Biquadratic functions: stationarity and invertibility in estimated time-series models.

Pollock, D. S. G.. "Biquadratic functions: stationarity and invertibility in estimated time-series models.." Qüestiió 13.1,2,3 (1989): 13-30. <http://eudml.org/doc/40147>.

@article{Pollock1989,
abstract = {It is important that the estimates of the parameters of an autoregressive moving-average (ARMA) model should satisfy the conditions of stationarity and invertibility. It can be shown that the unconditional maximum-likelihood estimates are bound to fill these conditions regardless of the size of the sample from which they are derived; and, in some quarters, it has been argued that they should be used in preference to any other estimates when the size of he sample is small. However, the maximum-likelihood estimates are difficult to obtain; and, in practice, estimates are usually derived from a least-squares criterion. In this paper we show that, if an appropriate form of least-squares criterion is adopted, then we can likewise guarantee that the conditions of stationarity and invertibility will be fulfilled. We also re-examine several of the alternative procedures for estimating ARMA models to see whether the criterion functions from which they are derived have the appropriate form.},
author = {Pollock, D. S. G.},
journal = {Qüestiió},
keywords = {Series temporales; Modelo ARMA; ARMA models; least-squares estimation; stationarity and invertibility},
language = {eng},
number = {1,2,3},
pages = {13-30},
title = {Biquadratic functions: stationarity and invertibility in estimated time-series models.},
url = {http://eudml.org/doc/40147},
volume = {13},
year = {1989},
}

TY - JOUR
AU - Pollock, D. S. G.
TI - Biquadratic functions: stationarity and invertibility in estimated time-series models.
JO - Qüestiió
PY - 1989
VL - 13
IS - 1,2,3
SP - 13
EP - 30
AB - It is important that the estimates of the parameters of an autoregressive moving-average (ARMA) model should satisfy the conditions of stationarity and invertibility. It can be shown that the unconditional maximum-likelihood estimates are bound to fill these conditions regardless of the size of the sample from which they are derived; and, in some quarters, it has been argued that they should be used in preference to any other estimates when the size of he sample is small. However, the maximum-likelihood estimates are difficult to obtain; and, in practice, estimates are usually derived from a least-squares criterion. In this paper we show that, if an appropriate form of least-squares criterion is adopted, then we can likewise guarantee that the conditions of stationarity and invertibility will be fulfilled. We also re-examine several of the alternative procedures for estimating ARMA models to see whether the criterion functions from which they are derived have the appropriate form.
LA - eng
KW - Series temporales; Modelo ARMA; ARMA models; least-squares estimation; stationarity and invertibility
UR - http://eudml.org/doc/40147
ER -