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Rank-Based Estimation for All-Pass Time Series Models

Summary: Rank-Based Estimation for
All-Pass Time Series Models
Beth Andrews1
Northwestern University
Richard A. Davis1,2
and F. Jay Breidt2
Colorado State University
July 6, 2006
An autoregressive-moving average model in which all roots of the autoregressive polyno-
mial are reciprocals of roots of the moving average polynomial and vice versa is called
an all-pass time series model. All-pass models are useful for identifying and model-
ing noncausal and noninvertible autoregressive-moving average processes. We establish
asymptotic normality and consistency for rank-based estimators of all-pass model pa-
rameters. The estimators are obtained by minimizing the rank-based residual dispersion
function in L.A. Jaeckel [Estimating regression coefficients by minimizing the dispersion
of the residuals, Ann. Math. Statist. 43 (1972) 14491458]. These estimators can have
the same asymptotic efficiency as maximum likelihood estimators and are robust. The
behavior of the estimators for finite samples is studied via simulation, and rank estimation
is used in the deconvolution of a simulated water gun seismogram.


Source: Andrews, Beth - Department of Statistics, Northwestern University


Collections: Mathematics