On optimal adaptive prediction of multivariate autoregression. (English) Zbl 1326.60050
Summary: The problem of asymptotic efficiency of adaptive one-step predictors for a stable multivariate first-order autoregressive process (AR(1)) with unknown parameters is considered. The predictors are based on the truncated estimators of the dynamic matrix parameter. The truncated estimation method is a modification of the truncated sequential estimation method that makes it possible to obtain estimators of ratio-type functionals with a given accuracy by samples of fixed size. The criterion of optimality is based on the loss function, defined as a sum of sample size and squared prediction error’s sample mean. The cases of known and unknown variance of the noise model are studied. In the latter case the optimal sample size is a special stopping time. The simulation results are given.
MSC:
| 60G25 | Prediction theory (aspects of stochastic processes) |
| 62M20 | Inference from stochastic processes and prediction |
| 60G40 | Stopping times; optimal stopping problems; gambling theory |
| 62F35 | Robustness and adaptive procedures (parametric inference) |
| 62H12 | Estimation in multivariate analysis |
| 62J05 | Linear regression; mixed models |
| 62L10 | Sequential statistical analysis |
Keywords:
adaptive prediction; multivariate autoregression; asymptotic risk efficiency; optimal sample size; stopping time; truncated parameter estimatorsReferences:
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