Nonlinearities and Garch Inadequacy for Modeling Stock Market Returns: Empirical Evidence From Latin America

Abstract

In this paper, we analyze the adequacy of using GARCH as the data-generating process to model conditional volatility of stock market index rates-of-return series. Using the Hinich portmanteau bicorrelation test, we find that a GARCH formulation or any of its variants fail to provide an adequate characterization for the underlying process of the main Latin American stock market indices. Policymakers need to be careful when using autoregressive models for policy analysis and forecast because the inadequacy of GARCH models has strong implications for the pricing of stock index options, portfolio selection, and risk management. In particular, measures of spillover effects and output volatility may not be correct when GARCH-type models are used to evaluate economic policy.

Nonlinearity in financial series: transitory or permanent?

“…Many studies have reported nonlinear behavior in different financial assets series all around the world, such as stocks, currencies, bonds and commodities, and with several time frames. For example, in North America (Hinich and Patterson, 1985;Scheinkman and LeBaron, 1989;Hsieh, 1991;Brock et al, 1996); in European markets (Abhyankar et al, 1995;Opong et al, 1999;Kosfeld and Robé, 2001;Todea and Zoicas-Ienciu, 2008); in Asian markets (Ammermann and Patterson, 2003;Lim and Hinich, 2005); and in Latin American markets (Bonilla et al, 2006;Bonilla et al, 2008;Bonilla et al, 2010;Bonilla et al, 2011;Espinosa et al, 2013).…”

“…In any case, the results are basically the same if we double or triple the window length (Brooks, Hinich and Molyneux, 2000). Brooks and Hinich (1998) suggest 35 observations as the best size of the window, while other articles employ 25 observations (Bonilla et al, 2006;Bonilla et al, 2010), 35 observations (Todea and Zoicas-Ienciu, 2008;Bonilla et al, 2008) and 50 observations (Lim, Brooks and Hinich, 2008), among others. The authors found that as the size of the window increases, the number of nonlinear windows also increases contradicting what is stated by Brooks, Hinich and Molyneux (2000), confirming a "window size effect" in financial assets series.…”

Testing for the Efficient Market Hypothesis in Stock Prices: International Evidence From Nonlinear Heterogeneous Panels

“…To this end, many research studies find that stock prices are consistent with a nonlinear datagenerating process [Boswijk et al (2007); Qian et al (2008); Lee et al (2010)]. The existence of nonlinearities in macroeconomic variables has also been addressed in the literature [Altug et al (1999); Bidarkota (2006); Panagiotidis and Pelloni (2007); Calza and Zaghini (2009); Bonilla et al (2011); Lee and Chiu (2012); Lee (2013)]. Until now, fewer studies in the literature have taken nonlinear heterogeneous unit root approaches in a panel framework to determine whether or not real stock prices are nonstationary or nonlinear.…”