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Abstract: We demonstrate that the parameters controlling skewness and kurtosis in popular equity return models estimated at daily frequency can be obtained almost as precisely as if volatility is observable by simply incorporating the strong information content of realized volatility measures extracted from high-frequency data. For this purpose, we introduce asymptotically exact volatility measurement equations in state space form and propose a Bayesian estimation approach. Our highly efficient estimates lead in turn to substantial gains for forecasting various risk measures at horizons ranging from a few days to a few months ahead when taking also into account parameter uncertainty. As a practical rule of thumb, we find that two years of high frequency data often suffice to obtain the same level of precision as twenty years of daily data, thereby making our approach particularly useful in finance applications where only short data samples are available or economically meaningful to use. Moreover, we find that compared to model inference without high-frequency data, our approach largely eliminates underestimation of risk during bad times or overestimation of risk during good times. We assess the attainable improvements in VaR forecast accuracy on simulated data and provide an empirical illustration on stock returns during the financial crisis of 2007-2008.

Keywords: Equity return models, parameter uncertainty, bayesian estimation, high-frequency data, jump-robust volatility measures, value at risk, forecasting

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