The Experts below are selected from a list of 294 Experts worldwide ranked by ideXlab platform
Marc G. Genton - One of the best experts on this subject based on the ideXlab platform.
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Nonparametric Autocovariance estimation from censored time series by Gaussian imputation.
Journal of nonparametric statistics, 2009Co-Authors: Jung Wook Park, Marc G. Genton, Sujit K. GhoshAbstract:One of the most frequently used methods to model the Autocovariance function of a second-order stationary time series is to use the parametric framework of autoregressive and moving average models developed by Box and Jenkins. However, such parametric models, though very flexible, may not always be adequate to model Autocovariance functions with sharp changes. Furthermore, if the data do not follow the parametric model and are censored at a certain value, the estimation results may not be reliable. We develop a Gaussian imputation method to estimate an Autocovariance structure via nonparametric estimation of the Autocovariance function in order to address both censoring and incorrect model specification. We demonstrate the effectiveness of the technique in terms of bias and efficiency with simulations under various rates of censoring and underlying models. We describe its application to a time series of silicon concentrations in the Arctic.
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Highly Robust Estimation of the Autocovariance Function
Journal of Time Series Analysis, 2000Co-Authors: Marc G. GentonAbstract:In this paper, the problem of the robustness of the sample Autocovariance function is addressed. We propose a new Autocovariance estimator, based on a highly robust estimator of scale. Its robustness properties are studied by means of the influence function, and a new concept of temporal breakdown point. As the theoretical variance of the estimator does not have a closed form, we perform a simulation study. Situations with various size of outliers are tested. They confirm the robustness properties of the new estimator. An S-Plus function for the highly robust Autocovariance estimator is made available on the Web at http://www-math.mit.edu/~yanyuan/Genton/Time/time.html. At the end, we analyze a time series of monthly interest rates of an Austrian bank.
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the correlation structure of the sample Autocovariance function for a particular class of time series with elliptically contoured distribution
Statistics & Probability Letters, 1999Co-Authors: Marc G. GentonAbstract:In the context of time series, the classical estimator of the Autocovariance function can be written as a quadratic form of the observations. If data have an elliptically contoured distribution with constant mean, then the correlation between the sample Autocovariance function at two different lags is a function of the time design matrix and the covariance matrix of the process. When data have a regular support, an explicit formula for this correlation is available for a particular family of covariance matrices. Surprisingly, this correlation structure is exactly the same as the one for a Gaussian white noise.
Valderio A. Reisen - One of the best experts on this subject based on the ideXlab platform.
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Robust estimation of the scale and of the Autocovariance function of Gaussian short‐ and long‐range dependent processes
Journal of Time Series Analysis, 2010Co-Authors: Céline Lévy-leduc, Hélène Boistard, Éric Moulines, Murad S. Taqqu, Valderio A. ReisenAbstract:A desirable property of an Autocovariance estimator is to be robust to the presence of additive outliers. It is well-known that the sample Autocovariance, being based on moments, does not have this property. Hence, the use of an Autocovariance estimator which is robust to additive outliers can be very useful for time-series modeling. In this paper, the asymptotic properties of the robust scale and Autocovariance estimators proposed by Rousseeuw and Croux (1993) and Genton and Ma (2000) are established for Gaussian processes, with either short-range or long-range dependence. It is shown in the short-range dependence setting that this robust estimator is asymptotically normal at the rate $\sqrt{n}$, where $n$ is the number of observations. An explicit expression of the asymptotic variance is also given and compared to the asymptotic variance of the classical Autocovariance estimator. In the long-range dependence setting, the limiting distribution displays the same behavior than that of the classical Autocovariance estimator, with a Gaussian limit and rate $\sqrt{n}$ when the Hurst parameter $H$ is less $3/4$ and with a non-Gaussian limit (belonging to the second Wiener chaos) with rate depending on the Hurst parameter when $H \in (3/4,1)$. Some Monte-Carlo experiments are presented to illustrate our claims and the Nile River data is analyzed as an application. The theoretical results and the empirical evidence strongly suggest using the robust estimators as an alternative to estimate the dependence structure of Gaussian processes.
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Robust estimation of the scale and of the Autocovariance function of Gaussian short and long-range dependent processes
2009Co-Authors: Céline Lévy-leduc, Hélène Boistard, Éric Moulines, Murad S. Taqqu, Valderio A. ReisenAbstract:A desirable property of an Autocovariance estimator is to be robust to the presence of additive outliers. It is well-known that the sample Autocovariance, being based on moments, does not have this property. Hence, the use of an Autocovariance estimator which is robust to additive outliers can be very useful for time-series modeling. In this paper, the asymptotic properties of the robust scale and Autocovariance estimators proposed by Rousseeuw and Croux (1993) and Genton and Ma (2000) are established for Gaussian processes, with either short-range or long-range dependence. It is shown in the short-range dependence setting that this robust estimator is asymptotically normal at the rate $\sqrt{n}$, where $n$ is the number of observations. An explicit expression of the asymptotic variance is also given and compared to the asymptotic variance of the classical Autocovariance estimator. In the long-range dependence setting, the limiting distribution displays the same behavior than that of the classical Autocovariance estimator, with a Gaussian limit and rate $\sqrt{n}$ when the Hurst parameter $H$ is less $3/4$ and with a non-Gaussian limit (belonging to the second Wiener chaos) with rate depending on the Hurst parameter when $H \in (3/4,1)$. Some Monte-Carlo experiments are presented to illustrate our claims and the Nile River data is analyzed as an application. The theoretical results and the empirical evidence strongly suggest using the robust estimators as an alternative to estimate the dependence structure of Gaussian processes.
