Skip navigation

Propagation of Memory Parameter from Durations to Counts

Authors: Deo, Rohit
Hurvich, Clifford M.
Soulier, Philippe
Wang, Yi
Keywords: Long Memory Stochastic Duration;Autoregressive Conditional Duration;Rosenthal type Inequality
Issue Date: 8-Nov-2005
Publisher: Stern School of Business, New York University
Series/Report no.: SOR-2005-5
Abstract: We establish sufficient conditions on durations that are stationary with finite variance and memory parameter d 2 [0; 1=2) to ensure that the corresponding counting process N(t) satisfies VarN(t) » Ct2d+1 (C > 0) as t ! 1, with the same memory parameter d 2 [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.
Appears in Collections:IOMS: Statistics Working Papers

Files in This Item:
File Description SizeFormat 
05-05.pdf268.3 kBAdobe PDFView/Open

Items in FDA are protected by copyright, with all rights reserved, unless otherwise indicated.