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The Representation and Decomposition of Integrated Stationary Time Series

Part of:Inference from stochastic processes

Published online by Cambridge University Press:  01 July 2016

Zhao-Guo Chen and
Oliver D. Anderson
Zhao-Guo Chen*
Affiliation:
Statistics Canada
Oliver D. Anderson*
Affiliation:
University of Western Ontario
*
* Postal address: Time Series Research and Analysis Center, R. H. Coats Building, Statistics Canada, Ottawa, Ontario, Canada K1A 0T6.
** Postal address: Department of Statistical and Actuarial Sciences, Room 262 Western Science Centre, University of Western Ontario, London, Ontario, Canada N6A 5B7.
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Abstract

Learning from Matheron's representation (1973), and using the increment vector (PIV) methodology introduced by Cressie (1988) and developed by Chen and Anderson (1994), this paper presents a theory for the representation and decomposition of integrated stationary time series and gives some applications.

Keywords

DEGREE OF DIFFERENCINGDIFFERENCE EQUATIONSFORECASTINGFUNDAMENTALGENERALISEDAND PRIMARY INCREMENT VECTORSId AND Īd-SERIESINTRINSIC RANDOM FUNCTION AND ITS REPRESENTATIONOVERINTEGRATED MODELSRATE OF DIVERGENCEWOLD DECOMPOSITION

MSC classification

Primary:62M10: Time series, auto-correlation, regression, etc.

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 26 , Issue 3 , September 1994, pp. 799 - 819
Copyright
Copyright © Applied Probability Trust 1994 

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References

Beyer, W. H. (1987) CRC Handbook of Mathematical Sciences, 6th edn. CRC Press, Boca Raton, FL.Google Scholar
Box, G. E. P. and Jenkins, G. M. (1976) Time Series Analysis, Forecasting and Control, revised edn. Holden-Day, San Francisco.Google Scholar
Chen, Z.-G. (1988a) Consistent estimates for hidden frequencies in a linear process. Adv. Appl. Prob. 20, 295–314.Google Scholar
Chen, Z.-G. (1988b) An alternative consistent procedure for detecting hidden frequencies. J. Time Ser. Anal. 9, 301–317.Google Scholar
Chen, Z.-G. and Anderson, O. D. (1994a) Increment vector methodology: transforming nonstationary series to stationary series. Submitted for publication.Google Scholar
Chen, Z.-G. and Anderson, O. D. (1994b) The divergence rates of an integrated stationary time series. Submitted for publication.Google Scholar
Chen, Z.-G. and Anderson, O. D. (1994c) Polyvariograms and their asymptotes. Submitted for publication.Google Scholar
Cressie, N. (1988) A graphical procedure for determining nonstationarity in time series. J. Amer. Statist. Assoc 83, 1108–1116. Correction 85, 272 (1990).CrossRefGoogle Scholar
Delfiner, P. (1976) Linear estimation of non stationary spatial phenomena. In Advanced Geostatistics in the Mining Industry, ed. Guarascio, M., David, M. and Huijbregts, C., pp. 49–68, Reidel, Boston.CrossRefGoogle Scholar
Doob, J. (1953) Stochastic Processes. Wiley, New York.Google Scholar
Hannan, E. J. (1970) Multiple Time Series. Wiley, New York.CrossRefGoogle Scholar
Hildebrand, F. B. (1968) Finite-Difference Equations and Solutions. Prentice Hall, Englewood Cliffs, NJ.Google Scholar
Lakshmikantham, V. and Trigiante, D. (1988) Theory of Difference Equations: Numerical Methods and Applications. Academic Press, Boston.Google Scholar
Matheron, G. (1973) The intrinsic random functions and their applications. Adv. Appl. Prob. 5, 439–468.CrossRefGoogle Scholar
Priestley, M. B. (1965) Evolutionary spectra and non-stationary processes (with Discussion). J. R. Statist. Soc. B 27, 204–237.Google Scholar
Priestley, M. B. (1981) Spectral Analysis and Time Series, Vol. 1. Academic Press, London.Google Scholar
Tiao, G. C. and Grupe, M. R. (1980) Hidden periodic autoregressive-moving average models in time series data. Biometrika 67, 365–373.Google Scholar
Tong, H. (1990) Non-linear Time Series: A Dynamical System Approach. Oxford University Press.CrossRefGoogle Scholar
Yaglom, A. M. (1958) Correlation theory of processes with random stationary nth increments. Amer. Math. Soc. Transl. (2) 8, 87–141.Google Scholar
Yaglom, A. M. (1962) An Introduction to the Theory of Random Functions. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
Yaglom, A. M. (1987) Correlation Theory of Stationary and Related Random Functions I: Basic Results. Springer-Verlag, New York.Google Scholar