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Title: Identification and validation of periodic autoregressive model with additive noise: Finite-variance case Authors:  Wojciech Zulawinski - Wroclaw University of Science and Technology (Poland) [presenting]
Aleksandra Grzesiek - Wroclaw Univeristy of Science and Technology (Poland)
Radoslaw Zimroz - Wroclaw University of Science and Technology (Poland)
Agnieszka Wylomanska - Wroclaw University of Science and Technology (Poland)
Abstract: The problem of modelling data containing periodic autoregressive (PAR) time series and additive noise is discussed. In most cases, such data are processed under noise-free model (i.e., without additive noise) assumptions that cannot be accepted in real life. The first two steps in PAR model identification are order selection and period estimation; thus, the main attention is paid to those issues. Finally, the model should be validated; thus the procedure for analysis of the residuals, considered here as multidimensional vectors, is proposed. Both issues (order and period selection, as well as model validation) are implemented here by using the characteristic function (CF) of the residual series. The CF is applied to receive the probability density function used in the information criterion. In the case of residuals analysis, it is used for the residuals distribution testing. To complete the PAR model, the procedure for estimation of the coefficients is required; however, this problem is just recalled, as it is a separate issue (prepared in parallel). The presented methodology can be considered as the general framework for analysis of data with periodically non-stationary characteristics disturbed by finite-variance external noise. The original contribution is related to optimal model order and period identification as well as analysis of residuals. All these findings have been inspired by our earlier work on machine condition monitoring using PAR modelling.