Prediction power of high-frequency based volatility measures: a model based approach

Abstract

This paper empirically compares the prediction power of popular high frequency measures of daily volatility, paying attention to different volatility models, loss functions and indices. We use data from 18 worldwide indices, covering a period from January 2000 till February 2013, and can show that the well known heterogeneous autoregressive (HAR) and mixed data sampling (MIDAS) models tend to prefer the same volatility measures, whereas a recently developed approach, relying on empirical similarity, shows some contrary results. The simultaneous consideration of volatility measures and models indicates that there is rather a best measure for one specific model, than for volatility prediction in general. This finding clarifies some contradicting results in existing literature on volatility forecasting and helps to derive straightforward recommendations for practitioners. Furthermore the usage of different loss functions for forecasting evaluation enables some interesting insights into the complex interplay between measure, model and loss function.