Volatility Forecasting via MIDAS, HAR and their Combination: An Empirical Comparative Study for IBOVESPA

Abstract

In this paper we compare several multi‐period volatility forecasting models, specifically from MIDAS and HAR families. We perform our comparisons in terms of out‐of‐sample volatility forecasting accuracy. We also consider combinations of the models' forecasts. Using intra‐daily returns of the BOVESPA index, we calculate volatility measures such as realized variance, realized power variation and realized bipower variation to be used as regressors in both models. Further, we use a nonparametric procedure for separately measuring the continuous sample path variation and the discontinuous jump part of the quadratic variation process. Thus MIDAS and HAR specifications with the continuous sample path and jump variability measures as separate regressors are estimated. Our results in terms of mean squared error suggest that regressors involving volatility measures which are robust to jumps (i.e. realized bipower variation and realized power variation) are better at forecasting future volatility. However, we find that, in general, the forecasts based on these regressors are not statistically different from those based on realized variance (the benchmark regressor). Moreover, we find that, in general, the relative forecasting performances of the three approaches (i.e. MIDAS, HAR and forecast combinations) are statistically equivalent. Copyright © 2014 John Wiley & Sons, Ltd.

Macroeconomic forecasting with mixed data sampling frequencies: Evidence from a small open economy

“…In other words, the reduction in squared errors for the end-of-period MIDAS model in comparison with TA-D and DR-M is not statistically significant at the 5% level. In contrast, Santos and Ziegelmann (2014) compare several multi-period volatility forecasting models, specifically from MIDAS and HAR families, using intra-daily returns of the BOVESPA index, and find that, in general, the relative forecasting performances of MIDAS, HAR, and forecast combinations are statistically equivalent. It is also considered better than the MIDAS model if a 10% significance level (−1.28) is adopted.…”

“…Aastveit, Foroni, and Ravazzolo (2017) use a parametric block wild bootstrap approach to evaluate density forecasts for quarterly US real output growth for various types of mixed-data sampling (MIDAS) regressions, and find that the new approach produces predictive densities for US real output growth that are well calibrated and that the relative accuracy improves for the various MIDAS specifications as more information becomes available. In contrast, Santos and Ziegelmann (2014) compare several multi-period volatility forecasting models, specifically from MIDAS and HAR families, using intra-daily returns of the BOVESPA index, and find that, in general, the relative forecasting performances of MIDAS, HAR, and forecast combinations are statistically equivalent.…”

The role of jumps in the agricultural futures market on forecasting stock market volatility: New evidence

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“…It is worth noting that volatility is a crucial input of derivative pricing, hedging, portfolio selection, and risk management (see, e.g., Andersen, Bollerslev, & Diebold, 2007;Bollerslev, Hood, Huss, & Pedersen, 2017). Therefore, a large body of literature describes and forecasts the RV of stock markets (see, e.g., Choi & Shin, 2018;Corsi, 2009;Engle & Gallo, 2006;Ghysels, Santa-Clara, & Valkanov, 2006;Hansen, Huang, & Shek, 2012;Qu & Ji, 2016;Santos & Ziegelmann, 2014;Wang, Pan, & Wu, 2017). Although there are a large number of studies on volatility forecasting, forecasting volatility accurately is still a daunting task.…”

Modeling Autoregressive Processes with Moving-Quantiles-Implied Nonlinearity

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