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On time-dependent linear transformations of non-stationary stochastic processes

Published online by Cambridge University Press:  14 July 2016

H. Tong
H. Tong*
Affiliation:
University of Manchester Institute of Science and Technology
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Abstract

We have introduced a definition of a slowly changing time-dependent linear transformation on a class of non-stationary stochastic processes and have studied the “spectral” relationship between the input and output processes. In addition, using this definition, we have extended one important property of coherency and the concept of residual variance bound pertinent to the theory of stationary stochastic processes to the non-stationary case.

Keywords

TIME-DEPENDENT LINEAR TRANSFORMATIONSNON-STATIONARY PROCESSESEVOLUTIONARY SPECTRACOHERENCYRESIDUAL VARIANCE BOUND

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 11 , Issue 1 , March 1974 , pp. 53 - 62
Copyright
Copyright © Applied Probability Trust 1974 

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References

Priestley, M. B. (1965) Evolutionary spectra and non-stationary processes J. Roy. Statist. Soc. B 27, 204–237.Google Scholar
Priestley, M. B. (1971) Fitting relationship between time series. Paper presented at the 38th Session of the International Statistical Institute, Washington, August 1971.Google Scholar
Priestley, M. B. and Tong, H. (1972) On the analysis of bi-variate non-stationary processes. Paper read to the Royal Statistical Society on 6th December 1972.Google Scholar