Prediction variance and information worth of observations in time series

Journal of Time Series Analysis

Volumn 21, Issue 4, 2000, Pages 413-434

  Pourahmadi, Mohsen ^a   Soofi, E S ^b  

^a NORTHERN ILLINOIS UNIVERSITY   (United States)

^b UNIVERSITY OF WISCONSIN MILWAUKEE   (United States)

Author keywords

Autoregressive and moving average (ARMA) models; Cram r Rao inequality; Entropy; Mutual information

Indexed keywords

EID: 0039027644     PISSN: 01439782     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9892.00191     Document Type: Article

References (21)

1. BAILEY, M. J. (1965) Prediction of an autoregressive variable subject both to disturbances and to errors of observation. J. Am. Stat. Assoc. 60, 164-81.
2. Box, G. E. P., JENKINS, G. M. and REINSEL, G. C. (1994) Time Series Analysis, Forecasting and Control, 3rd Edn. New Jersey: Prentice Hall.
3. BROCKWELL, P. J. and DAVIS, R. A. (1991) Time Series: Theory and Methods, 2nd Edn. New York: Springer.
4. CHENG, R. and POURAHMADI, M. (1997) Prediction with incomplete past and interpolation of missing values. Stat. Probab. Lett. 33, 341-46.
5. COVER, T. and THOMAS, S. (1990) Elements of Information Theory. New York: Wiley.
6. EBRAHIMI, N., PFLUGHOEFT, K. and SOOFI, E. S. (1994) Two measures of sample entropy. Stat. Probab. Lett. 20, 225-35.
7. GRANGER, C. W. J. and LIN, J. (1994) Using the mutual information coefficient to identify lags in nonlinear models. J. Time Ser. Anal. 15, 371-84.
8. JOE, H. (1989) Relative entropy measures of multivariate dependence. J. Am. Stat. Assoc. 84, 157-64.
9. KALATA, P. and PRIEMER, R. (1979) Linear prediction, filtering and smoothing: an information-theoretic approach. Inf. Sci. 17, 1-14.
10. Li, L. and XIE, Z. (1996) Model selection and order detemination for time series by information between the past and the future. J. Time. Ser. Anal. 17, 65-84.
11. MOHANTY, R. and POURAHMADI, M. (1996) Estimation of the generalized prediction error variance of a multiple time series. J. Am. Stat. Assoc. 91, 294-99.
12. PHADKE, M. S. and Wu, S. M. (1974) Modeling of continuous stochastic processes from discrete observations with application to sunspot data. J. Am. Stat. Assoc. 69, 325-29.
13. POURAHMADI, M. (1989) Estimation and interpolation of missing values of a stationary time series. J. Time Ser. Anal. 10, 149-69.
14. _ (1992) Alternating projections and interpolation of stationary processes. J. Appl. Probab. 29, 921-31.
15. ROBINSON, P. M. (1991) Consistent nonparametric entropy-based testing. Rev. Econ. Stud. 58, 437-53.
16. SHEPP, L. A., SLEPIAN, D. and WYNER, A. D. (1980) On prediction of moving-average processes. Bell Syst. Tech. J. 59, 367-415.
17. SHANNON, C. E. (1948) A mathematical theory of communication. Bell Syst. Tech. J. 27, 379-423.
18. SOOFI, E. S. (1994) Capturing the intangible concept of information. J. Am. Stat. Assoc. 89, 1243-54.
19. _, EBRAHIMI, N. and HABIBULLAH, M. (1995) Information distinguishability with application to analysis of failure data. J. Am. Stat. Assoc. 90, 657-68.
20. TOMITA, Y., OHMATSU, Y. and SOEDA, T. (1976a) An application of information theory to estimation problems. Inf. Control 32, 101-11.
21. _, OMATU, S. and SOEDA, T. (1976b) An application of information theory to filtering problems. Inf. Sci. 11, 13-27.