Structural breaks in Box-Cox transforms of realized volatility: a model selection perspective

Abstract

Autoregressive (AR) models such as the heterogeneous autoregressive (HAR) model capture the linear footprint inherent in realized volatility. We draw upon the fact that the HAR model is a constrained AR model and cast the problem of estimating structural breaks in the autoregressive volatility dynamics as a model selection problem. A two-step Lasso-type procedure is used to consistently estimate the unknown number and timing of structural breaks. Empirically, we find the number of breaks to be heavily influenced by Box-Cox transformations applied to realized volatility series of eight stock market indices: For example, while we find breaks in the original series, no breaks are found in log-realized volatility, a measure often used in applied research, across a wide range of lag lengths. These Box-Cox transformations lead to different volatility processes with distinct autoregressive dynamics and affect the estimation of structural breaks. Importantly, the log-transformation considerably reduces the number of price jumps which might otherwise be selected as structural breaks.