Forecasting realized covariances using HAR-type models

TL;DR

This paper introduces novel HAR-type models for forecasting multivariate realized covariance matrices, demonstrating that modeling log variances with bias correction improves forecast accuracy over existing methods.

Contribution

It proposes new methods using univariate log variance models with bias correction and analyzes modeling choices within HAR frameworks for covariance forecasting.

Findings

Modeling logs of marginal volatilities outperforms direct volatility modeling.

Bias correction in log variance models enhances forecast accuracy.

Time-varying parameter models perform comparably in forecasting performance.

Abstract

We investigate methods for forecasting multivariate realized covariances matrices applied to a set of 30 assets that were included in the DJ30 index at some point, including two novel methods that use existing (univariate) log of realized variance models that account for attenuation bias and time-varying parameters. We consider the implications of some modeling choices within the class of heterogeneous autoregressive models. The following are our key findings. First, modeling the logs of the marginal volatilities is strongly preferred over direct modeling of marginal volatility. Thus, our proposed model that accounts for attenuation bias (for the log-response) provides superior one-step-ahead forecasts over existing multivariate realized covariance approaches. Second, accounting for measurement errors in marginal realized variances generally improves multivariate forecasting performance, but to a lesser degree than previously found in the literature. Third, time-varying parameter models based on state-space models perform almost equally well. Fourth, statistical and economic criteria for comparing the forecasting performance lead to some differences in the models' rankings, which can partially be explained by the turbulent post-pandemic data in our out-of-sample validation dataset using sub-sample analyses.