Hostname: page-component-7b7567c8c-lpg2g Total loading time: 0 Render date: 2026-11-15T10:10:29.648Z Has data issue: false hasContentIssue false
  • English
  • Français

Time series regression with unequally spaced data

Published online by Cambridge University Press:  14 July 2016

Richard H. Jones
Get accessRights & Permissions [Opens in a new window]

Abstract

Regression analysis with stationary errors is extended to the case when observations are not equally spaced. The errors are modelled as either a discrete-time ARMA process with missing observations, or as a continuous-time autoregression with observational error observed at arbitrary times. Using a state-space representation, a Kalman filter is used to calculate the exact likelihood. The linear regression coefficients are separated out of the likelihood so non-linear optimization is required only with respect to the parameters modelling the error structure.

Keywords

CORRELATED ERRORSSTATE SPACEKALMAN FILTER

Information

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. 89 - 98
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.)

Article purchase

Temporarily unavailable

References

Box, G. E. P. and Jenkins, G. M. (1976) Time Series Analysis: Forecasting and Control. revised edn. Holden-Day, San Francisco.Google Scholar
Davis, G. A. and Nihan, N. L. (1984) Using time series designs to estimate changes in freeway level of service, despite missing data. Transportation Res. 18A, 431–438.CrossRefGoogle Scholar
Duncan, D. B. and Jones, R. H. (1966) Multiple regression with stationary errors. J. Amer. Statist. Assoc. 61, 917–928.Google Scholar
Golob, G. H. and Pereyra, V. (1973) The differentiation of pseudoinverses and non-linear least squares problems whose variables separate. SIAM J. Numerical Analysis 10, 413–452.CrossRefGoogle Scholar
Graybill, F. A. (1976) Theory and Application of the Linear Model. Duxbury Press, North Scituate, Massachusetts.Google Scholar
Grenander, U. and Rosenblatt, M. (1957) Statistical Analysis of Stationary Time Series. Wiley, New York.CrossRefGoogle Scholar
Hamon, B. V. and Hannan, E. J. (1963) Estimating relations between time series. J. Geophysical Res. 68, 6033–6041.Google Scholar
Hannan, E. J. (1963) Regression for time series. In Time Series Analysis , ed. Rosenblatt, M., Wiley, New York, 17–37.Google Scholar
Harvey, A. C. (1981) Time Series Models. Wiley, New York.Google Scholar
Harvey, A. C. and Phillips, G. D. A. (1979) Maximum likelihood estimation of regression models with autoregressive-moving average disturbances. Biometrika 66, 49–58.Google Scholar
Jones, R. H. (1980) Maximum likelihood fitting of ARMA models to time series with missing observations. Technometrics 22, 389–395.Google Scholar
Jones, R. H. (1981) Fitting a continuous time autoregression to discrete data. In Applied Time Series Analysis II, ed. Findley, D. F., Academic Press, New York, 651–682.Google Scholar
Jones, R. H. (1985) Time series analysis with unequally spaced data. In Handbook of Statistics, Volume 5: Time Series in the Time Domain , ed. Hannan, E. J., Krishnaiah, P. R. and Rao, M. M. North-Holland, Amsterdam.Google Scholar
Wecker, W. E. and Ansley, C. F. (1983) The signal extraction approach to nonlinear regression and spline smoothing. J. Amer. Statist. Assoc. 78, 81–89.CrossRefGoogle Scholar