The Experts below are selected from a list of 18438 Experts worldwide ranked by ideXlab platform
John N Haddad - One of the best experts on this subject based on the ideXlab platform.
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on the closed form of the covariance matrix and its inverse of the causal arma Process
2004Co-Authors: John N HaddadAbstract:Derivation of the theoretical autocovariance function of a causal autoregressive Moving-Average Process of order (p,q), ARMA(p,q), when q greater than or equal to 1 is considered. A recursive relationship is established between the covariance matrices of an ARMA(p,q) Process and its associated ARMA(p,q-1) Process. The obtained recursion is shown to produce the inverse of the covariance matrix and its determinant. Moreover, the introduced method can be easily implemented in any programming environment.
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the recursive property of the inverse of the covariance matrix of a Moving Average Process of general order
Journal of Time Series Analysis, 1995Co-Authors: John N HaddadAbstract:. The inverse of the covariance matrix of a Moving-Average Process of general order is considered. A recursive relationship between the inverses for any two consecutive orders has been established. Illustrative situations are derived and exact expressions are discussed.
Alexander Lindner - One of the best experts on this subject based on the ideXlab platform.
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a central limit theorem for the sample autocorrelations of a levy driven continuous time Moving Average Process
Journal of Statistical Planning and Inference, 2013Co-Authors: Serge Cohen, Alexander LindnerAbstract:In this article we consider Levy driven continuous time Moving Average Processes observed on a lattice, which are stationary time series. We show asymptotic normality of the sample mean, the sample autocovariances and the sample autocorrelations. A comparison with the classical setting of discrete Moving Average time series shows that in the last case a correction term should be added to the classical Bartlett formula that yields the asymptotic variance. An application to the asymptotic normality of the estimator of the Hurst exponent of fractional Levy Processes is also deduced from these results.
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strictly stationary solutions of autoregressive Moving Average equations
Biometrika, 2010Co-Authors: Peter J Brockwell, Alexander LindnerAbstract:Necessary and sufficient conditions for the existence of a strictly stationary solution of the equations defining an autoregressive Moving Average Process driven by an independent and identically distributed noise sequence are determined. No moment assumptions on the driving noise sequence are made. Copyright 2010, Oxford University Press.
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strictly stationary solutions of autoregressive Moving Average equations
Biometrika, 2010Co-Authors: Peter J Brockwell, Alexander LindnerAbstract:Necessary and sufficient conditions for the existence of a strictly stationary solution of the equations defining an autoregressive Moving Average Process driven by an independent and identically distributed noise sequence are determined. No moment assumptions on the driving noise sequence are made.
Ritva Luukkonen - One of the best experts on this subject based on the ideXlab platform.
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testing for a Moving Average unit root in autoregressive integrated Moving Average models
Journal of the American Statistical Association, 1993Co-Authors: Pentti Saikkonen, Ritva LuukkonenAbstract:Abstract Test procedures for detecting overdifferencing or a Moving Average unit root in Gaussian autoregressive integrated Moving Average (ARIMA) models are proposed. The tests can be used when an autoregressive unit root is a serious alternative but the hypothesis of primary interest implies stationarity of the observed time series. This is the case, for example, if one wishes to test the null hypothesis that a multivariate time series is cointegrated with a given theoretical cointegration vector. A priori knowledge of the mean value of the observations turns out to be crucial for the derivation of our tests. In the special case where the differenced series follows a first-order Moving Average Process, the proposed tests are exact and can be motivated by local optimality arguments. Specifically, when the mean value of the series is a priori known, we can obtain a locally best invariant (LBI) test that is identical to a one-sided version of the Lagrange multiplier test. But when the mean value is a prior...
Angeles Saavedra - One of the best experts on this subject based on the ideXlab platform.
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on the estimation of the marginal density of a Moving Average Process
Canadian Journal of Statistics-revue Canadienne De Statistique, 2000Co-Authors: Angeles SaavedraAbstract:The authors present a new convolution-type kernel estimator of the marginal density of an MA(1) Process with general error distribution. They prove the √n; -consistency of the nonparametric estimator and give asymptotic expressions for the mean square and the integrated mean square error of some unobservable version of the estimator. An extension to MA(q) Processes is presented in the case of the mean integrated square error. Finally, a simulation study shows the good practical behaviour of the estimator and the strong connection between the estimator and its unobservable version in terms of the choice of the bandwidth. RESUME Les auteurs montrent comment estimer par la methode du noyau la densite marginale d'un Processus de moyenne mobile MA(1) dont la loi des erreurs est quelconque. Ils demontrent la convergence d'ordre √n; de cet estimateur non parametrique de type convolution et donnent, pour une version non-observable dudit estimateur, des expressions asymptotiques pour les erreurs quadratiques moyennes classique et integreAe. Dans ce dernier cas, ils indiquent en outre comment leur resultat limite s'etend au modele MA(q). Une etude de simulation vient confirmerle bon comportement du nouvel estimateur, qui s'avere fortement lie a sa version non-observable en ce qui touche le choix de la fenětre
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a comparative study of two convolution type estimators of the marginal density of Moving Average Processes
Computational Statistics, 1999Co-Authors: Angeles SaavedraAbstract:In this paper, the mean integrated squared error of two convolution-type kernel estimators of the marginal density function of a Moving Average Process is studied. Direct calculations lead to an exact expression for the MISE when the Process is assumed to be Gaussian. Theses results, together with a simulation study carried out for some normal mixture distributions, are useful to compare the relative performance of these estimators with respect to the classical Parzen-Rosenblatt kernel density estimator.
Richard E Turner - One of the best experts on this subject based on the ideXlab platform.
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learning stationary time series using gaussian Processes with nonparametric kernels
Neural Information Processing Systems, 2015Co-Authors: Felipe Tobar, Thang D Bui, Richard E TurnerAbstract:We introduce the Gaussian Process Convolution Model (GPCM), a two-stage non-parametric generative procedure to model stationary signals as the convolution between a continuous-time white-noise Process and a continuous-time linear filter drawn from Gaussian Process. The GPCM is a continuous-time nonparametric-window Moving Average Process and, conditionally, is itself a Gaussian Process with a nonparametric kernel defined in a probabilistic fashion. The generative model can be equivalently considered in the frequency domain, where the power spectral density of the signal is specified using a Gaussian Process. One of the main contributions of the paper is to develop a novel variational free-energy approach based on inter-domain inducing variables that efficiently learns the continuous-time linear filter and infers the driving white-noise Process. In turn, this scheme provides closed-form probabilistic estimates of the covariance kernel and the noise-free signal both in denoising and prediction scenarios. Additionally, the variational inference procedure provides closed-form expressions for the approximate posterior of the spectral density given the observed data, leading to new Bayesian nonparametric approaches to spectrum estimation. The proposed GPCM is validated using synthetic and real-world signals.