Hostname: page-component-74656f9884-npj9w Total loading time: 0 Render date: 2026-11-09T05:35:48.821Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-linear time series regression

Published online by Cambridge University Press:  14 July 2016

E. J. Hannan
E. J. Hannan*
Affiliation:
Australian National University
Get access Rights & Permissions [Opens in a new window]

Extract

In Jennrich (1969) the model is considered, where x(n) is a sequence of i.i.d. (0, σ 2) random variables and z(n; θ) is a continuous but possibly non-linear function of θ ∈ Θ, Θ being a compact set in Rp . We shall use a second subscript when referring to a particular coordinate of θ 0 so that θ 0j is the jth coordinate. Jennrich establishes, under suitable conditions on z(n; θ) and x(n), the strong consistency and asymptotic normality of the least squares estimates of θ. Our main purpose here is to extend these results to the case where x(n) is generated by a stationary time series.

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 8 , Issue 4 , December 1971 , pp. 767 - 780
Copyright
Copyright © Applied Probability Trust 1971 

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.)

Article purchase

Temporarily unavailable

References

Hannan, E. J. (1970) Multiple Time Series. Wiley, New York.CrossRefGoogle Scholar
Jennrich, R. I. (1969) Non-linear least squares estimators. Ann. Math. Statist. 40, 633–643.Google Scholar
Kholevo, A. R. (1969) On estimates of regression coefficients. Theor. Probability Appl. 14, 79–104.Google Scholar
Parthasarathy, K. R. (1960) On the estimation of the spectrum of a stationary stochastic process. Ann. Math. Statist. 31, 568–573.CrossRefGoogle Scholar
Rosenblatt, M. (1956) A central limit theorem and a strong mixing condition. Proc. Nat. Acad Sci. 42, 43–47.CrossRefGoogle Scholar
Rozanov, Yu. A. (1967) Stationary Random Processes. Holden-Day, San Francisco.Google Scholar
Walker, A. M. (1969) On the estimation of a harmonic component in a time series with stationary residuals. Proc. Internat. Statist. Inst. 43, 374–376.Google Scholar
Whittle, P. (1952) The simultaneous estimation of a time series' harmonic components and covariance structure. Trab. Estadíst. 3, 43–57.CrossRefGoogle Scholar
Zygmund, A. (1968) Trigonometrical Series. Cambridge University Press, Cambridge.Google Scholar