Statistics Colloquium : Dr. Timothy McMurry
Univ of Virginia
Location
Sherman Hall : 145
Date & Time
September 7, 2018, 11:00 am – 12:00 pm
Description
Title: Time series inference and prediction through estimation of the autocovariance matrix
Abstract: This talk addresses the problem of estimating the autocovariance matrix of a stationary process. Under short range dependence assumptions, convergence rates are established for a gradually tapered version of the sample autocovariance matrix and for its inverse. The proposed estimator is formed by leaving the main diagonals of the sample autocovariance matrix intact while gradually down-weighting off-diagonal entries towards zero. We then develop 3 applications for this estimator: (i) the Linear Process Bootstrap, a new time-series bootstrap; (ii) a new approach to optimal time series prediction; and (iii) a modification of the innovations algorithm which can be shown to produce a consistent estimate for the sequence of MA parameters.
Abstract: This talk addresses the problem of estimating the autocovariance matrix of a stationary process. Under short range dependence assumptions, convergence rates are established for a gradually tapered version of the sample autocovariance matrix and for its inverse. The proposed estimator is formed by leaving the main diagonals of the sample autocovariance matrix intact while gradually down-weighting off-diagonal entries towards zero. We then develop 3 applications for this estimator: (i) the Linear Process Bootstrap, a new time-series bootstrap; (ii) a new approach to optimal time series prediction; and (iii) a modification of the innovations algorithm which can be shown to produce a consistent estimate for the sequence of MA parameters.
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