NONLINEAR DYNAMICS IN BRAZILIAN GROSS DOMESTIC PRODUCT BETWEEN 1947 AND 2012

Abstract

In this paper, we look for nonlinear dynamics in Brazilian gross domestic product (GDP) cycles between 1947 and 2012, by using BDS statistics to analyze autoregressive and Markovian models. Our results showed that AR(p) regressions could not completely describe the properties of the cyclic series, as they did not yield independent and identically distributed (iid) residuals. However, after estimating heteroscedastic Markovian models to the data, the null of iid was not rejected. As indicated by two-state Markov chains, Brazilian economy switched between phases of high and low volatility, with the latter more likely to occur after 1995. Furthermore, we estimated a three-state Markov chain, which pointed out the following regimes (annual growth rates inside brackets): recessions (-5.8%), with short duration and high volatility; accelerated growth (7.9%), frequent from 1947 to 1980, with long duration and high volatility; and, balanced growth (4.3%), with moderate growth rate and lower variance, prevalent since 1995. Thus, we conclude that the Brazilian GDP cycles are strongly nonlinear, presenting phase asymmetries in duration and amplitude, besides heteroscedasticity.