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Maximum Likelihood Estimation for a First‐Order Bifurcating Autoregressive Process with Exponential Errors
Author(s) -
Zhou J.,
Basawa I. V.
Publication year - 2005
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2005.00440.x
Subject(s) - autoregressive model , mathematics , star model , setar , estimator , autoregressive integrated moving average , exponential function , normalization (sociology) , nonlinear autoregressive exogenous model , maximum likelihood , estimation theory , statistics , mathematical analysis , time series , sociology , anthropology
. Exact and asymptotic distributions of the maximum likelihood estimator of the autoregressive parameter in a first‐order bifurcating autoregressive process with exponential innovations are derived. The limit distributions for the stationary, critical and explosive cases are unified via a single pivot using a random normalization. The pivot is shown to be asymptotically exponential for all values of the autoregressive parameter.