On the Existence of theMoments of the AsymptoticTrace Statistic

In this note we establish the existence of the first two moments of the asymptotic tracestatistic, which appears as weak limit of the likelihood ratio statistic for testing the cointe-gration rank in a vector autoregressive model and whose moments may be used to developpanel cointegration tests. Moreover, we justify the common practice to approximate thesemoments by simulating a certain statistic, which converges weakly to the asymptotic tracestatistic. To accomplish this we show that the moments of the mentioned statistic convergeto those of the asymptotic trace statistic as the time dimension tends to infinity.