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

Simon Behrendt

Quantitative Finance, 2021, vol. 21, issue 11, 1905-1919

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.

Date: 2021
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DOI: 10.1080/14697688.2021.1914855

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