Distinguishing between True and Spurious Long Memory in the Volatility of Stock Market Returns in Latin America

In this study, we investigate the long term dependence or long memory present in the volatility of the stock market returns of Peru, Brazil, Mexico, Chile, Argentina, and the S&P500. We start analyzing the form of the autocorrelation function (ACF) and the estimated spectral density. Moreover, volatility is modeled by way of FIGARCH processes that contribute additional indications of this behavior. Following a testing approach, the W statistics of Qu (2011), Wc, and Zt due to Shimotsu (2006), and the statistics td(1=2; 1; 4=5; 1), and mean td of Perron and Qu (2010) are used to verify for long memory. Also we show evidence about the behavior of the long memory estimator db for di§erent sample sizes included in the estimation procedure. The evidence reported graphically and through the statistics suggest that the generating process of the volatility series is spurious memory, except for Chile, whose evidence of spurious memory is weak. Moreover, the graphics contain important information on the spurious memory behavior. The results of this study suggest that in reality, the long memory that is usually found in empirical studies would rather be associated with spurious memory, which could be due to the presence of structural breaks. JEL Classification-JEL: C12, C14, C22, G12.