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.

自回归 (AR) 模型，例如异构自回归 (HAR) 模型，捕捉已实现波动率中固有的线性足迹。我们利用 HAR 模型是受约束的 AR 模型这一事实，并将估计自回归波动率动态中的结构断裂问题作为模型选择问题。两步套索型程序用于一致地估计结构断裂的未知数量和时间。从经验上看，我们发现中断的数量受到应用于八个股票市场指数的已实现波动率系列的 Box-Cox 变换的严重影响：例如，虽然我们在原始序列中发现了中断，但在对数实现波动率中没有发现中断，应用研究中经常使用的一种衡量标准，适用于各种滞后长度。这些 Box-Cox 变换导致具有不同自回归动力学的不同波动过程，并影响结构断裂的估计。重要的是，对数转换大大减少了可能被选为结构性突破的价格上涨次数。