Hostname: page-component-84b7d79bbc-c654p Total loading time: 0 Render date: 2024-07-30T03:44:12.683Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-linear regression for multiple time-series

Published online by Cambridge University Press:  14 July 2016

P. M. Robinson
P. M. Robinson*
Affiliation:
The Australian National University
Get access Rights & Permissions [Opens in a new window]

Abstract

A general multivariate non-linear regression model is considered, including as special cases linear regression when the regression matrix is of less than full rank, simultaneous equations systems and regression on an unobservable predetermined variable. Given a time-series of observations at unit intervals we consider the estimation of the parameters, subject to non-linear constraints, by minimizing a criterion based on the Fourier-transformed model. We allow the residuals to be generated by a stationary, linear, process and establish asymptotic properties of our estimates.

Keywords

NON-LINEAR MULTIVARIATE REGRESSIONSTATIONARY TIME-SERIESFOURIER METHODSSTRONG LAWCENTRAL LIMIT THEOREM
Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 4 , December 1972 , pp. 758 - 768
Copyright
Copyright © Applied Probability Trust 1972 

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

[1] Hannan, E. J. (1970) Multiple Time Series. Wiley, New York.Google Scholar
[2] Hannan, E. J. (1971) Non-linear time series regression. J. Appl. Prob. 8, 767–780.Google Scholar
[3] Jennrich, R. I. (1969) Asymptotic properties of non-linear least squares estimators. Ann. Math. Statist. 40, 633–643.Google Scholar
[4] Malinvaud, E. (1970) The consistency of nonlinear regressions. Ann. Math. Statist. 41, 956–969.Google Scholar
[5] Rohde, C. A. (1965) Generalized inverses of partitioned matrices. SIAM J. Appl. Math. 13, 1033–1035.Google Scholar