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Modeling and Forecasting Realized Volatility (2002)
| Citations: | 548 - 50 self |
BibTeX
@MISC{Andersen02modelingand,
author = {Torben G. Andersen and Tim Bollerslev and Francis X. Diebold and Paul Labys},
title = {Modeling and Forecasting Realized Volatility},
year = {2002}
}
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Abstract
this paper is built. First, although raw returns are clearly leptokurtic, returns standardized by realized volatilities are approximately Gaussian. Second, although the distributions of realized volatilities are clearly right-skewed, the distributions of the logarithms of realized volatilities are approximately Gaussian. Third, the long-run dynamics of realized logarithmic volatilities are well approximated by a fractionally-integrated long-memory process. Motivated by the three ABDL empirical regularities, we proceed to estimate and evaluate a multivariate model for the logarithmic realized volatilities: a fractionally-integrated Gaussian vector autoregression (VAR) . Importantly, our approach explicitly permits measurement errors in the realized volatilities. Comparing the resulting volatility forecasts to those obtained from currently popular daily volatility models and more complicated high-frequency models, we find that our simple Gaussian VAR forecasts generally produce superior forecasts. Furthermore, we show that, given the theoretically motivated and empirically plausible assumption of normally distributed returns conditional on the realized volatilities, the resulting lognormal-normal mixture forecast distribution provides conditionally well-calibrated density forecasts of returns, from which we obtain accurate estimates of conditional return quantiles. In the remainder of this paper, we proceed as follows. We begin in section 2 by formally developing the relevant quadratic variation theory within a standard frictionless arbitrage-free multivariate pricing environment. In section 3 we discuss the practical construction of realized volatilities from high-frequency foreign exchange returns. Next, in section 4 we summarize the salient distributional features of r...
Keyphrases
realized volatility forecasting realized volatility complicated high-frequency model superior forecast popular daily volatility model accurate estimate fractionally-integrated long-memory process plausible assumption practical construction well-calibrated density forecast high-frequency foreign exchange return logarithmic realized volatility fractionally-integrated gaussian vector autoregression simple gaussian var forecast conditional return quantiles lognormal-normal mixture forecast distribution raw return multivariate model salient distributional feature logarithmic volatility long-run dynamic volatility forecast measurement error relevant quadratic variation theory abdl empirical regularity