David B. Stanley - One of the best experts on this subject based on the ideXlab platform.
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Autocovariance based plant model mismatch estimation for linear model predictive control
Systems & Control Letters, 2017Co-Authors: Siyun Wang, Jodie M. Simkoff, Michael Baldea, Leo H. Chiang, Ivan Castillo, Rahul Bindlish, David B. StanleyAbstract:Abstract In this paper, we present Autocovariance-based estimation as a novel methodology for determining plant-model mismatch for multiple-input, multiple-output systems operating under model predictive control. Considering discrete-time, linear time invariant systems under reasonable assumptions, we derive explicit expressions of the Autocovariances of the system inputs and outputs as functions of the plant-model mismatch. We then formulate the mismatch estimation problem as a global optimization aimed at minimizing the discrepancy between the theoretical Autocovariance estimates and the corresponding values computed from historical closed-loop operating data. Practical considerations related to implementing these ideas are discussed, and the results are illustrated with a chemical process case study.
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Autocovariance-based plant-model mismatch estimation for linear model predictive control ☆
Systems & Control Letters, 2017Co-Authors: Siyun Wang, Jodie M. Simkoff, Michael Baldea, Leo H. Chiang, Ivan Castillo, Rahul Bindlish, David B. StanleyAbstract:Abstract In this paper, we present Autocovariance-based estimation as a novel methodology for determining plant-model mismatch for multiple-input, multiple-output systems operating under model predictive control. Considering discrete-time, linear time invariant systems under reasonable assumptions, we derive explicit expressions of the Autocovariances of the system inputs and outputs as functions of the plant-model mismatch. We then formulate the mismatch estimation problem as a global optimization aimed at minimizing the discrepancy between the theoretical Autocovariance estimates and the corresponding values computed from historical closed-loop operating data. Practical considerations related to implementing these ideas are discussed, and the results are illustrated with a chemical process case study.
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Autocovariance-based MPC model mismatch estimation for systems with measurable disturbances
Journal of Process Control, 2017Co-Authors: Siyun Wang, Jodie M. Simkoff, Michael Baldea, Leo H. Chiang, Ivan Castillo, Rahul Bindlish, David B. StanleyAbstract:Abstract In this paper, we propose a novel Autocovariance-based plant-model mismatch estimation approach for linear MPC MIMO control loops with changing setpoints and measurable disturbances. Assuming a noise model is available and that there are of periods of operating data where the active set of the controller is fixed and the plant-model mismatch is invariant, we establish an explicit relation between the Autocovariance matrices of the mean-centered process outputs and the plant-model mismatch. We then formulate the mismatch estimation problem as an optimization aimed at minimizing the difference between the theoretical Autocovariance, computed from the established relation, and actual output Autocovariances, calculated from the plant data. We elaborate our results for step-response models typically used in MPC, as well as for parametric (transfer function models) in both continuous time and discrete time. A simulation case study for an unconstrained MPC controller with measurable disturbances is used to illustrate the theoretical results.
Yoshihide Kakizawa - One of the best experts on this subject based on the ideXlab platform.
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Note on the Asymptotic Efficiency of Sample Covariances in Gaussian Vector Stationary Processes
Journal of Time Series Analysis, 1999Co-Authors: Yoshihide KakizawaAbstract:In this note certain results obtained by Porat (J. Time Ser. Anal. 8 (1987), 205–20) and Kakizawa and Taniguchi (J. Time Ser. Anal. 15 (1994), 303–11) concerning the asymptotic efficiency of sample Autocovariances of a zero-mean Gaussian stationary process are extended to the case of m-vector processes. It is shown that, for Gaussian vector AR(p) processes, the sample Autocovariance matrix at lag k is asymptotically efficient if 0 ≤k≤p. Further, none of the sample Autocovariance matrices is asymptotically efficient for Gaussian vector MA(q) processes.
Jingjing Yang - One of the best experts on this subject based on the ideXlab platform.
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Exactly/Nearly Unbiased Estimation of Autocovariances of a Univariate Time Series With Unknown Mean
Journal of Time Series Analysis, 2016Co-Authors: Timothy J. Vogelsang, Jingjing YangAbstract:This article proposes an exactly/nearly unbiased estimator of the Autocovariance function of a univariate time series with unknown mean. The estimator is a linear function of the usual sample Autocovariances computed using the observed demeaned data. The idea is to stack the usual sample Autocovariances into a vector and show that the expectation of this vector is a linear combination of population Autocovariances. A matrix that we label, A, collects the weights in these linear combinations. When the population Autocovariances of high lags are zero (small), exactly (nearly) unbiased estimators of the remaining Autocovariances can be obtained using the inverse of upper blocks of the A matrix. The A-matrix estimators are shown to be asymptotically equivalent to the usual sample Autocovariance estimators. The A-matrix estimators can be used to construct estimators of the autocorrelation function that have less bias than the usual estimators. Simulations show that the A-matrix estimators can substantially reduce bias while not necessarily increasing mean square error. More powerful tests for the null hypothesis of white noise are obtained using the A-matrix estimators.
