Article contents
CONDITIONS FOR THE PROPAGATION OF MEMORY PARAMETER FROM DURATIONS TO COUNTS AND REALIZED VOLATILITY
Published online by Cambridge University Press: 01 June 2009
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
- Copyright
- Copyright © Cambridge University Press 2009
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
REFERENCES
- 22
- Cited by