On The Identification and Estimation of Partially Nonstationary ARMAX Systems
This paper extends current theory on the identification and estimation of vector time series models to nonstationary processes. It examines the structure of dynamic simultaneous equations systems or ARMAX processes that start from a given set of initial conditions and evolve over a given, possibly infinite, future time horizon. The analysis proceeds by deriving the echelon canonical form for such processes. The results are obtained by amalgamating ideas from the theory of stochastic difference equations with adaptations of the Kronecker index theory of dynamic systems. An extension of these results to the analysis of unit-root, partially nonstationary (cointegrated) time series models is also presented, leading to straightforward identification conditions for the error correction, echelon canonical form. An innovations algorithm for the evaluation of the exact Gaussian likelihood is given and the asymptotic properties of the approximate Gaussian estimator and the exact maximum likelihood estimator based upon the algorithm are derived. Examples illustrating the theory are discussed and some experimental evidence is also presented.
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- Phillips, P C B, 1991.
"Optimal Inference in Cointegrated Systems,"
Econometric Society, vol. 59(2), pages 283-306, March.
- Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-80, November.
- Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
- Lutkepohl, Helmut & Poskitt, D S, 1996.
"Specification of Echelon-Form VARMA Models,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 14(1), pages 69-79, January.
- Poskitt, Don S, 2000. "Strongly Consistent Determination of Cointegrating Rank via Canonical Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(1), pages 77-90, January.
- Lutkepohl, Helmut & Claessen, Holger, 1997. "Analysis of cointegrated VARMA processes," Journal of Econometrics, Elsevier, vol. 80(2), pages 223-239, October.
- Wickens, Michael R., 1996. "Interpreting cointegrating vectors and common stochastic trends," Journal of Econometrics, Elsevier, vol. 74(2), pages 255-271, October.
- Breusch, Trevor S & Wickens, Michael R., 1987. "Dynamic Specification, the Long Run and the Estimation of Transformed Regression Models," CEPR Discussion Papers 154, C.E.P.R. Discussion Papers.
- Brockwell, P. J. & Davis, R. A., 1988. "Simple consistent estimation of the coefficients of a linear filter," Stochastic Processes and their Applications, Elsevier, vol. 28(1), pages 47-59, April.
- Hosoya, Yuzo, 1977. "On the Granger Condition for Non-Causality," Econometrica, Econometric Society, vol. 45(7), pages 1735-36, October.
- Banerjee, Anindya & Dolado, Juan J. & Galbraith, John W. & Hendry, David, 1993. "Co-integration, Error Correction, and the Econometric Analysis of Non-Stationary Data," OUP Catalogue, Oxford University Press, number 9780198288107.
- Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
- Poskitt, D. S., 2003. "On the specification of cointegrated autoregressive moving-average forecasting systems," International Journal of Forecasting, Elsevier, vol. 19(3), pages 503-519.
- Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
- Saikkonen, Pentti, 1995. "Problems with the Asymptotic Theory of Maximum Likelihood Estimation in Integrated and Cointegrated Systems," Econometric Theory, Cambridge University Press, vol. 11(05), pages 888-911, October.
- Cheng Hsiao, 1997. "Cointegration and Dynamic Simultaneous Equations Model," Econometrica, Econometric Society, vol. 65(3), pages 647-670, May.
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