Sparse Parameter Estimation in Overcomplete Time Series Models
| Authors | |
|---|---|
| Year of publication | 2005 |
| Type | Article in Proceedings |
| Conference | Perspectives in Modern Statistical Inference III, July 18--22, 2005 in Mikulov, Program and Abstracts |
| MU Faculty or unit | |
| Citation | |
| Field | Applied statistics, operation research |
| Keywords | ARMA model; overcomplete; functional model; sparse parameter estimates; simulation study |
| Description | We suggest a new approach to parameter estimation in univariate time series AR(I)MA models with large number of parameters. The estimation procedure is based on the technique of sparse atomic decomposition and utilizes a modified version of the Basis Pursuit Algorithm [Chen et al, SIAM Review 43 (2001), No. 1]. After having accomplished and analyzed a lot of numerical simulations we were able to reliably identify nearly zero parameters in the model allowing us to reduce the originally badly conditioned overparametrized model. Among others we need not take care about model orders the fixing of which is a common preliminary step used by standard techniques. For small sample sizes the new procedure yields better precision of one-step predictions when compared with those based on standard ML-estimates as obtained from the MATLAB System identification toolbox. |
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