Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-16T07:28:22.278Z Has data issue: false hasContentIssue false
  • English
  • Français

On a model for a time series of cross-sections

Published online by Cambridge University Press:  14 July 2016

P. M. Robinson
Get access Rights & Permissions [Opens in a new window]

Abstract

Dynamic stationary models for mixed time series and cross-section data are studied. The models are of simple, standard form except that the unknown coefficients are not assumed constant over the cross-section; instead, each cross-sectional unit draws a parameter set from an infinite population. The models are framed in continuous time, which facilitates the handling of irregularly-spaced series, and observation times that vary over the cross-section, and covers also standard cases in which observations at the same regularly-spaced times are available for each unit. A variety of issues are considered, in particular stationarity and distributional questions, inference about the parameter distributions, and the behaviour of cross-sectionally aggregated data.

Keywords

RANDOM COEFFICIENT MODELSCONTINUOUS-TIME PROCESSESASYMPTOTIC EXPANSIONS
Type
Part 2—Estimation for Time Series
Information
Journal of Applied Probability , Volume 23 , Issue A: Essays in Time Series and Allied Processes , 1986 , pp. 113 - 125
Copyright
Copyright © 1986 Applied Probability Trust 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Azzalini, A. (1981) Replicated observations of low order autoregressive time series. J. Time Series Analysis 2, 63–70.CrossRefGoogle Scholar
Balestra, P. and Nerlove, M. (1966) Pooling cross section and time series data in the estimation of a dynamic model: the demand for natural gas. Econometrica 34, 585–612.CrossRefGoogle Scholar
Bleistein, N. and Handelsman, R. A. (1975) Asymptotic Expansions of Integrals. Holt, Rinehart and Winston, New York.Google Scholar
Erdelyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G. (1954) Tables of Integral Transforms , Vol. 1. McGraw-Hill, New York.Google Scholar
Hannan, E. J. (1970) Multiple Time Series. Wiley, New York.CrossRefGoogle Scholar
Hsiao, C. (1975) Some estimation methods in a random coefficient model. Econometrica 43, 305–325.CrossRefGoogle Scholar
Lenz, H.-J. and Robinson, P. M. (1983) Sampling of cross-sectional time series. In Recent Trends in Statistics. ed. Heiler, S. Vandenhoek and Ruprecht, Göttingen.Google Scholar
Robinson, P. M. (1977) Estimation of a time series model from unequally spaced data. Stoch. Proc. Appl. 6, 9–24.CrossRefGoogle Scholar
Robinson, P. M. (1978a) Statistical inference for a random coefficient autoregressive model. Scand. J. Statist. 5, 163–168.Google Scholar
Robinson, P. M. (1978b) Alternative models for stationary stochastic processes. Stoch. Proc. Appl. 8, 141–152.CrossRefGoogle Scholar
Soong, T. T. (1973) Random Differential Equations in Science and Engineering. Academic Press, New York.Google Scholar
Swamy, P. A. V. B. (1970) Efficient inference in a random coefficient regression model. Econometrica 38, 311–323.CrossRefGoogle Scholar
Wallace, T. D. and Hussain, A. (1969) The use of error components models in combining cross section with time series data. Econometrica 37, 55–72.CrossRefGoogle Scholar