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.
Publié le : 2001-08-14
Classification:
Laplacian density,
noncausal,
noninvertible,
nonminimum phase,
white noise,
62M10,
62E20,
62F10
@article{1013699987,
author = {Breidt, F. Jay and Davis, Richard A. and Trindade, A. Alexandre},
title = {Least absolute deviation estimation for all-pass time series
models},
journal = {Ann. Statist.},
volume = {29},
number = {2},
year = {2001},
pages = { 919-946},
language = {en},
url = {http://dml.mathdoc.fr/item/1013699987}
}
Breidt, F. Jay; Davis, Richard A.; Trindade, A. Alexandre. Least absolute deviation estimation for all-pass time series
models. Ann. Statist., Tome 29 (2001) no. 2, pp. 919-946. http://gdmltest.u-ga.fr/item/1013699987/