The Principle of Overcompleteness in VARMA Models

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Authors

TONNER Jaromír

Year of publication 2007
Type Article in Proceedings
Conference Summer School DATASTAT 06, Proceedings, Masaryk Univeristy, 2007
MU Faculty or unit

Faculty of Economics and Administration

Citation
Field Economy
Keywords multivariate time series; sparse system; overcomplete system; VARMA models; l1 norm optimization; stationary time series
Description In this paper we derive essential relations which are necessary for application of the principle of overcompleteness to sparse parameter estimation in multivariate ARMA models (VARMA models). This new approach is based on the Basis Pursuit Algorithm originally suggested by Chen et al [SIAM Review 43 (2001), No.1]. Overcompleteness means that we admit higher range of orders within which we are looking for lowest possible number of significant parameters (sparsity). A previous study [V. Veselý and J. Tonner: Austrian Journal of Statistics, Special Issue 2006] confirmed that this relaxation of the commonly used low-order assumption may yield more precise forecasts from ARMA models when compared with standard statistical estimation techniques. The results of the numerical simulation study and the tests on real data can be seen in [Mathematical Methods in Economics 2006, J. Tonner: The Principle of Overcompleteness in Economic Multivariate Time Series Models].
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