151
Views
33
CrossRef citations to date
0
Altmetric
Theory and Method

A Smoothness Priors–State Space Modeling of Time Series with Trend and Seasonality

&
Pages 378-389 | Received 01 Jul 1982, Published online: 12 Mar 2012

References

  • Akaike , H. “Information Theory and an Extension of the Maximum Likelihood Principle” . Second International Symposium on Information Theory . Edited by: Petrov , B. N. and Csaki , F. pp. 267 – 281 . Budapest : Akademiai Kiado .
  • Akaike , H. 1974 . “A New Look at the Statistical Model Identification” . IEEE Transactions on Automatic Control , AC-19 : 716 – 723 .
  • Akaike , H. 1980a . “Likelihood and the Bayes Procedure in Bayesian Statistics” . In Bayesian Statistics , Edited by: Bernado , J. N. , DeGroot , M. H. , Lindley , D. V. and Smith , A. F.M. 141 – 166 . Valencia , , Spain : University Press .
  • Akaike , H. 1980b . “Seasonal Adjustment by a Bayesian Modeling” . Journal of Time Series Analysis , 1 : 1 – 13 .
  • Akaike , H. and Ishiguro , M. 1980 . “BAYSEA, A Bayesian Seasonal Adjustment Program” . In Computer Science Monographs No. 13 , Tokyo : The Institute of Statistical Mathematics .
  • Akaike , H. and Ishiguro , M. 1983 . “Comparative Study of the X-11 and BAYSEA Procedures of Seasonal Adjustment” . In Applied Time Series Analysis of Economic Data , Edited by: Zellner , A. Washington , D.C. : U.S. Department of Commerce, Bureau of the Census .
  • Anderson , B. D.O. and Moore , J. B. 1979 . Optimal Filtering , Englewood Cliffs , N.J. : Prentice Hall .
  • Box , G. E.P. and Jenkins , G. M. 1970 . Time Series Analysis, Forecasting and Control , San Francisco : Holden-Day .
  • Brotherton , T. and Gersch , W. “A Data Analytic Approach to the Smoothing Problem and Some of Its Variations” . Proceedings of the 20th IEEE Conference on Decision and Control . pp. 1061 – 1099 .
  • Chan , S. W. , Goodwin , G. C. and Sin , K. S. “Convergence Properties of the Solutions of the Ricatti Difference Equation” . Proceedings of the 21st IEEE Conference on Decision and Control . pp. 300 – 305 .
  • Cleveland , W. S. and Devlin , S. J. 1980 . “Calendar Effects in Monthly Time Series; Detection by Spectrum Analysis and Graphical Methods” . Journal of the American Statistical Association , 75 : 487 – 496 .
  • Cleveland , W. P. and Grupe , M. R. 1983 . “Modeling Time Series When Calendar Effects Are Present” . In Applied Time Series Analysis of Economic Data , Edited by: Zellner , A. Washington , D.C. : Department of Commerce, Bureau of the Census .
  • Cleveland , W. P. and Tiao , G. C. 1976 . “Decomposition of Seasonal Time Series: A Model for the Census X-11 Program” . Journal of the American Statistical Association , 71 : 581 – 587 .
  • Duncan , D. and Horn , S. 1972 . “Linear Dynamic Recursive Estimation From the Viewpoint of Regression Analysis” . Journal of the American Statistical Association , 67 : 815 – 821 .
  • Gersch , W. and Kitagawa , G. 1983 . “The Prediction of Time Series with Trends and Seasonalities” . Journal of Business & Economic Statistics , 1 : 253 – 264 .
  • Good , I. J. 1965 . The Estimation of Probabilities , Cambridge , Mass. : MIT Press .
  • Good , I. J. and Gaskins , R. A. 1980 . “Density Estimation and Bump Hunting by the Penalized Likelihood Method Exemplified by Scattering and Meteorite Data” . Journal of the American Statistical Association , 75 : 42 – 73 .
  • Harvey , A. C. and Phillips , G. P.A. 1979 . “Maximum Likelihood Estimation of Regression Models with Autoregressive-Moving Average Disturbances” . Biometrika , 66 : 49 – 58 .
  • Hillmer , S. C. 1982 . “Forecasting Time Series with Trading Day Variation” . Journal of Forecasting , 1 : 385 – 395 .
  • Hillmer , S. C. , Bell , W. R. and Tiao , G. C. 1983 . “Modeling Considerations in the Seasonal Adjustment of Economic Time Series” . In Applied Time Series Analysis of Economic Data , Edited by: Zellner , A. Washington , D.C. : U.S. Department of Commerce, Bureau of the Census .
  • Hillmer , S. C. and Tiao , G. C. 1982 . “An ARIMA-Based Approach to Seasonal Adjustment” . Journal of the American Statistical Association , 77 : 63 – 70 .
  • Kalman , R. E. 1960 . “A New Approach to Linear Filtering and Prediction Problems” . Trans. ASME, Journal of Basic Engineering , 80 : 35 – 45 . Ser. D
  • Kitagawa , G. 1981 . “A Nonstationary Time Series Model and Its Fitting by a Recursive Technique” . Journal of Time Series Analysis , 2 : 103 – 116 .
  • Lindley , D. V. and Smith , A. F.M. 1972 . “Bayes Estimate for the Linear Model” . Journal of the Royal Statistical Society , 34 : 1 – 41 . Ser. B
  • Meditch , J. S. 1969 . Stochastic Optimal Linear Estimation and Control , New York : McGraw Hill .
  • Pierce , D. A. 1978 . “Seasonal Adjustment When Both Deterministic and Stochastic Seasonality Are Present” . In Seasonal Analysis of Economic Time Series , Edited by: Zellner , A. Washington , D.C. : U.S. Department of Commerce, Bureau of the Census .
  • Shiller , R. 1973 . “A Distributed Lag Estimator Derived From Smoothness Priors” . Econometrica , 41 : 775 – 778 .
  • Shiskin , J. and Plewes , T. J. 1978 . “Seasonal Adjustment of the U.S. Employment Rate” . The Statistician , 27 : 181 – 202 .
  • Shiskin , J. , Young , A. H. and Musgrave , J. C. 1967 . “The X-11 Variant of Census Method II Seasonal Adjustment Program” , Washington , D.C. : U.S. Bureau of the Census . Technical Paper 15
  • Thompson , H. E. and Tiao , G. C. 1971 . “Analysis of Telephone Data: A Case of Forecasting Seasonal Time Series” . The Bell System Journal of Economics and Management Science , 2 : 515
  • Wahba , G. 1977 . “A Survey of Some Smoothing Problems and the Method of Generalized Cross-Validation for Solving Them” . In Applications of Statistics , Edited by: Krishnaiah , P. R. 507 – 524 . Amsterdam : North Holland .
  • Wahba , G. and Wold , S. 1975 . “A Complete Automatic French Curve: Fitting Spline Functions by Cross Validations” . Communications in Statistics , 4 : 1 – 17 .
  • Wecker , W. E. and Ansley , C. F. 1983 . “The Signal Extraction Approach to Nonlinear Regression and Spline Smoothing” . Journal of the American Statistical Association , 78 : 81 – 89 .
  • Whittaker , E. T. 1923 . “On a New Method of Graduation” . Proceedings of the Edinborough Mathematical Society , 41 : 63 – 75 .
  • Young , P. C. and Jakeman , A. J. 1979 . “The Estimation of Input Variables in Stochastic Dynamic Systems” , Canberra , , Australia : Australian National University, Centre for Resource and Environmental Studies . Report No. AS/R28

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.