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Abstract:
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One of the common approaches in time series is to approximate the true model by "long" autoregressive (AR) models. Usually the order of an AR model is selected by information criterions and then parameters are obtained by the least squares method etc. However, as sample size increases, it often implies that the model order should be refined, and hence all the parameters need to be recalculated. Thus, the cost of approximation increases. In this talk we propose a regularized approximation which enables to estimate AR coefficients with different level of accuracy. Thus, the model selection step is "smoothed" as the sample size increases. The regularized AR approximation can be considered therefore as a version of a shrinkage regression. We illustrate applications of the regularized AR approximation to estimation of ARMA models, frequency detection and forecasting of long memory processes.
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