A NONLINEAR TIME SERIES MODEL AND ESTIMATION OF MISSING OBSERVATIONS

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

1Department of Statistics and Actuarial Sciences, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1 2Department 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.