Intervention Analysis in Multivariate Time Series via the Kalman Filter
The Kalman filter has been found useful in fitting ARIMA models. This paper uses the multivariate extension of the state-space approach to fit multivariate time series which include covariates and periodic interventions. An example will be presented in which these techniques are applied to the study of the pink cotton boll worm moth, Pectinophora gossypiella (Saunders), (Lepidoptera: Gelechiidae). Moth counts were taken at various locations in a large cotton field over time. A special type of multivariate time series will be used, namely a spatial time series. The amount of irrigation water at each location will be included in the model as a covariate and periodic applications of insecticide will be included as interventions. Previously developed techniques for handling missing data, aggregate data, and nonlinear data transformation are also incorporated. Maximum likelihood estimates of the model parameters are obtained by imbedding the filter in a quasi-Newton optimization routine.
KeywordsIrrigation Water Kalman Filter Time Series Analysis Time Series Model ARMA Model
Unable to display preview. Download preview PDF.
- Box, G. E. P. & G. M. Jenkins. 1970. Time Series Analysis, Forecasting, Control. San Francisco: Holden-Day.Google Scholar
- Harvey, A. C. 1981. The kalman filter and its applications in econometrics and time series analysis. In Methods of Operations Research, 44, [ed.] R. Henn, et al., Cambridge: Oelgeschlager, Gunn and Hain.Google Scholar
- Harvey, A. C. & G. D. A. Phillips. 1981. The estimation of regression models with time-varying parameters. In M. Deistier, E. F and G. Schwodiauer, [eds.], Games, Economic Dynamics, and Time Series Analysis, Physica-Verlag, Wein, pp. 306–321.Google Scholar
- Haugh, L. D. 1984. An introductory overview of some recent approaches to modeling spatial time series. In Time Series Analysis: Theory and Practice, [ed.] O. D. Anderson, New York: North-Holland.Google Scholar
- Kennedy, W. J., Jr. & J. E. Gentle. 1980. Statistical Computing. New York: Marcel Dekker.Google Scholar
- Shea, B. L. 1984. Maximum likelihood estimation of multivariate ARMA processes via the kalman filter. In Time Series Analysis: Theory and Practice, [ed.] O. D. Anderson, New York: North-Holland.Google Scholar