The highfrequency package for the R programming language provides functionality for pre-processing financial high-frequency data, analyzing intraday stock returns, and forecasting stock market volatility. For academics and practitioners alike, it provides a tool chain required to work with such datasets and to conduct statistical analyses dedicated to spot volatility, jumps, realized measures, and many more. We showcase our implemented routines and models on raw high-frequency data from large US-American stock exchanges.
Economic variables are often reported on different scales or with measurement error, e.g. in macroeconomic and financial applications. We examine the sensitivity of scoring rules for distribution forecasts in two dimensions: linear rescaling of the data and the influence of noise on the forecast evaluation outcome. First, we show that all commonly used scoring rules for distribution forecasts are robust to rescaling the data. Second, it is revealed that the forecast ranking based on the continuous ranked probability score is less sensitive to measurement error than the log score. Our theoretical results are complemented by a simulation study based on forecasting quarterly GDP growth and an empirical application forecasting realized variances of 28 DJIA constituents. In line with its proven gross-error-insensitivity, the ranking of the continuous ranked probability score is the most consistent between evaluations based on the true outcome and the observations with measurement error.
We examine the properties and forecast performance of multiplicative volatility specifications that belong to the class of GARCH-MIDAS models suggested in Engle et al.~(2013). In those models volatility is decomposed into a short-term GARCH component and a long-term component that is driven by an explanatory variable. We derive the kurtosis of returns, the autocorrelation function of squared returns, and the $R^2$ of a Mincer-Zarnowitz regression and evaluate these models in a Monte-Carlo simulation. For S&P 500 data, we compare the forecast performance of GARCH-MIDAS models with a wide range of competitor models such as HAR, Realized GARCH, HEAVY and Markov-Switching GARCH. Our results show that the GARCH-MIDAS based on housing starts as an explanatory variable significantly outperforms all competitor models at forecast horizons of two and three months ahead.