Modelos econométricos dinámicos no invertibles

Abstract

The dissertation proposes a general procedure to test the presence of multiple MA unit roots in a wide variety of ARIMA models, which also may include another MA unit roots to those that are of interest. These additional unit MA roots may be considered as an alternative to the inclusion of deterministic terms (linear trend), and are also useful to extend the test statistic to seasonal models. Thus, the model used allows for a wide range of noninvertibility and parameter stability testing problems. The testing procedure is similar to that proposed by Saikkonen and Luukkonen (1993) for the case of a regular MA unit root in the sense that it takes into account the additional ARMA structure, but it has two main differences: the strategy used to obtain the test statistic and the expressions provided. First, the test statistic is obtained using a structural model, which facilitates its obtaining because it only requires calculating the first derivative of the likelihood function. Second, the proposed expressions are convenient to calculate the statistical in terms of the residuals, and to assess both its sampling distribution under the null and the alternative hypothesis.