The HAR model dominates current volatility forecasting. This model implies a restricted lag approach, with three parameters accounting for an AR(22) structure. This paper uses the Lasso method, which selects a parsimonious lag structure, while allowing both a flexible lag structure and lags greater than 22. In-sample results suggest that while significance is largely found among the first 22 lags, consistent with the HAR model, there is evidence that longer lags contain information, as Lasso models provide an improved fit. Out-of-sample forecasts for daily, weekly and monthly volatility, evaluated using MSE, QLIKE, MCS and VaR measures, suggest that the ordered Lasso model provides the preferred forecasts using an AR(1 0 0) at the daily level and an AR(22) for the weekly and monthly horizons. The results support the view that a more flexible lag structure is preferred over the HAR approach.

HAR 模型主导了当前的波动率预测。该模型暗示了一种受限滞后方法，其中三个参数解释了 AR(22) 结构。本文使用 Lasso 方法，该方法选择简约的滞后结构，同时允许灵活的滞后结构和大于 22 的滞后。样本内结果表明，虽然在前 22 个滞后中主要发现显着性，与 HAR 模型一致，有证据表明更长的滞后包含信息，因为 Lasso 模型提供了更好的拟合。使用 MSE、QLIKE、MCS 和 VaR 度量评估的每日、每周和每月波动率的样本外预测表明，有序套索模型使用 AR(1  0 0) 在每日级别和 AR(22) 为每周和每月的范围。结果支持更灵活的滞后结构优于 HAR 方法的观点。