The Selection of ARIMA Models With or Without Regressors

32 Pages Posted: 15 Nov 2012

See all articles by Soren Johansen

Soren Johansen

University of Copenhagen - Department of Economics; Aarhus University - CREATES

Marco Riani

University of Parma

Anthony Atkinson

London School of Economics & Political Science (LSE)

Date Written: November 8, 2012

Abstract

We develop a Cp 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 X (2/n). 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 Cp 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 Cp 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 Cp.

Keywords: AIC, ARMA models, bias correction, BIC, Cp plot, generalized RIC, Kalman filter, Kullback-Leibler distance, state-space formulation

JEL Classification: C22

Suggested Citation

Johansen, Soren and Riani, Marco and Atkinson, Anthony, The Selection of ARIMA Models With or Without Regressors (November 8, 2012). Univ. of Copenhagen Dept. of Economics Discussion Paper No. 12-17, Available at SSRN: https://ssrn.com/abstract=2175553 or http://dx.doi.org/10.2139/ssrn.2175553

Soren Johansen (Contact Author)

University of Copenhagen - Department of Economics ( email )

Ă˜ster Farimagsgade 5
Bygning 26
1353 Copenhagen K.
Denmark

Aarhus University - CREATES ( email )

Nordre Ringgade 1
Aarhus, DK-8000
Denmark

Marco Riani

University of Parma ( email )

Via Amendola 10
Parma, 43100
United States

Anthony Atkinson

London School of Economics & Political Science (LSE) ( email )

Houghton Street
London, WC2A 2AE
United Kingdom

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