A transfer function relating a time series $y_t$ to present and past values of a series $x_t$ need not possess an inverse. When $(x_t, y_t)$ is a covariance stationary process, it is shown that noninvertibility in this transfer function has the effect of reducing the error variance of the minimum mean-square-error predictor of $y_t$ one or more steps ahead. In deriving these results a "dual" series to $x_t$ is constructed, which has univariate stochastic structure identical to that of $x_t$ itself, and an associated dual transfer function relating it to $y_t$ which is invertible.
Publié le : 1975-11-14
Classification:
Transfer-function models,
dynamic models,
distributed lag models,
forecasting,
invertibility (of transfer function models),
prediction,
62M20,
62M10
@article{1176343290,
author = {Pierce, David A.},
title = {Noninvertible Transfer Functions and their Forecasts},
journal = {Ann. Statist.},
volume = {3},
number = {1},
year = {1975},
pages = { 1354-1360},
language = {en},
url = {http://dml.mathdoc.fr/item/1176343290}
}
Pierce, David A. Noninvertible Transfer Functions and their Forecasts. Ann. Statist., Tome 3 (1975) no. 1, pp. 1354-1360. http://gdmltest.u-ga.fr/item/1176343290/