Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-25T22:30:10.298Z Has data issue: false hasContentIssue false
  • English
  • Français

The Box-Jenkins approach to random coefficient autoregressive modelling

Published online by Cambridge University Press:  14 July 2016

D. F. Nicholls
Get access Rights & Permissions [Opens in a new window]

Abstract

Recent time series research has been directed towards the relaxation of the assumption that time series models have constant coefficients. One class of models to emerge as a result of this has been that of random coefficient autoregressive models. This paper demonstrates how the Box-Jenkins three-step approach of model specification, estimation and diagnostic checking may be applied to this class of models.

Keywords

IDENTIFICATIONESTIMATIONDIAGNOSTIC CHECKSSECOND-ORDER STATIONARITYSCORE TESTTWO-STEP ESTIMATION PROCEDURE
Type
Part 4—Non-linear and Non-stationary Systems in Time Series
Information
Journal of Applied Probability , Volume 23 , Issue A: Essays in Time Series and Allied Processes , 1986 , pp. 231 - 240
Copyright
Copyright © 1986 Applied Probability Trust 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Andel, J. (1976) Autoregressive series with random parameters. Math. Operationsforsch. u. Statist. 7, 735–741.CrossRefGoogle Scholar
Box, G. E. P. and Jenkins, G. M. (1976) Time Series Analysis: Forecasting and Control (revised edition). Holden-Day, San Francisco.Google Scholar
Box, G. E. P. and Pierce, D. A. (1970) Distribution of residual autocorrelations in autoregressive integrated moving average time series models. J. Amer. Statist. Assoc. 65, 1509–1526.CrossRefGoogle Scholar
Chant, D. (1974) On asymptotic tests of composite hypotheses in non-standard conditions. Biometrika 61, 291–298.Google Scholar
Durbin, J. (1970) Testing for serial correlation in least squares regression when some of the regressors are lagged dependent variables. Econometrica 38, 410–421.Google Scholar
Hannan, E. J. (1980) The estimation of the order of an ARMA process. Ann. Statist. 8, 1071–1081.Google Scholar
Hannan, E. J. and Kavalieris, L. (1983) The convergence of autocorrelations and autoregression. Austral. J. Statist. 25, 287–297.CrossRefGoogle Scholar
Hannan, E. J. and Quinn, B. G. (1979) The determination of the order of an autoregression. J. R. Statist. Soc. B 41, 190–195.Google Scholar
Henderson, H. V. and Searle, S. R. (1979) Vec and vech operators for matrices with some uses in Jacobian and multivariate statistics. Canad. J. Statist. 7, 65–81.Google Scholar
Heyde, C. C. and Hannan, E. J. (1972) On limit theorems for quadratic functions of discrete time series. Ann. Math. Statist. 43, 2058–2066.Google Scholar
Johnson, L. W. (1977) Stochastic parameter regression; an annotated bibliography. Internat. Statist. Rev. 45, 257–272.Google Scholar
Johnson, L. W. (1980) Stochastic parameter regression: an additional annotated bibliography. Internat. Statist. Rev. 48, 95–102.Google Scholar
Moran, P. A. P. (1971) Maximum likelihood estimation in non standard conditions. Proc. Camb. Phil. Soc. 70, 441–445.Google Scholar
Neyman, J. (1959) Optimal asymptotic tests for composite statistical hypotheses. In Probability and Statistics , ed. Grenander, U., Wiley, New York, 213–234.Google Scholar
Nicholls, D. F. and Quinn, B. G. (1982) Random Coefficient Autoregressive Models: An Introduction. Springer-Verlag, New York.Google Scholar
Priestley, M. B. (1981) Spectral Analysis and Time Series , Vols 1 and 2. Academic Press, New York.Google Scholar
Shibata, R. (1976) Selection of the order of an autoregressive model by Akaike's information criterion. Biometrika 63, 117–126.Google Scholar