Spectral Density Of Stationary Process Research Articles

Robust empirical likelihood for time series

This article introduces a robust frequency domain empirical likelihood inference procedure for the parametric component in the spectral densities of stationary processes. We construct the empirical likelihood function by using a new spectral estimating function to achieve robustness against contamination in the spectral density. Simulation studies demonstrate the good performance of the proposed robust frequency domain empirical likelihood method, which produces more accurate confidence regions than the ordinary empirical likelihood counterpart.

Robust parameter estimation for stationary processes by an exotic disparity from prediction problem

A new class of disparities from the point of view of prediction problem is proposed for minimum contrast estimation of spectral densities of stationary processes. We investigate asymptotic properties of the minimum contrast estimators based on the new disparities for stationary processes with both finite and infinite variance innovations. The relative efficiency and the robustness against randomly missing observations are shown in our numerical simulations.

A Single-Pass Algorithm for Spectrum Estimation With Fast Convergence

We propose a single-pass algorithm for estimating spectral densities of stationary processes. Our algorithm is computationally fast in the sense that, when a new observation arrives, it can provide a real-time update within O(1) computation. The proposed algorithm is probabilistically fast in that, for stationary processes whose auto-covariances decay geometrically, the estimates from the algorithm converge at a rate which is optimal up to a multiplicative logarithmic factor. We also establish asymptotic normality for the recursive estimate. A simulation study is carried out and it confirms the superiority over the classical batched mean estimates.

ASYMPTOTICS OF SPECTRAL DENSITY ESTIMATES

We consider nonparametric estimation of spectral densities of stationary processes, a fundamental problem in spectral analysis of time series. Under natural and easily verifiable conditions, we obtain consistency and asymptotic normality of spectral density estimates. Asymptotic distribution of maximum deviations of the spectral density estimates is also derived. The latter result sheds new light on the classical problem of tests of white noises.

Sequential Estimation for a Functional of the Spectral Density of a Gaussian Stationary Process

Integral functional of the spectral density of stationary process is an important index in time series analysis. In this paper we consider the problem of sequential point and fixed-width confidence interval estimation of an integral functional of the spectral density for Gaussian stationary process. The proposed sequential point estimator is based on the integral functional replaced by the periodogram in place of the spectral density. Then it is shown to be asymptotically risk efficient as the cost per observation tends to zero. Next we provide a sequential interval estimator, which is asymptotically efficient as the width of the interval tends to zero. Finally some numerical studies will be given.

Distribution of the coates-diggle test statistic in case of replicated observations

A closed form expression for the distribution of a test statistic for comparing the spectral densities of stationary processes is given. This test statistic was introduced by COATES and DIGGLE ( 1986 ) for the unreplicated case and has been extended to the case of replicated observations by POTSCHER and RESCHENHOFER ( 1988 ). A simple method for computing approximate critical values in case of large numbers of replications is also provided. As a by-product an explicit expression for the distribution function of the range of independent variates each distributed as the logarithm of an F-variate i.e up to a factor of 2 each followin Fishers z-distriution is obtained

