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A NONLINEAR TIME SERIES MODEL AND ESTIMATION

OF MISSING OBSERVATIONS

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BOVAS ABRAHAM^{1} AND A. THAVANESWARAN^{2}

^{1} *Department of Statistics and Actuarial Sciences, University of Waterloo,*

Waterloo, Ontario, Canada, N2L 3G1

^{2} *Department of Statistics, University of Manitoba, Winnipeg,*

Manitoba, Canada, R3T 2N2
(Received August 10, 1989; revised January 8, 1990)

**Abstract.**
This paper formulates a nonlinear time series
model which encompasses several standard nonlinear models for time
series as special cases. It also offers two methods for estimating
missing observations, one using prediction and fixed point smoothing
algorithms and the other using optimal estimating equation theory.
Recursive estimation of missing observations in an autoregressive
conditionally heteroscedastic (ARCH) model and the estimation of
missing observations in a linear time series model are shown to be
special cases. Construction of optimal estimates of missing
observations using estimating equation theory is discussed and applied
to some nonlinear models.

*Key words and phrases*:
Kalman filter, missing
observations, nonlinear time series, optimal estimation,
robustness.

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