The Selection of ARIMA Models with or without Regressors

Søren Johansen, Marco Riani, Anthony C. Atkinson

Publikation: Working paper/Preprint Working paperForskning

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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.
UdgiverInstitut for Økonomi, Aarhus Universitet
Antal sider31
StatusUdgivet - 13 nov. 2012
NavnCREATES Research Paper


  • AIC, ARMA models, bias correction, BIC, $C_{p}$ plot, generalized RIC, Kalman filter, Kullback-Leibler distance, state-space formulation