Time Series Model Selection Research Articles

Regression and Time Series Model Selection

Regression and Time Series Model Selection

Increasing seasonal variation; unit roots versus shifts in mean and trend

In this paper we consider model selection for time series with increasing (or decreasing) seasonal variation, where this variation can be described by (seasonal) unit root models with significant deterministic components or by models with less unit roots but with shiftsin seasonal means or trends.

Increasing seasonal variation; unit roots versus shifts in mean and trend

In this paper we consider model selection for time series with increasing (or decreasing) seasonal variation, where this variation can be described by (seasonal) unit root models with significant deterministic components or by models with less unit roots but with shifts in seasonal means or trends. As a model selection device we use tests based on the Osborn et al. regression, which we modify to allow for shifts in mean and trend. An application to disposable income in Japan yields that apparent unit roots are not robust to structural shifts induced by the Oil Crisis in the fourth quarter of 1973. © 1998 John Wiley & Sons, Ltd.

The model selection criterion AICu

For regression and time series model selection, Hurvich and Tsai (1989) obtained a bias correction Akaike information criterion, AICc, which provides better model order choices than the Akaike information criterion, AIC (Akaike, 1973). In this paper, we propose an alternative improved regression model selection criterion, AICu, which is an approximate unbiased estimator of Kullback-Leibler information. We show that AICu is neither a consistent (Shibata, 1986) nor an efficient (Shibata, 1980, 1981) criterion. Our simulation studies indicate that the behavior of AICu is a compromise between that of efficient (AICc) and consistent (BIC, Akaike, 1978) criteria. Specifically, AICu performs better than AICc for moderate to large sample sizes except when the true model is of infinite order. In addition, it outperforms BIC except when a true model exists and the sample size is large.

Regression and time series model selection using variants of the schwarz information criterion

The Schwarz (1978) information criterion, SIC, is a widely-used tool in model selection, largely due to its computational simplicity and effective performance in many modeling frameworks. The derivation of SIC (Schwarz, 1978) establishes the criterion as an asymptotic approximation to a transformation of the Bayesian posterior probability of a candidate model. In this paper, we investigate the derivation for the identification of terms which are discarded as being asymptotically negligible, but which may be significant in small to moderate sample-size applications. We suggest several SIC variants based on the inclusion of these terms. The results of a simulation study show that the variants improve upon the performance of SIC in two important areas of application:multiple linear regression and time series analysis.

Improved estimators of Kullback–Leibler information for autoregressive model selection in small samples

SUMMARY A new estimator, AICI, of the Kullback-Leibler information is proposed for Gaussian autoregressive time series model selection. The expected information is decomposed into two terms, the first being estimated without bias. The second term is a penalty function which depends only weakly on the model parameters, and hence can be tabulated by simulation from a white noise process. The estimated information, AICI, is very nearly unbiased when the model is either correct or overfitted. It is shown that the penalty term of AIC, is asymptotically equivalent to that of the AICC criterion of Hurvich & Tsai (1989). For autoregressive models estimated from small samples by Burg's method, simulation provides strong support for the use of the simpler criterion AICC, perhaps using an unbiased version of the first term. If the autoregressive models are estimated by maximum likelihood, then: (a) if none of the candidate model dimensions exceeds one-half the sample size, AIC, provides somewhat better model selections than AICC; (b) if some of the candidate models have large dimension, a case considered particularly in engineering applications, then AIC, provides much better model selections in small samples than AICc.

Regression and Time Series Model Selection in Small Samples

Regression and Time Series Model Selection in Small Samples

Regression and time series model selection in small samples

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, or when the number of fitted parameters is a moderate to large fraction of the sample size. The corrected method, called AICC, is asymptotically efficient if the true model is infinite dimensional. Furthermore, when the true model is of finite dimension, AICC is found to provide better model order choices than any other asymptotically efficient method. Applications to nonstationary autoregressive and mixed autoregressive moving average time series models are also discussed.

A simultaneous test in the presence of nested alternative hypotheses

This paper considers the generalized likelihood ratio (GLR) test or its modification dealing with nested models. The algorithm for evaluating the critical values and the error-rates for the canonical tests are provided; a table of critical values of a class of GLR tests is also given. The test proposed in the paper has applications in time-series model selection.

A simultaneous test in the presence of nested alternative hypotheses

This paper considers the generalized likelihood ratio (GLR) test or its modification dealing with nested models. The algorithm for evaluating the critical values and the error-rates for the canonical tests are provided; a table of critical values of a class of GLR tests is also given. The test proposed in the paper has applications in time-series model selection.