009Josu Arteche Abstract., The choice of the bandwidth in the local log-periodogram regression is of crucial importance for estimation of the memory parameter of a long memory time series. Different choices may give rise to completely different estimates, which may lead to contradictory conclusions, for example about the stationarity of the series. We propose here a data-driven bandwidth selection strategy that is based on minimizing a bootstrap approximation of the mean-squared error (MSE). Its behaviour is compared with other existing techniques for optimal bandwidth selection in a MSE sense, revealing its better performance in a wider class of models. The empirical applicability of the proposed strategy is shown with two examples: the widely analysed in a long memory context Nile river annual minimum levels and the input gas rate series of Box and Jenkins. [source] Estimation of the location and exponent of the spectral singularity of a long memory processJOURNAL OF TIME SERIES ANALYSIS, Issue 1 2004Javier Hidalgo Abstract., We consider the estimation of the location of the pole and memory parameter ,0 and d of a covariance stationary process with spectral density We investigate optimal rates of convergence for the estimators of ,0 and d, and the consequence that the lack of knowledge of ,0 has on the estimation of the memory parameter d. We present estimators which achieve the optimal rates. A small Monte-Carlo study is included to illustrate the finite sample performance of our estimators. [source] A Time-Domain Semi-parametric Estimate for Strongly Dependent Continuous-Time Stationary ProcessesJOURNAL OF TIME SERIES ANALYSIS, Issue 6 2003Takeshi Kato Abstract., A covariance-based estimator of the memory parameter of strongly dependent continuous-time stationary processes is proposed. The consistency and asymptotic normality of the estimator are established. All assumptions, the form of the estimator, and the proofs are made in time-domain only. [source] Model Selection for Broadband Semiparametric Estimation of Long Memory in Time SeriesJOURNAL OF TIME SERIES ANALYSIS, Issue 6 2001Clifford M. Hurvich We study the properties of Mallows' CL criterion for selecting a fractional exponential (FEXP) model for a Gaussian long-memory time series. The aim is to minimize the mean squared error of a corresponding regression estimator dFEXP of the memory parameter, d. Under conditions which do not require that the data were actually generated by a FEXP model, it is known that the mean squared error MSE=E[dFEXP,d]2 can converge to zero as fast as (log n)/n, where n is the sample size, assuming that the number of parameters grows slowly with n in a deterministic fashion. Here, we suppose that the number of parameters in the FEXP model is chosen so as to minimize a local version of CL, restricted to frequencies in a neighborhood of zero. We show that, under appropriate conditions, the expected value of the local CL is asymptotically equivalent to MSE. A combination of theoretical and simulation results give guidance as to the choice of the degree of locality in CL. [source] Inducing normality from non-Gaussian long memory time series and its application to stock return dataAPPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 4 2010Kyungduk Ko Abstract Motivated by Lee and Ko (Appl. Stochastic Models. Bus. Ind. 2007; 23:493,502) but not limited to the study, this paper proposes a wavelet-based Bayesian power transformation procedure through the well-known Box,Cox transformation to induce normality from non-Gaussian long memory processes. We consider power transformations of non-Gaussian long memory time series under the assumption of an unknown transformation parameter, a situation that arises commonly in practice, while most research has been devoted to non-linear transformations of Gaussian long memory time series with known transformation parameter. Specially, this study is mainly focused on the simultaneous estimation of the transformation parameter and long memory parameter. To this end, posterior estimations via Markov chain Monte Carlo methods are performed in the wavelet domain. Performances are assessed on a simulation study and a German stock return data set. Copyright © 2009 John Wiley & Sons, Ltd. [source] | ||||||||||