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http://hdl.handle.net/2451/28092
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| Title: | Conditions for the Propagation of Memory Parameter from Durations to
Counts and Realized Volatility |
| Authors: | Deo, Rohit
Hurvich, Clifford M.
Soulier, Philippe
Wang, Yi |
| Keywords: | Long Memory Stochastic Duration
Autoregressive Conditional Duration
Rosenthal type Inequality |
| Issue Date: | 2-Jun-2009 |
| Series/Report no.: | CeDER-09-03 |
| Abstract: | We establish sufficient conditions on durations that are stationary with
finite variance and memory parameter $d \in [0,1/2)$ to ensure that the
corresponding counting process $N(t)$ satisfies $Var N(t) \sim C
t^{2d+1}$ ($C>0$) as $t \rightarrow \infty$, with the same memory
parameter $d \in [0,1/2)$ 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, while 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. |
| URI: | http://hdl.handle.net/2451/28092 |
| Appears in Collections: | CeDER Working Papers
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