Statistical Properties of the Roll Serial Covariance Bid/Ask Spread Estimator
推导了Roll买卖价差模型中序列协方差和方差估计量的小样本精确矩，发现噪声导致序列协方差估计常为正，且Roll价差估计量因詹森不等式存在严重偏误。
ABSTRACT Exact small sample population moments of the standard serial covariance and variance estimators are derived under the assumptions of the Roll bid/ask spread model. Noise explains why serial covariance estimates are often positive in annual samples of daily and weekly returns. Small sample estimator bias partially explains why weekly estimates are more negative than daily estimates. Noise causes the Roll spread estimator to be severely biased by Jensen's inequality. The French‐Roll adjusted variance estimator is unbiased but noisy. Empirical tests confirm the major implications.