Large sample properties of estimation in time series observed at unequally spaced times. (English) Zbl 0566.62078

Dunsmuir, W.

Time series analysis of irregularly observed data, Proc. Symp., Texas A & M Univ., College Station/Tex. 1983, Lect. Notes Stat., Springer-Verlag 25, 58-77 (1984).

[For the entire collection see Zbl 0542.00014.]
This readable paper reviews the current state of large sample theory for estimation in stationary discrete time-series observed at unequally spaced times. The following topics are covered:
a) nonparametric estimation of sample covariances, correlations and spectra, and b) estimation of finite-dimensional parameter models for stationary time series. For both a) and b) conditions for consistency and asymptotic normality results are presented and illustrated by considering examples of periodic sampling, of sparse early sampling, and of asymptotically stationary sampling.
The difficulty of handling the non-Gaussian data in case b) is briefly discussed as is the important and interesting problem of the design of sampling patterns.

Reviewer: P.Stoica

MSC:

62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M15	Inference from stochastic processes and spectral analysis
93E12	Identification in stochastic control theory
62G05	Nonparametric estimation
62F12	Asymptotic properties of parametric estimators

Keywords:

review; large sample theory; stationary discrete time-series; unequally spaced times; sample covariances; correlations; spectra; finite- dimensional parameter models; consistency; asymptotic normality; periodic sampling; sparse early sampling; asymptotically stationary sampling; non- Gaussian data