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Measurement of a wandering signal amid noise

Published online by Cambridge University Press:  14 July 2016

E. J. Hannan
E. J. Hannan*
Affiliation:
Australian National University
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Abstract

A formula is given for the response function of a filter which extracts a signal generated by a non-stationary process from amid noise. The non-stationarity is due to the presence of zeros on the unit circle of the function characterising the difference equation generating the signal. The signal is broken into a trend component and a stochastic integral in which t occurs only through the factor exp it λ and it is shown that the filter which optimally extracts the latter perfectly represents the former. The considerations cover the case of a vector series. Applications to problems in seasonal variation measurement are indicated.

Type
Research Papers
Information
Journal of Applied Probability , Volume 4 , Issue 1 , November 1967 , pp. 90 - 102
Copyright
Copyright © Applied Probability Trust 

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References

[1] Hannan, E. J. (1964) The estimation of a changing seasonal pattern. J. Amer. Statist. Ass. 59, 1063–1077.CrossRefGoogle Scholar
[2] Hoffman, K. (1962) Banach Spaces of Analytic Functions. Prentice-Hall.Google Scholar
[3] Macduffee, C. C. (1956) The Theory of Matrices. Chelsea, New York.Google Scholar
[4] Potapov, V. P. (1955) The multiplicative structure of J-contractive matrix functions. Trudy Moskov. Mat. Obšc. 4, 125–236 (Amer. Math. Soc. Translation 15, 131–244).Google Scholar
[5] Sobel, E. (1965) Extraction of Slowly Changing Signals and of Sums of Accumulating Sequences. Thesis, The Johns Hopkins University, Baltimore.Google Scholar
[6] Sobel, E. (1966) Prediction of a noise corrupted, non-stationary signal (to appear).Google Scholar
[7] Whittle, P. (1963) Prediction and Regulation. English Universities Press, London.Google Scholar
[8] Wiener, N. and Masani, P. (1957) The prediction theory of multivariate stochastic processes. Acta Math. 98, 111–150.Google Scholar