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DISCRETE TIME REPRESENTATIONS OF COINTEGRATED CONTINUOUS TIME MODELS WITH MIXED SAMPLE DATA

Published online by Cambridge University Press:  01 August 2009

Marcus J. Chambers
Marcus J. Chambers*
Affiliation:
University of Essex
*
*Address correspondence to Professor Marcus J. Chambers, Department of Economics, University of Essex, Wivenhoe Park, Colchester, Essex CO4 3SQ, England. Tel: +44 1206 872756; fax: +44 1206 872724; e-mail: [email protected].
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Abstract

This paper derives an exact discrete time representation corresponding to a triangular cointegrated continuous time system with mixed stock and flow variables and observable stochastic trends. The discrete time model inherits the triangular structure of the underlying continuous time system and does not suffer from the apparent excess differencing that has been found in some related work. It can therefore serve as a basis for the study of the asymptotic sampling properties of estimators of the model's parameters. Some further analytical and computational results that enable Gaussian estimation to be implemented are also provided.

Type
ARTICLES
Information
Econometric Theory , Volume 25 , Issue 4: Bergstrom Memorial Dedication Issue , August 2009 , pp. 1030 - 1049
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Abadir, K.M. & Magnus, J.R. (2005) Matrix Algebra. Cambridge University Press.CrossRefGoogle Scholar
Agbeyegbe, T.D. (1987) An exact discrete analog to a closed linear first-order continuous time system with mixed sample. Econometric Theory 3, 143–149.CrossRefGoogle Scholar
Bergstrom, A.R. (1984) Continuous time stochastic models and issues of aggregation over time. In Griliches, Z. & Intriligator, M.D. (eds.), Handbook of Econometrics, vol. 2, pp. 1145–1212. North-Holland.CrossRefGoogle Scholar
Bergstrom, A.R. (1985) The estimation of parameters in nonstationary higher-order continuous time dynamic models. Econometric Theory 1, 369–385.CrossRefGoogle Scholar
Bergstrom, A.R. (1990) Hypothesis testing in continuous time econometric models. In Bergstrom, A.R., Continuous Time Econometric Modelling, pp. 145–164. Oxford University Press.Google Scholar
Bergstrom, A.R. (1997) Gaussian estimation of mixed-order continuous time dynamic models with unobservable stochastic trends from mixed stock and flow data. Econometric Theory 13, 467–505.CrossRefGoogle Scholar
Bergstrom, A.R. (2009) The effects of differencing on the Gaussian likelihood of models with unobservable stochastic trends: a simple example. Econometric Theory 25 (this issue), 903–913.CrossRefGoogle Scholar
Bergstrom, A.R. & Nowman, K.B. (2007) A Continuous Time Econometric Model of the United Kingdom with Stochastic Trends. Cambridge University Press.CrossRefGoogle Scholar
Chambers, M.J. (1999) Discrete time representation of stationary and non-stationary continuous time systems. Journal of Economic Dynamics and Control 23, 619–639.CrossRefGoogle Scholar
Chambers, M.J. (2003) The asymptotic efficiency of cointegration estimators under temporal aggregation. Econometric Theory 19, 49–77.CrossRefGoogle Scholar
Chambers, M.J. (2006) On excess differencing in discrete time representations of cointegrated continuous time models with mixed sample. Unpublished, University of Essex.Google Scholar
Chambers, M.J. & McCrorie, J.R. (2007) Frequency domain estimation of temporally aggregated Gaussian cointegrated systems. Journal of Econometrics 136, 1–29.CrossRefGoogle Scholar
Hansen, L.P. & Sargent, T.J. (1983) The dimensionality of the aliasing problem in models with rational spectral densities. Econometrica 51, 377–388.CrossRefGoogle Scholar
Harvey, A.C. & Stock, J.H. (1985) The estimation of higher-order continuous time autoregressive models. Econometric Theory 1, 97–117.CrossRefGoogle Scholar
Harvey, A.C. & Stock, J.H. (1988) Continuous time autoregressive models with common stochastic trends. Journal of Economic Dynamics and Control 12, 365–384.CrossRefGoogle Scholar
Hastings, C. (1955) Approximations for Digital Computers. Princeton University Press.CrossRefGoogle Scholar
Jewitt, G. & McCrorie, J.R. (2005) Computing estimates of continuous time macroeconometric models on the basis of discrete data. Computational Statistics and Data Analysis 49, 397–416.CrossRefGoogle Scholar
Johansen, S. (1991) Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica 59, 1551–1580.CrossRefGoogle Scholar
Lütkepohl, H. & Claessen, H. (1997) Analysis of cointegrated VARMA processes. Journal of Econometrics 80, 223–239.CrossRefGoogle Scholar
McCrorie, J.R. (2000) Deriving the exact discrete analog of a continuous time system. Econometric Theory 16, 998–1015.CrossRefGoogle Scholar
McCrorie, J.R. (2003) The problem of aliasing in identifying finite parameter continuous time stochastic models. Acta Applicandae Mathematicae 79, 9–16.CrossRefGoogle Scholar
Pesaran, H.M., Shin, Y., & Smith, R.J. (2000) Structural analysis of vector error correction models with exogenous I(1) variables. Journal of Econometrics 97, 293–343.CrossRefGoogle Scholar
Phillips, P.C.B. (1973) The problem of identification in finite parameter continuous time models. Journal of Econometrics 1, 351–362.CrossRefGoogle Scholar
Phillips, P.C.B. (1978) The treatment of flow data in the estimation of continuous time systems. In Bergstrom, A.R., Catt, A.J.L., Peston, M.H., & Silverstone, B.D.J. (eds.), Stability and Inflation, pp.257–274. Wiley.Google Scholar
Phillips, P.C.B. (1991a) Optimal inference in cointegrated systems. Econometrica 59, 283–306.CrossRefGoogle Scholar
Phillips, P.C.B. (1991b) Error correction and long run equilibrium in continuous time. Econometrica 59, 967–980.CrossRefGoogle Scholar
Poskitt, D. (2006) On the identification and estimation of nonstationary and cointegrated ARMAX systems. Econometric Theory 22, 1138–1175.CrossRefGoogle Scholar
Robinson, P.M. & Hualde, J. (2003) Cointegration in fractional systems with unknown integration orders. Econometrica 71, 1727–1766.CrossRefGoogle Scholar
Simos, T. (1996) Gaussian estimation of a continuous time dynamic model with common stochastic trends. Econometric Theory 12, 361–373.CrossRefGoogle Scholar
van Loan, C.F. (1978) Computing integrals involving the matrix exponential. IEEE Transactions on Automatic Control AC–23, 395–404.CrossRefGoogle Scholar
Yap, S.F. & Reinsel, G.C. (1995) Estimation and testing for unit roots in a partially nonstationary vector autoregressive moving average model. Journal of the American Statistical Association 90, 253–267.CrossRefGoogle Scholar
Zadrozny, P. (1988) Gaussian likelihood of continuous time ARMAX models when data are stocks and flows at different frequencies. Econometric Theory 4, 108–124.CrossRefGoogle Scholar