Análise do valor p determinado pela estatística τ na aplicação do teste de Dickey-Fuller aumentado

Abstract

In this paper we evaluate how much influence the number of selected lagshas in the p-value obtained from the statistic considered in an augmented Dickey-Fuller test(ADF). Three experiments with different series sizes were carried out considering the pre-sence (or not) of a constant and/or trend, and also different number of lags. Autoregressivemodels (AR1) are used in the data generating process through the Monte Carlo method,considering different values for the coefficient associated with the first lag. After the ap-plication of the ADF test, we calculate the proportion of times when the null hypothesiswas rejected in each scenario, and perform an analysis of variance (considering chi-squarestatistic) to verify the influence of the number of selected lags in the p-value. Results showthat if a unit root is verified, then the test presents a good performance, regardless of thenumber of lags. However, the same was not observed in cases where the time series doesnot present a unit root.