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Further results on Kendall's autoregressive series

Published online by Cambridge University Press:  14 July 2016

Jay C. Hardin  and
Thomas J. Brown
Jay C. Hardin
Affiliation:
NASA Langley Research Center, Hampton, Virginia
Thomas J. Brown
Affiliation:
U. S. Army Air Mobility Research and Development Laboratory, Hampton, Virginia
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Abstract

Theoretical expressions for the cross correlation and cross spectra of the input and output variables in the difference equation Xt=aXt−1 + bXt−2+ Yt are derived. These expressions are compared with estimates of these expectations obtained by employing a Fast Fourier Transform technique on digitally generated series.

Keywords

TIME SERIES ANALYSISSPECTRAL ANALYSISREGRESSION SERIES
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 1 , March 1975 , pp. 180 - 182
Copyright
Copyright © Applied Probability Trust 1975 

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References

Bartlett, M. S. (1966) Stochastic Processes. Cambridge University Press, London.Google Scholar
Brown, T. J. and Hardin, J. C. (1973) A note on Kendall's autoregressive series. J. Appl. Prob. 10, 475–478.Google Scholar
Kendall, M. G. (1946) Researches in Oscillatory Time Series. Cambridge University Press, London.Google Scholar
Welch, P. D. (1967) The use of Fast Fourier Transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms. IEEE Trans on Audio and Electroacoustics. vol. AU-15, no. 2, 70–73, June 1967.Google Scholar