ESTIMATION OF SECOND-ORDER PROPERTIES FROM JITTERED TIME SERIES

PETER J. THOMSON^{1} AND PETER M. ROBINSON^{2}

1Institute of Statistics and Operations Research, Victoria University of Wellington,

P.O. Box 600, Wellington, New Zealand

2Department of Economics, London School of Economics, Houghton Street, London, U.K.

(Received March 4, 1994; revised February 15, 1995)

Abstract. This paper considers spectral and autocovariance estimation for a zero-mean, band-limited, stationary process that has been sampled at time points jittered from a regular, equi-interval, sampling scheme. The case of interest is where the sampling scheme is near regular so that the jitter standard deviation is small compared to the sampling interval. Such situations occur with many time series collected in the physical sciences including, in particular, oceanographic profiles.

Spectral estimation procedures are developed for the case of independent jitter and autocovariance estimation procedures for both independent and dependent jitter. These are typically modifications of general estimation procedures proposed elsewhere, but tailored to the particular jittered sampling scheme considered. The theoretical properties of these estimators are developed and their relative efficiencies compared.

The properties of the jittered sampling point process are also developed. These lead to a better understanding, in this situation, of more general techniques available for processes sampled by stationary point processes.

Key words and phrases: Jittered sampling, stationary processes, spectral estimation, autocovariance estimation, kernel density estimation.