Gassiat, Elisabeth Semi-parametric estimation of a stationary, non-necessary causal AR(P) process with infinite variance. (English) Zbl 0679.62068 J. Multivariate Anal. 32, No. 1, 161-170 (1990). Summary: We study the estimation problem of the parameter of a stationary AR(p) process with infinite variance when there is no assumption on the causality of the model. We propose consistent estimates. In the causal case, we obtain a speed of convergence. Cited in 1 Document MSC: 62M09 Non-Markovian processes: estimation 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 60E07 Infinitely divisible distributions; stable distributions Keywords:autoregressive model of order p; non-causal model; stable process; stationary AR(p) process; infinite variance; causality; consistent estimates; speed of convergence PDF BibTeX XML Cite \textit{E. Gassiat}, J. Multivariate Anal. 32, No. 1, 161--170 (1990; Zbl 0679.62068) Full Text: DOI References: [1] Beneviste, A; Goursat, M; Ruget, G, Robust identification of a non-minimum phase system: blind adjustment of a linear equalizer in data communications, IEEE trans. automat. control, AC-25, 3, (1980) [2] Billinsley, P, () [3] Chaterjii, S, Notes on an Lp convergence theorem, Ann. math. statist., 40, No. 3, 1068-1070, (1969) · Zbl 0176.48101 [4] \scGassiat, E. (in press). Estimation semi-paramétrique d’un processus autorégressif stationnaire non nécessairement causal. Ann. Inst. H. Poincaré Probab. Statist. [5] Hannan, E.J; Kanter, M, Autoregressive proceses with infinite variance, J. appl. probab., 14, 411-415, (1977) · Zbl 0366.60033 [6] Kanter, M, On quotients of moving average processes with infinite Mean, (), 281-287 · Zbl 0366.60032 [7] Miller, H.D, A note on sums of independent random variables with infinite first moment, Ann. math. statist., 38, 751-758, (1967) · Zbl 0153.19601 [8] Rosenblatt, M; Lii, K.S, Deconvolution and estimation of transfer/function phase and coefficients for non-Gaussian linear processes, Ann. statist., 10, No. 4, 1195-1208, (1982) · Zbl 0512.62090 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.