  The identification of the lag length for vector autoregressive models by mean
of Akaike Information Criterion (AIC), Partial Autoregressive and Correlation
Matrices (PAM and PCM hereafter) is studied in the framework of processes with
time varying variance. It is highlighted that the use of the standard tools are
not justified in such a case. As a consequence we propose an adaptive AIC which
is robust to the presence of unconditional heteroscedasticity. Corrected
confidence bounds are proposed for the usual PAM and PCM obtained from the
Ordinary Least Squares (OLS) estimation. The volatility structure of the
innovations is used to develop adaptive PAM and PCM. We underline that the
adaptive PAM and PCM are more accurate than the OLS PAM and PCM for identifying
the lag length of the autoregressive models. Monte Carlo experiments show that
the adaptive $AIC$ have a greater ability to select the correct autoregressive
order than the standard AIC. An illustrative application using US international
finance data is presented.
