Assuming N available calendar days, each with M intraday returns, the realized volatility literature suggests creating N end-of-day estimators by summing the M squared returns from each particular date. Instead of this “Calendar” [realized variance (RV)] approach, we propose a “Rolling” [rolling RV (RRV)] approach that simply sums trailing M returns at each timestamp, regardless if all M returns belong to the same calendar date. When estimating an out-of-sample 1-day realized volatility model, the former results in an ordinary least squares (OLS) regression with N−1 datapoints while the latter incorporates M(N−2)+1 datapoints, effectively lowering the standard errors, and potentially resulting in more accurate forecasts. We compare both models for the S&P 500 and 26 Dow Jones Industrial Average stocks; our results generally suggest that the Rolling approach yields both statistically and economically significant superior out-of-sample performance over the traditional Calendar approach.

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增加已实现波动率预测的信息内容

假设 N 个可用日历日，每个日历日有 M 个日内收益，已实现波动率文献建议通过将每个特定日期的 M 平方收益相加来创建 N 个日终估计量。代替这种“日历”[已实现方差 (RV)] 方法，我们提出了一种“滚动”[滚动 RV (RRV)] 方法，该方法简单地将每个时间戳的尾随 M 回报相加，而不管所有 M 回报是否属于同一日历日期. 在估计样本外的 1 天已实现波动率模型时，前者导致具有 N−1 个数据点的普通最小二乘 (OLS) 回归，而后者包含 M(N−2)+1 个数据点，有效降低了标准错误，并可能导致更准确的预测。我们比较了标准普尔 500 指数和 26 只道琼斯工业平均指数股票的两种模型；