# 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

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## 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).…