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DISTRIBUTIONS OF LEAST SQUARES ESTIMATORS OF AUTOREGRESSIVE PARAMETERS FOR A PROCESS WITH COMPLEX ROOTS ON THE UNIT CIRCLE
Author(s) -
Ahtola Juha,
Tiao George C.
Publication year - 1987
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.1467-9892.1987.tb00416.x
Subject(s) - mathematics , autoregressive model , unit circle , estimator , unit root , asymptotic distribution , monte carlo method , polynomial , asymptotic analysis , least squares function approximation , statistics , mathematical analysis
. Asymptotic distributions of the autoregressive parameters in the AR(2) model are derived, when the characteristic polynomial has a pair of complex roots on the unit circle. Percentage points are tabulated based on simulations from the asymptotic formulae. The usefulness of the asymptotic results in finite sample situations is investigated by a Monte Carlo study, and an illustrative example is given.