Accumulated prediction errors, information criteria and optimal forecasting for autoregressive time series
| dc.creator | Ing, Ching-Kang | |
| dc.date | 2007-08-17 | |
| dc.date.accessioned | 2026-07-07T08:24:39Z | |
| dc.date.available | 2026-07-07T08:24:39Z | |
| dc.description | The predictive capability of a modification of Rissanen's accumulated prediction error (APE) criterion, APE$_{δ_n}$, is investigated in infinite-order autoregressive (AR($\infty$)) models. Instead of accumulating squares of sequential prediction errors from the beginning, APE$_{δ_n}$ is obtained by summing these squared errors from stage $nδ_n$, where $n$ is the sample size and $1/n\leq δ_n\leq 1-(1/n)$ may depend on $n$. Under certain regularity conditions, an asymptotic expression is derived for the mean-squared prediction error (MSPE) of an AR predictor with order determined by APE$_{δ_n}$. This expression shows that the prediction performance of APE$_{δ_n}$ can vary dramatically depending on the choice of $δ_n$. Another interesting finding is that when $δ_n$ approaches 1 at a certain rate, APE$_{δ_n}$ can achieve asymptotic efficiency in most practical situations. An asymptotic equivalence between APE$_{δ_n}$ and an information criterion with a suitable penalty term is also established from the MSPE point of view. This offers new perspectives for understanding the information and prediction-based model selection criteria. Finally, we provide the first asymptotic efficiency result for the case when the underlying AR($\infty$) model is allowed to degenerate to a finite autoregression. | |
| dc.description | Published at http://dx.doi.org/10.1214/009053606000001550 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/0708.2373 | |
| dc.identifier | http://arxiv.org/abs/0708.2373 | |
| dc.identifier | Annals of Statistics 2007, Vol. 35, No. 3, 1238-1277 | |
| dc.identifier | doi:10.1214/009053606000001550 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/136410 | |
| dc.subject | Statistics Theory | |
| dc.subject | 60M20 (Primary); 62F12, 62M10 (Secondary) | |
| dc.title | Accumulated prediction errors, information criteria and optimal forecasting for autoregressive time series | |
| dc.type | text |