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Propagation of Memory Parameter from Durations to Counts

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Author Info

  • Rohit Deo

    (New York University)

  • Clifford Hurvich

    (New York University)

  • Philippe Soulier

    (University of Paris X)

  • Yi Wang

    (New York University)

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 $\textmd{Var} \, N(t) \sim C t^{2d+1}$ ($C>0$) 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 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 present a result implying that the only way for a series of counts aggregated over a long time period to have nontrivial autocorrelation is for the short-term counts to have long memory. In other words, aggregation ultimately destroys all autocorrelation in counts, if and only if the counts have short memory.

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File URL: http://128.118.178.162/eps/em/papers/0511/0511010.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Econometrics with number 0511010.

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Length: 27 pages
Date of creation: 08 Nov 2005
Date of revision:
Handle: RePEc:wpa:wuwpem:0511010

Note: Type of Document - pdf; pages: 27
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Web page: http://128.118.178.162

Related research

Keywords: Long Memory Stochastic Duration; Autoregressive Conditional Duration; Rosenthal-type Inequality.;

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References

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  1. Clifford Hurvich & Eric Moulines & Philippe Soulier, 2004. "Estimating Long Memory in Volatility," Econometrics 0412006, EconWPA.
  2. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
  3. Peter M. Robinson & M. Henry, 1999. "Long and short memory conditional heteroskedasticity in estimating the memory parameter of levels," LSE Research Online Documents on Economics 304, London School of Economics and Political Science, LSE Library.
  4. Comte, F. & Renault, E., 1996. "Long Memory in Continuous Time Stochastic Volatility Models," Papers 96.406, Toulouse - GREMAQ.
  5. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-059, New York University, Leonard N. Stern School of Business-.
  6. Deo, Rohit S. & Hurvich, Clifford M., 2001. "On The Log Periodogram Regression Estimator Of The Memory Parameter In Long Memory Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 17(04), pages 686-710, August.
  7. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July.
  8. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
  9. Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, vol. 47(1), pages 67-84, January.
  10. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, February.
  11. Deo, Rohit & Hurvich, Clifford & Lu, Yi, 2006. "Forecasting realized volatility using a long-memory stochastic volatility model: estimation, prediction and seasonal adjustment," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 29-58.
  12. Rohit Deo & Mengchen Hsieh & Clifford Hurvich, 2005. "Tracing the Source of Long Memory in Volatility," Econometrics 0501005, EconWPA.
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Cited by:
  1. repec:hal:wpaper:hal-00583372 is not listed on IDEAS
  2. Hurvich, Clifford & Wang, Yi, 2009. "A Pure-Jump Transaction-Level Price Model Yielding Cointegration, Leverage, and Nonsynchronous Trading Effects," MPRA Paper 12575, University Library of Munich, Germany.
  3. Rohit Deo & Meng-Chen Hsieh & Clifford M. Hurvich & Philippe Soulier, 2007. "Long Memory in Nonlinear Processes," Papers 0706.1836, arXiv.org.

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