Why Aggregate Long Memory Time Series?
证明，在满足一定条件时，对长记忆时间序列进行时间聚合以改进估计意义不大，因为通过选择合适带宽可从原始序列获得几乎相同的估计，但该结论不适用于波动率聚合或虚假长记忆检验。
This article shows that, for large samples, temporally aggregating a true long memory time series (in order to get an improved estimator) may make little or no sense, as the practitioner can get virtually the same estimates as those from the aggregated series by choosing the appropriate bandwidths on the original one, provided some fairly general conditions apply. Besides, the practitioner has a wider choice of bandwidths than she has of aggregating levels. However, these results apply only to two specific and commonly used estimators, and do not apply to the aggregation procedure undertaken to compute the realized volatility. Also, aggregating a time series in order to test true versus spurious long memory (as in Ohanissian et al., 2008 Ohanissian , A. , Russell , J. , Tsay , R. ( 2008 ). True or spurious long memory? A new test. Forthcoming . Journal of Business and Economic Statistics .[Taylor & Francis Online] , [Google Scholar]) is a relevant issue, particularly regarding stochastic and/or realized volatility, as many nonlinear processes display spurious long memory where the above result does not apply.