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August 2001 Least absolute deviation estimation for all-pass time series models
F. Jay Breidt, Richard A. Davis, A. Alexandre Trindade
Ann. Statist. 29(4): 919-946 (August 2001). DOI: 10.1214/aos/1013699987


An autoregressive moving average model in which all of the roots of the autoregressive polynomial are reciprocals of roots of the moving average polynomial and vice versa is called an all-pass time series model. All-pass models generate uncorrelated (white noise) time series, but these series are not independent in the non-Gaussian case. An approximation to the likelihood of the model in the case of Laplacian (two-sided exponential) noise yields a modified absolute deviations criterion, which can be used even if the underlying noise is not Laplacian. Asymptotic normality for least absolute deviation estimators of the model parameters is established under general conditions. Behavior of the estimators in finite samples is studied via simulation. The methodology is applied to exchange rate returns to show that linear all-pass models can mimic “nonlinear” behavior, and is applied to stock market volume data to illustrate a two-step procedure for fitting noncausal autoregressions.


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F. Jay Breidt. Richard A. Davis. A. Alexandre Trindade. "Least absolute deviation estimation for all-pass time series models." Ann. Statist. 29 (4) 919 - 946, August 2001.


Published: August 2001
First available in Project Euclid: 14 February 2002

zbMATH: 1012.62094
MathSciNet: MR1869234
Digital Object Identifier: 10.1214/aos/1013699987

Primary: 62M10
Secondary: 62E20 , 62F10

Keywords: Laplacian density , noncausal , noninvertible , nonminimum phase , White noise

Rights: Copyright © 2001 Institute of Mathematical Statistics


Vol.29 • No. 4 • August 2001
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