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Abstract:
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Many real life processes can be modeled as a noised sum of sinusoids. Unknown frequencies can be obtained by approximating generalized spectral density of a process by an autoregressive (AR) model. The advantage is that an AR model has a simple structure, and its estimation and asymptotic properties are well-known. Usually, the order of the AR approximation is chosen by information criteria. However, with an increase of a sample size in on-line applications, model order may change, which leads to re-estimation of all parameters. We propose a regularized AR (RAR) approximation, which enables to estimate parameters with different level of accuracy. Hence, the repeated model selection and parameter estimation are avoided. Regularizer is chosen by cross-validation. In this talk, we discuss asymptotic properties of RAR, links to other regularization techniques and present numerical studies.
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