On models and methods for Bayesian time series analysis. (English) Zbl 0584.62191
A new approach to the applied econometric problems of adjusting and forecasting univariate time series with component models is described. The models used differ from the familiar ARIMA class by having components derived from fractionally differenced Gaussian processes and by allowing for simultaneous estimation of deterministic along with random components.
Methodology proposed for fitting these models is based on Bayesian principles, with particular emphasis placed on assessing sensitivity of conclusions to model assumptions. The methods require extensive likelihood-related computations, using frequency domain representations to produce a range of new graphical diagnostic displays. They are illustrated with an extended example.
Methodology proposed for fitting these models is based on Bayesian principles, with particular emphasis placed on assessing sensitivity of conclusions to model assumptions. The methods require extensive likelihood-related computations, using frequency domain representations to produce a range of new graphical diagnostic displays. They are illustrated with an extended example.
MSC:
| 62P20 | Applications of statistics to economics |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
Keywords:
prediction; adjustment; forecasting univariate time series; component models; fractionally differenced Gaussian processes; simultaneous estimation of deterministic along with random components; Bayesian principles; sensitivity; frequency domain representations; graphical diagnostic displaysReferences:
| [1] | Bell, W. R., Signal extraction for nonstationary time series, Annals of Statistics, 12, 646-664 (1984) · Zbl 0542.62081 |
| [2] | Bell, W. R.; Hillmer, S. C., Issues involved with the seasonal adjustment of economic time series, Journal of Business and Economic Statistics, 2, 291-320 (1984) |
| [3] | Box, G. E.P.; Hillmer, S. C.; Tiao, G. C., Analysis and modelling of seasonal time series, (Zellner, A., Seasonal analysis of economic time series (1978), U.S. Department of Commerce, Bureau of the Census: U.S. Department of Commerce, Bureau of the Census Washington, DC), 309-334 |
| [4] | Box, G. E.P.; Jenkins, G. M., Time series analysis: Forecasting and control (1976), Holden Day: Holden Day San Francisco, CA · Zbl 0109.37303 |
| [5] | Burman, J. P., Seasonal adjustment by signal extraction, Journal of the Royal Statistical Society, A 143, 321-337 (1980) · Zbl 0461.62074 |
| [6] | Cleveland, W. P.; Tiao, G. C., Decomposition of seasonal time series: A model for the X-11 program, Journal of the American Statistical Association, 71, 581-587 (1976) · Zbl 0336.62077 |
| [7] | Cramér, H., On harmonic analysis in certain functional spaces, Arkiv Mat. Astr. Fysik, 28B, no. 12, 17 (1942) · JFM 68.0237.04 |
| [8] | Dempster, A. P., Some formulas useful for covariance estimation with Gaussian linear component models, (Kallianpur, G.; Krishnaiah, P. R.; Ghosh, J. K., Statistics and probability: Essays in honor of C.R. Rao (1982), North-Holland: North-Holland Amsterdam), 213-220 · Zbl 0539.62082 |
| [9] | Dempster, A. P., Derivative and related computations for Gaussian time series analysis, (Krishnaiah, P. R., Multivariate analysis — VI: Proceedings of the sixth international symposium on multivariate analysis (1985), North-Holland: North-Holland Amsterdam), 165-176 · Zbl 0588.62161 |
| [10] | Geweke, J.; Porter-Hudak, S., The estimation and application of long-memory time series models, Journal of Time Series Analysis, 4, 221-238 (1983) · Zbl 0534.62062 |
| [11] | Granger, C.; Joyeux, R., An introduction to long-memory time series models and fractional differencing, Journal of Time Series Analysis, 1, 15-29 (1980) · Zbl 0503.62079 |
| [12] | Hillmer, S. C., Measures of variability for model-based seasonal adjustment procedures, Journal of Business and Economic Statistics, 3, 60-68 (1985) |
| [13] | Hosking, J., Fractional differencing, Biometrika, 68, 165-176 (1981) · Zbl 0464.62088 |
| [14] | Jonas, A. B., Persistent memory random processes, (Unpublished Ph.D Thesis (1983), Department of Statistics, Harvard University: Department of Statistics, Harvard University Cambridge, MA) |
| [15] | Kolmogorov, A. N., Wienersche Spiralen und einige andere interessante Kurven im Hilbertschen Raum, Comptes Rendus (Doklady) de l’Academie des Sciences de l’URSS, 26, no. 2 (1940), (in German). · Zbl 0022.36001 |
| [16] | Pierce, D. A., Seasonal adjustment when both deterministic and stochastic seasonality are present, (Zellner, A., Seasonal analysis of economic time series (1978), U.S. Department of Commerce, Bureau of the Census: U.S. Department of Commerce, Bureau of the Census Washington, DC), 242-269 |
| [17] | Pierce, D. A., A survey of recent developments in seasonal adjustment, The American Statistician, 34, 125-134 (1980) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
