We propose a new family of easy-to-implement realized volatility based forecasting models.The models exploit the asymptotic theory for high-frequency realized volatility estimation to improve the accuracy of the forecasts. By allowing the parameters of the models to vary explicitly with the (estimated) degree of measurement error, the models exhibit stronger persistence, and in turn generate more responsive forecasts, when the measurement error is relatively low. Implementing the new class of models for the S&P500 equity index and the individual constituents of the Dow Jones Industrial Average, we document significant improvements in the accuracy of the resulting forecasts compared to the forecasts from some of the most popular existing models that implicitly ignore the temporal variation in the magnitude of the realized volatility measurement errors.

We introduce tests for multi-horizon superior predictive ability (SPA). Rather than comparing forecasts of different models at multiple horizons individually, we propose to jointly consider all horizons of a forecast path. We define the concepts of uniform and average SPA. The former entails superior performance at each individual horizon, while the latter allows inferior performance at some horizons to be compensated by others. The article illustrates how the tests lead to more coherent conclusions, and how they are better able to differentiate between models than the single-horizon tests. We provide an extension of the previously introduced model confidence set to allow for multi-horizon comparison of more than two models. Simulations demonstrate appropriate size and high power. An illustration of the tests on a large set of macroeconomic variables demonstrates the empirical benefits of multi-horizon comparison.

We propose a new framework for modeling and forecasting common financial risks based on (un)reliable realized covariance measures constructed from high-frequency intraday data. Our new approach explicitly incorporates the effect of measurement errors and time-varying attenuation biases into the covariance forecasts, by allowing the ex-ante predictions to respond more (less) aggressively to changes in the ex-post realized covariance measures when they are more (less) reliable. Applying the new procedures in the construction of minimum variance and minimum tracking error portfolios results in reduced turnover and statistically superior positions compared to existing procedures. Translating these statistical improvements into economic gains, we find that under empirically realistic assumptions a risk-averse investor would be willing to pay up to 170 basis points per year to shift to using the new class of forecasting models.

We propose a decomposition of the realized covariance matrix into components based on the signs of the underlying high‐frequency returns, and we derive the asymptotic properties of the resulting realized semicovariance measures as the sampling interval goes to zero. The first‐order asymptotic results highlight how the same‐sign and mixed‐sign components load differently on economic information related to stochastic correlation and jumps. The second‐order asymptotic results reveal the structure underlying the same‐sign semicovariances, as manifested in the form of co‐drifting and dynamic “leverage” effects. In line with this anatomy, we use data on a large cross‐section of individual stocks to empirically document distinct dynamic dependencies in the different realized semicovariance components. We show that the accuracy of portfolio return variance forecasts may be significantly improved by exploiting the information in realized semicovariances.

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