Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Accumulated prediction errors, information criteria and optimal
  forecasting for autoregressive time series   The predictive capability of a modification of Rissanen's accumulated
prediction error (APE) criterion, APE$_{\delta_n}$, is investigated in
infinite-order autoregressive (AR($\infty$)) models. Instead of accumulating
squares of sequential prediction errors from the beginning, APE$_{\delta_n}$ is
obtained by summing these squared errors from stage $n\delta_n$, where $n$ is
the sample size and $1/n\leq \delta_n\leq 1-(1/n)$ 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$_{\delta_n}$. This expression shows that the prediction performance of
APE$_{\delta_n}$ can vary dramatically depending on the choice of $\delta_n$.
Another interesting finding is that when $\delta_n$ approaches 1 at a certain
rate, APE$_{\delta_n}$ can achieve asymptotic efficiency in most practical
situations. An asymptotic equivalence between APE$_{\delta_n}$ 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.

7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg