publicado em Annals of Finance (Print,0), v. 6, p. 51-82, 2009

This paper performs a thorough statistical examination of the time-series properties of the daily market volatility index (VIX) from the Chicago Board Options Exchange (CBOE). The motivation lies on the widespread consensus that the VIX is a barometer to the overall market sentiment as to what concerns investors’ risk appetite. Our preliminary analysis suggests that the VIX index displays long-range dependence. This is well line with the strong empirical evidence in the literature supporting long memory in both options-implied and realized variances. We thus resort to both parametric and semiparametric heterogeneous autoregressive (HAR) processes for modeling and forecasting purposes. Our main findings are as follows. First, we confirm the evidence in the literature that there is a strong negative relationship between the VIX index and the S&P 500 index return as well as a positive contemporaneous link with the volume of the S&P 500 index. Second, we find that the VIX index tends to decline as the long-run oil price increases. This is not entirely surprising given the high demand from oil in the last years as well as the recent trend of shorting energy prices in the hedge fund industry. Third, the term spread has no long-run impact in the VIX index despite of the positive contemporaneous link. Fourth, there is some weak evidence that increases in the value of the US dollar tend to move down options-implied market volatility. Finally, we cannot reject the linearity of the above relationships, neither in sample nor out of sample. As for the latter, we actually show that it is pretty hard to beat the pure HAR process because of the very persistent nature of the VIX index. It is not impossible, though. We set out a semiparametric HAR-type model that performs very well across different forecasting horizons by using the above explanatory variables in a quite efficient manner.

Publicado no  Journal of Banking and Finance, 40, 1-10, 2014

This paper shows that bagging can improve the forecast accuracy of time series models for realized volatility. We consider 23 stocks from the Dow Jones Industrial Average over the sample period 1995 to 2005 and employ two different forecast models, a log-linear specification in the spirit of the heterogeneous autoregressive model and a nonlinear specification with logistic transitions. Both forecast model types benefit from bagging, in particular in the 1990s part of our sample. The log-linear specification shows larger improvements than the nonlinear model. Bagging the log-linear model yields the highest forecast accuracy on our sample.

Publicado no Econometric Reviews, 29, 571-593. 

In this paper we propose a flexible model to capture nonlinearities and long-range dependence in time series dynamics. The new model is a multiple regime smooth transition extension of the Heterogenous Autoregressive (HAR) model, which is specifically designed to model the behaviour of the volatility inherent in financial time series. The model is able to describe simultaneously long memory, as well as sign and size asymmetries. A sequence of tests is developed to determine the number of regimes, and an estimation and testing procedure is presented. Monte Carlo simulations evaluate the finite-sample properties of the proposed tests and estimation procedures. We apply the model to several Dow Jones Industrial Average index stocks using transaction level data from the Trades and Quotes database that covers ten years of data. We find strong support for long memory and both sign and size asymmetries. Furthermore, the new model, when combined with the linear HAR model, is viable and flexible for purposes of forecasting volatility

Publicado no Journal of Econometrics, v. 147, 2008