Measurement of a wandering signal amid noise
- 1 November 1967
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 4 (1) , 90-102
- https://doi.org/10.2307/3212301
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.Keywords
This publication has 2 references indexed in Scilit:
- The Estimation of a Changing Seasonal PatternJournal of the American Statistical Association, 1964
- The prediction theory of multivariate stochastic processes: I. The regularity conditionActa Mathematica, 1957