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November 1996 Limit theory for bilinear processes with heavy-tailed noise
Richard A. Davis, Sidney I. Resnick
Ann. Appl. Probab. 6(4): 1191-1210 (November 1996). DOI: 10.1214/aoap/1035463328


We consider a simple stationary bilinear model $X_t = cX_{t-1} Z_{t-1} + Z_t, t = 0, \pm 1, \pm 2, \dots,$ generated by heavy-tailed noise variables ${Z_t}$. A complete analysis of weak limit behavior is given by means of a point process analysis. A striking feature of this analysis is that the sample correlation converges in distribution to a nondegenerate limit. A warning is sounded about trying to detect nonlinearities in heavy-tailed models by means of the sample correlation function.


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Richard A. Davis. Sidney I. Resnick. "Limit theory for bilinear processes with heavy-tailed noise." Ann. Appl. Probab. 6 (4) 1191 - 1210, November 1996.


Published: November 1996
First available in Project Euclid: 24 October 2002

zbMATH: 0879.60053
MathSciNet: MR1422982
Digital Object Identifier: 10.1214/aoap/1035463328

Primary: 60E07 , 60F17 , 60G55 , 60G70 , 62M10

Keywords: bilinear and nonlinear processes , Extreme value theory , Point processes , Poisson processes , sample correlation , Stable laws , Stationary processes

Rights: Copyright © 1996 Institute of Mathematical Statistics


Vol.6 • No. 4 • November 1996
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