The Selection of ARIMA Models with or without Regressors

Soren Johansen, Marco Riani and Anthony C. Atkinson ()
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Anthony C. Atkinson: Department of Statistics, London School of Economics, Postal: London WC2A 2AE, UK

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

Abstract: We develop a $C_{p}$ statistic for the selection of regression models with stationary and nonstationary ARIMA error term. We derive the asymptotic theory of the maximum likelihood estimators and show they are consistent and asymptotically Gaussian. We also prove that the distribution of the sum of squares of one step ahead standardized prediction errors, when the parameters are estimated, differs from the chi-squared distribution by a term which tends to infinity at a lower rate than $\chi _{n}^{2}$. We further prove that, in the prediction error decomposition, the term involving the sum of the variance of one step ahead standardized prediction errors is convergent. Finally, we provide a small simulation study. Empirical comparisons of a consistent version of our $C_{p}$ statistic with BIC and a generalized RIC show that our statistic has superior performance, particularly for small signal to noise ratios. A new plot of our time series $C_{p}$ statistic is highly informative about the choice of model. On the way we introduce a new version of AIC for regression models, show that it estimates a Kullback-Leibler distance and provide a version for small samples that is bias corrected. We highlight the connections with standard Mallows $C_{p}$.

Keywords: AIC; ARMA models; bias correction; BIC; $C_{p}$ plot; generalized RIC; Kalman filter; Kullback-Leibler distance; state-space formulation (search for similar items in EconPapers)
JEL-codes: C22 (search for similar items in EconPapers)
Pages: 31
Date: 2012-11-08
New Economics Papers: this item is included in nep-ecm, nep-ets, nep-for and nep-ore
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Working Paper: The Selection of ARIMA Models with or without Regressors (2012)
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Persistent link: https://EconPapers.repec.org/RePEc:aah:create:2012-46

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