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Article Dans Une Revue Econometric Theory Année : 2009

Propagation of Memory Parameter from Durations to Counts

Rohit Deo
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Philippe Soulier
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Yi Wang
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Résumé

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 $\textmd{Var} \, N(t) \sim C t^{2d+1}$ ($C>0$) 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 in durations propagates to the same memory parameter in counts and therefore in realized volatility. We then show that any utoregressive 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 $d$.
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Dates et versions

hal-00018224 , version 1 (30-01-2006)

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Rohit Deo, Clifford M. Hurvich, Philippe Soulier, Yi Wang. Propagation of Memory Parameter from Durations to Counts. Econometric Theory, 2009, 25 (3), pp.764-792. ⟨10.1017/S0266466608090294⟩. ⟨hal-00018224⟩
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