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Biometrika 1978 65(3):497-502; doi:10.1093/biomet/65.3.497
© 1978 by Biometrika Trust
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Some consideration of decomposition of a time series

G. C. TIAO1 and S. C. HILLMER2

1Department of Statistics, University of Wisconsin Madison
2School of Business, University of Kansas Lawrence

Suppose that an observable Gaussian time series Z1 can be written as the sum of an unobservable signal component Tt and a white noise component et. This paper proposes a procedure to estimate the Tt component uniquely by maximizing the variance of et with respect to a known model for Zt. Properties of this procedure are discussed and a comparison is made with a number of smoothing and filtering procedures commonly used in practice.

Key Words: Autoregressive-moving average model • Canonical decomposition • Covariance generating function • Smoothing spline • Symmetric moving average filter • Time series


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