Modelos preditivos da variância de mercados financeiros e análise de agrupamento das volatilidades

Abstract

The volatility models or autoregressive econometric models of conditional heteroscedasticity (ARCH) that popped up from 1982, onwards have given a new way of understanding the much studied behavior of financial markets through the premise of that the return of an asset is not serially correlated and that variance conditional is a function of the returns passed squared. This paper proposes the construction of predictive models for the volatility of the returns of 16 representative financial indices. These are pure models of the ARCH family, as well as of composite models of mean and variances conditional ARMA + ARCH. The general methodology used is that of Box-Jenkins and, specifically, the proposals in the seminal articles in the construction of ARCH and GARCH models, articles on which the theoretical basis of this work is based. By means of the adjusted volatility models and the grouping analysis, we can characterize the behavior of the logarithmic returns of daily prices of financial indexes, each with 3861 observations in the period from March 11, 1997 to 31, 2016. The indices financial models modeled using pure models of conditional variance are: Brazil (BVSP), U.S (IXIC), U.S (DJI), Canada (GSPTSE), China (HSI), China (SSE), France (FCHI), Switzerland (SSMI), Germany (GDAX) e Austria (ATX), being modeled by GARCH (1,1), except China (HSI), which is GARCH (1,2). The financial indices modeled using conditional variance and averaged models are: Mexico (MXX), U.S (GSPC), Australia (AORD), Malaysia (KLSE), Japan (N225) and Belgium (BFX), being modeled by the ARMA(1,1)+EGARCH(2,3), ARMA(1,1)+EGARCH(2,2), ARMA(4,3)+EGARCH(2,2), ARMA(2,1)+EGARCH(4,4), ARMA(4,4)+EGARCH(2,2) and AR(1)+EGARCH(1,1), respectively. All of these adjusted models are assumed to be derived from a Student distribution, as they proved to be of better fit than models under the assumption that innovations are from a Gaussian distribution. In the clustering analysis, the "Euclidian", "Canberra" and "Manhattan" distance measures were combined with the "k-mean" grouping method. The first combination, applied to the observed returns, grouped the indices in relation to the geographical location. The second, applied the predictions of returns and variances, grouped the indices in relation to the model of adjusted variance and the proximity of the variance that they present, respectively. The last combination, applied to volatility forecasts, grouped the indices in relation to the proximity of the risk they present. As a measure for the improvement of this model, it is suggested the test of other econometric models, as well as other distribution functions for the innovations.