Relationship between missing data likelihoods and complete data restricted likelihoods for regressiontime series models: an application to total ozone data

Journal of the Royal Statistical Society. Series C: Applied Statistics

Volumn 45, Issue 1, 1996, Pages 63-72

  Basu, Sabyasachi ^a   Reinsel, Gregory C ^b  

^a SOUTHERN METHODIST UNIVERSITY   (United States)

^b UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

Additive outlier; Autoregressive moving average models; Maximum likelihood; Missing data; Regression models; Restricted maximum likelihood; Total ozone

Indexed keywords

EID: 0030554449     PISSN: 00359254     EISSN: None     Source Type: Journal    
DOI: 10.2307/2986223     Document Type: Article

References (17)

1. Box, G. E. P., Jenkins, G. M. and Reinsel, G. C. (1994) Time Series Analysis: Forecasting and Control, 3rd edn. Englewood Cliffs: Prentice Hall.
2. Box, G. E. P. and Tiao, G. C. (1975) Intervention analysis with applications to economic and environmental problems. J. Am. Statist. Ass., 70, 70-79.
3. Fox, A. J. (1972) Outliers in time series. J. R. Statist. Soc. B, 34, 350-363.
4. Harvey, A. C. and Pierse, R. G. (1984) Estimating missing observations in economic time series. J. Am. Statist. Ass., 79, 125-131.
5. Harville, D. A. (1974) Bayesian inference for variance components using only error contrasts. Biometrika, 61, 383-385.
6. Jones, R. H. (1980) Maximum likelihood fitting of ARMA models to time series with missing observations. Technometrics, 22, 389-395.
7. Kohn, R. and Ansley, C. F. (1986) Estimation, prediction, and interpolation for ARIMA models with missing data. J. Am. Statist. Ass., 81, 751-761.
8. Ljung, G. M. (1989) A note on the estimation of missing values in time series. Communs Statist. Computn Simuln, 18, 459-465.
9. _(1993) On outlier detection in time series. J. R. Statist. Soc. B, 55, 559-567.
10. Numerical Algorithms Group (1994) Numerical Algorithm Library. Downers Grove: Numerical Algorithms Group.
11. Patterson, H. D. and Thompson, R. (1971) Recovery of interblock information when block sizes are unequal. Biometrika, 58, 545-554.
12. Rao, C. R. (1973) Linear Statistical inference and Its Applications, 2nd edn. New York: Wiley.
13. Reinsel, G. C., Tiao, G. C., Wuebbles, D. J., Kerr, J. B., Miller, A. J., Nagatani, R. M., Bishop, L. and Ying, L. H. (1994) Seasonal trend analysis of published ground-based and TOMS total ozone data through 1991. J. Geophys. Res. D, 99, 5449-5464.
14. Russell, T. S. and Bradley, R. A. (1958) One-way variances in a two-way classification. Biometrika, 45, 111-129.
15. Stolarski, R. S., Bojkov, R., Bishop, L., Zerefos, C., Staehelin, J. and Zawodny, J. (1992) Measured trends in stratospheric ozone. Science, 256, 342-349.
16. Tunnicliffe Wilson, G. (1989) On the use of marginal likelihood in time series model estimation. J. R. Statist. Soc. B, 51, 15-27.
17. Wincek, M. A. and Reinsel, G. C. (1986) An exact maximum likelihood estimation procedure for regression-ARMA time series models with possibly nonconsecutive data. J. R. Statist. Soc. B, 48, 303-313.