Abstract
Let y(n)=f(n)+ε(n), n=1, ..., N with the ε(n) i.i.d. from N(0,σ2), σ2 unknown and f(·) an unknown "smooth" function. The problem is to estimate f(n), n=1,...,N in a statistically satisfactory manner. This problem was proposed by Whittaker, 1919. Wahba and Wold, 1975, is an 0(N3) cubic spline solution; Akaike, 1979, is an 0(N2) marginal likelihood "smoothness priors" solution.
In our approach alternative candidate smoothness constraint models are imbedded into dynamic state space forms. The recursive computational Kalman smoother procedure is invoked to achieve an 0(N) computation. Akaike's AIC statistical decision criterion is employed to determine the best of the alternative constraint Kalman filter-predictor modeled data. The Kalman smoother solution corresponding the AIC best Kalman filter, is then the best fixed interval smooth solution of the data.
Examples are shown including one in which the smoothing problem is generalized to the smoothing of econometric time series with trends and seasonalities.
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References
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© 1982 Springer-Verlag
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Gersch, W., Brotherton, T. (1982). The smoothing problem — a state space recursive computational approach: Applications to econometric time series with trends and seasonalities. In: Drenick, R.F., Kozin, F. (eds) System Modeling and Optimization. Lecture Notes in Control and Information Sciences, vol 38. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006142
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DOI: https://doi.org/10.1007/BFb0006142
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