On a Condition of Almost Markov Regularity

Previous article Next article On a Condition of Almost Markov RegularityV. A. StatulyavichusV. A. Statulyavichushttps://doi.org/10.1137/1128030PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] B. Ryauba, The central limit theorem for sums of series of weakly dependent random variables, Litovsk. Mat. Sb., 2 (1962), 193–205, (In Russian.) 29:6526 Google Scholar[2] I. G. Zhurbenko, On the estimation of mixed cumulants for a class of random processes, Theory Prob. Appl., 15 (1970), 525–528 LinkGoogle Scholar[3] I. G. Zhurbenko, On strong estimates of mixed cumulants of random processes, Siberian Math. J., 13 (1972), 302–303 CrossrefGoogle Scholar[4] I. G. Zhurbenko and , N. M. Zuev, The higher spectral densities of stationary processes with mixing, Ukrain. Mat. Ž., 27 (1975), 452–463, 572 53:14620 0325.60039 Google Scholar[5] I. G. Zhurbenko, Mixing conditions and asymptotic theory of stationary time seriesStochastic processes and related topics (Proc. Summer Res. Inst. on Statist. Inference for Stochastic Processes, Indiana Univ., Bloomington, Ind., 1974, Vol. 1; dedicated to Jerzy Neyman), Academic Press, New York, 1975, 259–265 51:9177 0349.60031 Google Scholar[6] V. A. Statulyavichus, Limit theorems for random functions. I, Litovsk. Mat. Sb., 10 (1970), 583–592, (In Russian.) 43:2765 Google Scholar[7] V. A. Statulyavichus, Limit theorems for dependent random variables under various regularity conditions, Proceedings of the International Congress of Mathematicians (Vancouver, B. C., 1974), Vol. 2, Canad. Math. Congress, Montreal, Que., 1975, 173–181 55:1420 Google Scholar[8] V. A. Statulyavichus, Application of semi-invariants to asymptotic analysis of distributions of random processesMultivariate analysis, IV (Proc. Fourth Internat. Sympos., Dayton, Ohio, 1975), North-Holland, Amsterdam, 1977, 325–337 57:1614 Google Scholar[9] R. L. Dobrushin, The description of a random field by means of conditional probabilities and conditions for its regularity, Theory Prob. Appl., 13 (1968), 197–224 LinkGoogle Scholar[10] I. A. Ibragimov, Some limit theorems for stationary processes, Theory Prob. Appl., 7 (1962), 349–382 LinkGoogle Scholar[11] M. Rosenblatt, Some remarks on a mixing condition, Ann. Probab., 7 (1979), 170–172 80k:60071a 0925.60052 CrossrefGoogle Scholar[12] V. A. Statulyavichus, Large-deviation theorems for sums of dependent random variables, Lithuanian Math. J., 19 (1979), 289–295 CrossrefGoogle Scholar[13] A. V. Bulinskii, Limit Theorems for Random Processes and Fields, MGU, Moscow, 1981, (In Russian.) Google Scholar[14] V. Statulyavichus, On limit theorems for dependent random variables, Abstracts of Communications of the Third International Vilnius Conference on Probability Theory and Mathematical Statistics, Vilnius: In-t matem. i kibern. AN Lit SSR, 1981, 320–323 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails An Almost-Markov-Type Mixing Condition and Large Deviations for Boolean Models on the LineActa Applicandae Mathematicae, Vol. 96, No. 1-3 | 23 March 2007 Cross Ref Approximation of Distributions of Sums of Weakly Dependent Random Variables by the Normal DistributionLimit Theorems of Probability Theory | 1 Jan 2000 Cross Ref Limit Theorems on Large DeviationsLimit Theorems of Probability Theory | 1 Jan 2000 Cross Ref Every “lower psi-mixing” Markov chain is “interlaced rho-mixing”Stochastic Processes and their Applications, Vol. 72, No. 2 | 1 Dec 1997 Cross Ref Random fields: Applications in cell biologyStochastic Spatial Processes | 16 September 2006 Cross Ref Volume 28, Issue 2| 1984Theory of Probability & Its Applications219-469 History Submitted:10 January 1983Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1128030Article page range:pp. 379-383ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

Estimation of spectral densities of stationary processes

Estimation of spectral densities of stationary processes

On higher spectral densities of stationary processes with mixing

On higher spectral densities of stationary processes with mixing

Estimates of the higher-order spectral densities of stationary processes which satisfy the Cramer condition with ?Rosenblatt? mixing

Estimates of the higher-order spectral densities of stationary processes which satisfy the Cramer condition with ?Rosenblatt? mixing

Spectral Semi-Invariants of Stationary Processes with Sufficiently Strong Mixing

Previous article Next article Spectral Semi-Invariants of Stationary Processes with Sufficiently Strong MixingI. G. ZhurbenkoI. G. Zhurbenkohttps://doi.org/10.1137/1117013PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] I. G. Zhurbenko, On the estimation of mixed semi-invariants for a certain class of random processes, Theory Prob. Applications, 15 (1970), 525–528 10.1137/1115057 0221.62038 LinkGoogle Scholar[2] A. N. Shiryaev, Some problems in the theory of higher-order moments, I, Theory Prob. Application, 5 (1970), 265–284 10.1137/1105026 LinkGoogle Scholar[3] V. P. Leonov, Some Applications of Higher Semi-Invariants to the Theory of Stationary Processes, Izdat. Nauka, Moscow, 1964, (In Russian.) Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails On higher spectral densities of stationary processes with mixingUkrainian Mathematical Journal, Vol. 27, No. 4 Cross Ref Volume 17, Issue 1| 1972Theory of Probability & Its Applications History Submitted:08 May 1970Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1117013Article page range:pp. 151-153ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics