A Smoothness Priors Time-Varying AR Coefficient Modeling of Nonstationary Covariance Time Series

IEEE Transactions on Automatic Control

Volumn 30, Issue 1, 1985, Pages 48-56

  Kitagawa, Genshiro ^a   Gersch, Will ^b  

^a INSTITUTE OF STATISTICAL MATHEMATICS   (Japan)

^b UNIVERSITY OF HAWAII   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

STATISTICAL METHODS;

ESTIMATION OF CHANGING POWER; NONSTATIONARY COVARIANCE TIME SERIES; SMOOTHING PROBLEM; SMOOTHNESS PRIORS TIME-VARYING AR COEFFICIENT MODELING;

CONTROL SYSTEMS;

EID: 0021819062     PISSN: 00189286     EISSN: 15582523     Source Type: Journal    
DOI: 10.1109/TAC.1985.1103788     Document Type: Article

References (45)

1. T. Brotherton and W. Gersch, “A data analytic approach to the smoothing problem and some of its variations,” in Proc. 20th IEEE Conf. Decision Contr., 1981, pp. 1061–1069.
2. G. Kitagawa “A nonstationary time series model and its fitting by a recursive filter,” J. Time Series Anal., vol. 2, pp. 103–116, 1981.
3. G. Kitagawa and W. Gersch, “A smoothing problem approach to the modeling of time series with trends and seasonalities,” JASA, vol. 79, 378–389, 1984.
4. W. Gersch and G. Kitagawa “The prediction of time series with trends and seasonalities,” J. Business Econ. Stat., vol. 1, pp. 253–264, 1983.
5. G. Kitagawa, and W. Gersch, “A smoothness priors-long AR model method for spectral estimation,” IEEE Trans. Automat. Contr., this issue, pp. 57–65.
6. E. T. Whittaker, “On a new method of graduation,” in Proc. Edinborough Math. Soc., vol. 41, 1923, pp. 63–75.
7. R. Shiller “A distributed lag estimator derived from smoothness priors,” Econometrica, vol. 41, pp. 775–778, 1973.
8. H. Akaike, “Likelihood and the Bayes procedure,” in Bayesian Statistics, J. M. Bernado, M. H. DeGroot, D. V. Lindley, and A. F. M. Smith, Eds. Valencia, Spain: University Press, 1980, pp. 141–166.
9. D. V. Lindley and A. F. M. Smith, “Bayes estimates for the linear model,” J. Royal Stat. Soc. B, vol. 34, pp. 1–41, 1972.
10. I. J. Good, Estimating Probabilities. Cambridge, MA: M.I.T. Press, 1965.
11. A. N. Tikhonov “Incorrect problems of linear algebra and a stable method for their solution,” Soviet Math. Pokl., vol. 6, pp. 988–991, 1965.
12. I. J. Good and R. A. Gaskins “Density estimation and bump-hunting by the penalized likelihood method exemplified by scattering and meteorite data,” J. Amer. Stat. Assoc., vol. 75, pp. 43–73, 1980.
13. G. Wahba, “A survey of some smoothing problems and the method of generalized cross-validation for solving them,” in Applications of Statistics, P. R. Krishnaiah, Ed. Amsterdam, The Netherlands: North-Holland, 1977, 507–524.
14. G. E. P. Box “Sampling and Bayes inference in scientific modeling and robustness,” J. Royal Stat. Soc. A. vol. 143, pp. 383–430, 1980.
15. C. N. Morris, “Parametric empirical Bayes inference: Theory and application,” in Proc. 1982 Amer. Stat. Assoc. Nat. Meet., to be published.
16. P. Whittle “Recursive relations for predictors of non-stationary processes,” J. Royal Stat. Soc., vol. 27, pp. 523–532, 1965.
17. F. Kozin, “Estimation and modeling of nonstationary time series,” in Proc. Symp. Appl. Comput. Methods in Eng., Univ. Southern Calif., Los Angeles, 1977, pp. 603–612.
18. D. Nicholls and B. G. Quinn “The estimation of random coefficient autoregressive models I,” J. Time Series Anal., vol. 1, pp. 37–46, 1980.
19. G. B. Quinn and D. F. Nicholls “The estimation of random coefficient autoregressive models, II,” J. Time Series Anal., vol. 2, pp. 185–203, 1981.
20. T. Ozaki and H. Tong, “On the fitting of nonstationary autoregressive models in time series analysis,” in Proc. 8th Hawaii Int. Conf. Syst. Sci., Western Periodal Co., 1975, 224–226.
21. G. Kitagawa and H. Akaike “A procedure for the modeling of nonstationary time series,” Ann. Inst. Stat. Math., vol. 30-B, pp. 351–363, 1978.
22. W. Gersch and T. Brotherton “Estimation of stationary structural system parameters from nonstationary random vibration data. A locally stationary model method,” J. Sound Vibration, vol. 81, no. 2, pp. 215–227, 1982.
23. W. Gersch, T. Brotherton, and S. Braun, “Nearest neighbor time series analysis classification of faults in rotating machinery,” Trans. ASME, vol. 105, pp. 178–184, 1983; and T. Yokata, X. Shengkui, M. Mizoue, and I. Nakamura, “An automatic measurement of arrival time of seismic waves and its applications to an on-line processing system,” Bull Earthquake Res. Inst., vol. 55, 449–484, 1981.
24. W. Gersch and G. Kitagawa, “A time varying multivariate autoregressive modeling of econometric time series,” Stat. Res. Division, Bureau of the Census, U.S. Dep. Commerce, Tech. Paper 9, 1983.
25. F. Kozin and F. Nakajima “The order determination problem for linear time-varying AR models,” IEEE Trans. Automat. Contr., vol. AC-45, pp. 250–257, 1980.
26. K. J. A. A strom and B. Whittenmark “Problems of identification and control,” J. Math. Anal. Appl., vol. 34, pp. 90–113, 1971.
27. P. J. Harrison and C. F. Stevens, “Bayesian forecasting,” J. Royal Stat. Soc. B, vol. 38, pp. 205–248 (with discussion), 1976.
28. T. Bohlin, “Four cases of identification of changing systems,” in System Identification Advances and Case Studies, R. Mehra and D. G. Lainotis, Eds. New York: Academic, 1976.
29. A. H. Lev and T. Kailath, “Ladder-form filters for nonstationary processes,” in Proc. 19th IEEE Conf. Decision Contr., pp. 960–961, 961, 1980.
30. Y. Grenier, “Time varying lattices and AR model parameter estimation,” in Proc. ICASSP, 1982, pp. 1337–1340.
31. G. Kitagawa, “Changing spectrum estimation,” J. Sound Vibration, vol. 89, no. 4, pp. 433–445, 1983.
32. S. W. Chan, G. C. Goodwin, and K. S. Sin, “Convergence and properties of the solutions of the Ricatti difference equation,” in Proc. 21st IEEE Conf. Decision Contr., 1982, vol. 1, pp. 300–305.
33. B. D. O. Anderson and J. B. Moore, Optimal Filtering. Englewood Cliffs, NJ: Prentice-Hall, 1979.
34. H. Akaike, “A new look at the statistical model identification,” IEEE Trans. Automat. Contr., vol. AC-10, pp. 716–723. 1974.
35. G. S. Kimeldorf and G. Wahba “A correspondence between Bayesian estimation on stochastic processes and smoothing by splines,” Ann. Math. Stat., vol. 41, pp. 495–502, 1971.
36. P. A. V. B. Swamy and P. A. Tinsley “Linear prediction and estimation methods for regression models with stationary stochastic coefficients,” J. Econ., vol. 12, pp. 103–1452, 1980.
37. G. Wahba “Automatic smoothing of the log periodogram,” J. Amer. Stat. Assoc., vol. 75, pp. 122–132, 1980.
38. C. H. Page “Instantaneous power spectra,” J. Appl. Phys., vol. 23, pp. 103–106, 1952.
39. H. Cramér, “On some classes of non-stationary processes,” in Proc. 4th Berkeley Symp. Math. Stat. Probability, Univ. Calif. Press, 1981, pp. 57–78.
40. D. Tjostheim “Spectral generating operators for non-stationary processes,” Ad. Appl. Probability, vol. 8, pp. 831–846, 1976.
41. M. B. Priestly “Evolutionary spectra and non-stationary processes,” J. Royal Stat. Soc. B, vol. 27, pp. 204–237, 1965.
42. — “Power spectral analysis of non-stationary random processes,” J. Sound Vibration, vol. 6, pp. 86–97, 1967.
43. “Strong motion earthquake accelograms,” Earthquake Eng. Labs., Calif. Inst. Technol., vol. I, 1970; vol. II, 1973.
44. R. Shibata “Asymptotically efficient selection of the order of the model for estimating the parameters of a linear process,” Ann. Stat., vol. 8, pp. 147–164, 1980.
45. — “An optimal selection of regression variables,” Biometrika, vol. 68, pp. 45–54, 1981.