This paper presents a framework for integrating high-frequency intraday data into the measurement, modeling, and forecasting of daily and lower frequency volatility and return distributions. The authors argue that traditional parametric multivariate ARCH or stochastic volatility models often perform poorly at intraday frequencies. Instead, they propose using realized volatility, constructed from high-frequency intraday returns, which allows for the use of traditional time series procedures. The paper develops the theoretical links between the conditional covariance matrix and realized volatility, and uses continuously recorded observations of the Deutschemark/Dollar and Yen/Dollar spot exchange rates over more than a decade to evaluate the performance of a simple long-memory Gaussian vector autoregression for logarithmic daily realized volatilities. The results show that these forecasts perform admirably compared to popular daily ARCH and related models. The authors also show that the vector autoregressive volatility forecast, combined with a parametric lognormal-normal mixture distribution, gives rise to well-calibrated density forecasts of future returns and accurate quantile estimates. The paper concludes that their results hold promise for practical modeling and forecasting of large covariance matrices relevant in asset pricing, asset allocation, and financial risk management.This paper presents a framework for integrating high-frequency intraday data into the measurement, modeling, and forecasting of daily and lower frequency volatility and return distributions. The authors argue that traditional parametric multivariate ARCH or stochastic volatility models often perform poorly at intraday frequencies. Instead, they propose using realized volatility, constructed from high-frequency intraday returns, which allows for the use of traditional time series procedures. The paper develops the theoretical links between the conditional covariance matrix and realized volatility, and uses continuously recorded observations of the Deutschemark/Dollar and Yen/Dollar spot exchange rates over more than a decade to evaluate the performance of a simple long-memory Gaussian vector autoregression for logarithmic daily realized volatilities. The results show that these forecasts perform admirably compared to popular daily ARCH and related models. The authors also show that the vector autoregressive volatility forecast, combined with a parametric lognormal-normal mixture distribution, gives rise to well-calibrated density forecasts of future returns and accurate quantile estimates. The paper concludes that their results hold promise for practical modeling and forecasting of large covariance matrices relevant in asset pricing, asset allocation, and financial risk management.