| dc.description.abstract |
We provide a general framework for integration of high-frequency intraday data into
the measurement, modeling, and forecasting of daily and lower frequency return volatilities
and return distributions. Most procedures for modeling and forecasting financial asset
return volatilities, correlations, and distributions rely on potentially restrictive
and complicated parametric multivariate ARCH or stochastic volatility models. Use
of realized volatility constructed from high-frequency intraday returns, in contrast,
permits the use of traditional time-series methods for modeling and forecasting. Building
on the theory of continuous-time arbitrage-free price processes and the theory of
quadratic variation, we develop formal links between realized volatility and the conditional
covariance matrix. Next, using continuously recorded observations for the Deutschemark
/ Dollar and Yen / Dollar spot exchange rates covering more than a decade, we find
that forecasts from a simple long-memory Gaussian vector autoregression for the logarithmic
daily realized volatilities perform admirably compared to a variety of popular daily
ARCH and more complicated high-frequency models. Moreover, the vector autoregressive
volatility forecast, coupled with a parametric lognormal-normal mixture distribution
implied by the theoretically and empirically grounded assumption of normally distributed
standardized returns, produces well-calibrated density forecasts of future returns,
and correspondingly accurate quantile predictions. Our results hold promise for practical
modeling and forecasting of the large covariance matrices relevant in asset pricing,
asset allocation and financial risk management applications.
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