TESTING THE COINTEGRATING RANK WHEN THE ERRORS ARE UNCORRELATED BUT NONINDEPENDENT

International audienceWe study the asymptotic behaviour of the reduced rank estimator of the cointegrating space and adjustment space for vector error correction time series models with nonindependent innovations. It is shown that the distribution of the adjustment space can be quite different for models with iid innovations and models with nonindependent innovations. It is also shown that the likelihood ratio test remains valid when the assumption of iid Gaussian errors is relaxed. Monte Carlo experiments illustrate the finite sample performance of the likelihood ratio test using various kinds of weak error processes

Comparison of procedures for fitting the autoregressive order of a vector error correction model

International audienceThis paper investigates the lag length selection problem of a vector error correction model by using a convergent information criterion and tools based on the Box-Pierce methodology recently proposed in the literature. The performances of these approaches for selecting the optimal lag length are compared via Monte Carlo experiments. The effects of misspecified deterministic trend or cointegrating rank on the lag length selection are studied. Noting that processes often exhibit nonlinearities, the cases of iid and conditionally heteroscedastic errors will be considered. Strategies that can avoid misleading situations are proposed

On the correlation analysis of illiquid stocks

The serial correlations of illiquid stock's price changes are studied, allowing for unconditional heteroscedasticity and time-varying zero returns probability. Depending on the set up, we investigate how the usual autocorrelations can be accommodated, to deliver an accurate representation of the price changes serial correlations. We shed some light on the properties of the different serial correlations measures, by mean of Monte Carlo experiments. The theoretical arguments are illustrated considering shares from the Chilean stock market

Lag length identification for VAR models with non-constant variance

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

Estimation adaptative des modeles vectoriels autoregréssifs avec une variance dependant du temps

International audienceNous analysons les modèles Vectoriels AutoRegressifs (VAR) quand les innovations sont non conditionnellement hétéroscédastiques. La structure de la volatilité est détermin-iste et générale, incluant des discontinuités ou des tendances comme cas particuliers. Dans ce cadre nous proposons des estimateurs des Moindres Carrés Ordinaires (MCO) et des estimateurs des Moindres Carrés Adaptatifs (MCA). L'estimateur des MCA est calculé en estimant la volatilité de façon non paramétrique. Nous obtenons la distribution asymptotique des estimateurs et comparons leur propriétés. En particulier nous montrons que l'estimateur des MCA est asymptotiquement équivalent à l'estimateur des Moindres Carrés Généralisés (MCG) obtenus en supposant que la volatilité des erreurs est connue

Multivariate Portmanteau test for Autoregressive models with uncorrelated but nonindependent errors

International audienceIn this paper we consider estimation and test of fit for multiple autoregressive time series models with nonindependent innovations. We derive the asymptotic distribution of the residual autocorrelations. It is shown that this asymptotic distribution can be quite different for models with iid innovations and models in which the innovations exhibit conditional heteroscedasticity or other forms of dependence. Consequently, the usual chi-square distribution does not provide adequate approximation to the distribution of the Box-Pierce goodness-of-fit portmanteau test in the presence of nonindependent innovations. We then propose a method to adjust the critical values of the portmanteau tests. Monte Carlo experiments illustrate the finite sample performance of the modified portmanteau test