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CONDITIONS FOR THE PROPAGATION OF MEMORY PARAMETER FROM DURATIONS TO COUNTS AND REALIZED VOLATILITY

Published online by Cambridge University Press:  01 June 2009

Rohit Deo ,
Clifford M. Hurvich ,
Philippe Soulier  and
Yi Wang
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Abstract

We establish sufficient conditions on durations that are stationary with finite variance and memory parameter to ensure that the corresponding counting process N(t) satisfies Var N(t) ~ Ct2d+1 (C > 0) as t → ∞, with the same memory parameter that was assumed for the durations. Thus, these conditions ensure that the memory parameter in durations propagates to the same memory parameter in the counts. We then show that any autoregressive conditional duration ACD(1,1) model with a sufficient number of finite moments yields short memory in counts, whereas any long memory stochastic duration model with d > 0 and all finite moments yields long memory in counts, with the same d. Finally, we provide some results about the propagation of long memory to the empirically relevant case of realized variance estimates affected by market microstructure noise contamination.

Type
Research Article
Information
Econometric Theory , Volume 25 , Issue 3 , June 2009 , pp. 764 - 792
Copyright
Copyright © Cambridge University Press 2009

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Footnotes

The authors thank the referees for invaluable suggestions that led to more elegant and shorter proofs and a better economic interpretation of the results. They also thank Jushan Bai, Xiaohong Chen, and Raymond Thomas for helpful comments and suggestions. Part of this research was conducted while Deo was at the University of Texas–Austin.

References

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