Physical Sciences and Mathematics Commons^™

Penalized Estimation Of Autocorrelation, Xiyan Tan

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This dissertation explored the idea of penalized method in estimating the autocorrelation (ACF) and partial autocorrelation (PACF) in order to solve the problem that the sample (partial) autocorrelation underestimates the magnitude of (partial) autocorrelation in stationary time series. Although finite sample bias corrections can be found under specific assumed models, no general formulae are available. We introduce a novel penalized M-estimator for (partial) autocorrelation, with the penalty pushing the estimator toward a target selected from the data. This both encapsulates and differs from previous attempts at penalized estimation for autocorrelation, which shrink the estimator toward the target value of zero. …