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

Qüestiió (1989)

- Volume: 13, Issue: 1,2,3, page 13-30
- ISSN: 0210-8054

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topPollock, 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 -

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