The Principle of Overcompleteness in VARMA Models
| Authors | |
|---|---|
| Year of publication | 2007 |
| Type | Article in Proceedings |
| Conference | Summer School DATASTAT 06, Proceedings, Masaryk Univeristy, 2007 |
| MU Faculty or unit | |
| 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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