ASYMPTOTIC EFFICIENCY OF THE ORDER SELECTION OF A NONGAUSSIAN AR PROCESS
@inproceedings{Karagrigoriou1997ASYMPTOTICEO, title={ASYMPTOTIC EFFICIENCY OF THE ORDER SELECTION OF A NONGAUSSIAN AR PROCESS}, author={Alex Karagrigoriou}, year={1997} }
Motivated by Shibata's (1980) asymptotic efficiency results for the order selected for a zero mean Gaussian AR process this paper establishes the asymp- totic efficiency of AIC-like model selection criteria for infinite order autoregressive processes with zero mean and unobservable errors that constitute a sequence of nongaussian random variables. Furthermore, from the spectral density point of view, the asympotic efficiency of AIC-like information criteria is established when the underlying…
25 Citations
On Efficient AR Spectral Estimation for Long-Range Predictions
- Mathematics
- 2005
ABSTRACT This article discusses the concept of asymptotic efficiency from the frequency domain point of view making use of the direct method for multiple prediction. In particular, it is shown that…
Asymptotically efficient order selection in nonstationary AR processes
- Mathematics
- 2000
In this paper we investigate the issue of asymptotic efficiency in nonstationary AR(∞) processes. Since the inverse of the autocovariance matrix of the underlying process cannot be evaluated due to…
Model selection for integrated autoregressive processes of infinite order
- MathematicsJ. Multivar. Anal.
- 2012
Order selection for same-realization predictions in autoregressive processes
- Computer Science
- 2005
This paper presents the first theoretical verification that AIC and its variants are still asymptotically elficient (in the sense defined in Section 4) for same-realization predictions, and shows that A IC also yields a satisfactory saute- realization prediction in finite samples.
Ecient selection of the order of an AR(1): a unified approach without knowing the order of integratedness a
- Mathematics
- 2011
This paper suggests several information criteria to select an integrated autoregressive (AR) model without knowing the order of integratedness. When the underlying AR process is known to be…
Order selection for possibly infinite-order non-stationary time series
- Computer ScienceAStA Advances in Statistical Analysis
- 2018
This study proposes a two-stage information criterion (TSIC), and shows that TSIC is asymptotically efficient in predicting integrated AR models when the underlying AR coefficients satisfy a wide range of conditions.
Vector autoregressive order selection and forecasting via the modified divergence information criterion
- Computer Science
- 2010
The VAR modified divergence information criterion (VAR/MDIC) shows remarkable good results by choosing the correct model more frequently than the known traditional information criteria with the smallest mean squared forecast error.
ORDER SELECTION FOR THE SAME-REALIZATION PREDICTION IN AUTOREGRESSIVE PROCESSES
- Computer Science
- 2000
The first theoretical justification that AIC and its variants still possess the asymptotic efficiency for the same-realization prediction is presented, and a moment bound for the norm of the inverse sample covariance matrix with an increasing dimension is established.
On the Use of Model Selection in Multivariate Processes with Applications in Economics
- Mathematics
In this article we introduce a multivariate version of the AIC selection criterion, which is based on the trace of the autocovariance matrix. This new criterion follows naturally from the quadratic…
References
SHOWING 1-10 OF 24 REFERENCES
Asymptotic efficiency of model selection criteria: the nonzero mean Gaussian AR(∞) case
- Mathematics
- 1995
Motivated by Shibata’s (1980) asymptotic efficiency results this paper dis-cusses the asymptotic efficiency of the order selected by a selection procedure for an infinite order autoregressive process…
Selection of the order of an autoregressive model by Akaike's information criterion
- Mathematics
- 1976
SUMMARY The asymptotic distribution is obtained of the order of regression selected by Akaike's information criterion in autoregressive models. The asymptotic quadratic risks of estimates of…
Regression and time series model selection in small samples
- Mathematics
- 1989
SUMMARY A bias correction to the Akaike information criterion, AIC, is derived for regression and autoregressive time series models. The correction is of particular use when the sample size is small,…
THE CRITERION AUTOREGRESSIVE TRANSFER FUNCTION OF PARZEN
- Mathematics
- 1986
. A mathematical derivation of the Criterion Autoregressive Transfer Function (CAT) of Parzen (1974) is given and a generalization of this criterion is introduced. The asymptotic distribution of the…
On selection of the order of the spectral density model for a stationary process
- Mathematics
- 1980
SummaryLet {X(t)} be a stationary process with mean zero and spectral densityg(x). We shall use akth order parametric spectral modelfτ(k)(x) for this process. Without Gaussianity we can obtain an…
Some properties of the order of an autoregressive model selected by a generalization of Akaike∘s EPF criterion
- Mathematics
- 1977
SUMMARY The asymptotic distribution of the order of an autoregression selected by a generalization of Akaike's FPE criterion is given. Some of the properties of the distribution are investigated. The…
REGRESSION, AUTOREGRESSION MODELS
- Mathematics
- 1986
. The accuracy of least squares fitted regression autoregression models as approximations to more general stochastic structures is considered, attention being paid to the accuracy of the estimates of…
Asymptotically Efficient Selection of the Order by the Criterion Autoregressive Transfer Function
- Mathematics
- 1986
On montre que la propriete d'optimalite obtenue par Shibata (1980, 1981) est valable pour l'approche CAT (Parzen, 1974), CAT * (Parzen, 1977) et CAT 2 (Bhansali, 1985)
The determination of the order of an autoregression
- Business
- 1979
SUMMARY It is shown that a strongly consistent estimation procedure for the order of an autoregression can be based on the law of the iterated logarithm for the partial autocorrelations. As compared…
Some recent advances in time series modeling
- Mathematics
- 1974
The aim of this paper is to describe some of the important concepts and techniques which seem to help provide a solution of the stationary time series problem (prediction and model identification).…