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A NOTE ON GENERALIZING THE CONCEPT OF COINTEGRATION

Published online by Cambridge University Press:  30 July 2014

Stephen G. Hall ,
P.A.V.B. Swamy  and
George S. Tavlas
Stephen G. Hall
Affiliation:
Leicester University, Bank of Greece and Pretoria University
P.A.V.B. Swamy
Affiliation:
Federal Reserve Board (Retired)
George S. Tavlas*
Affiliation:
Bank of Greece
*
Address correspondence to: George S. Tavlas, Monetary Policy Council, Bank of Greece, 21 El. Venizelos Ave., 102 50 Athens, Greece; e-mail: gtavlas@bankofgreece.gr.
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Abstract

Building on the time-varying-coefficient (TVC) model, we propose a generalization of the concept of cointegration, allowing for the possibility that a set of variables measured with error entails a nonlinear relationship with unknown functional form. Both the dependent and explanatory variables of this relationship may be nonstationary (not necessarily of unit-root type), but there exists a nonlinear combination of all these explanatory variables that completely explains all the variation in the dependent variable. The TVC model allows us to test for the presence of this generalized cointegration in the absence of knowledge of the true nonlinear functional form and the full set of explanatory variables. We present the basic stages of the technique and discuss in detail how the issues of nonstationarity and cointegration affect each stage of the TVC estimation procedure.

Keywords

Generalized CointegrationTime-Varying-Coefficient Model
Type
Notes
Information
Macroeconomic Dynamics , Volume 19 , Issue 7 , October 2015 , pp. 1633 - 1646
Copyright
Copyright © Cambridge University Press 2014 

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References

REFERENCES

Al-Abri, A.S. and Goodwin, B.K. (2009) Re-examining the exchange rate pass-through into import prices using nonlinear estimation techniques: Threshold cointegration. International Review of Economics and Finance 18 (1), 142–161.CrossRefGoogle Scholar
Arouri, M., Jawadi, D., and Nguyen, D. (2012) Modeling nonlinear and heterogeneous links in international monetary markets. Macroeconomic Dynamics 16, 232–251.CrossRefGoogle Scholar
Banerjee, A. and Pitarakis, J. (2012) Functional Cointegration: Definition and Nonparametric Estimation. MPRA Paper 38846, University Library of Munich.Google Scholar
Berenguer-Rico, V. and Gonzalo, J. (2012) Summability of Stochastic Processes: A Generalization of Integration and Co-integration Valid for Non-linear Processes. Working paper, Universidad Carlos III de Madrid.Google Scholar
Cavanagh, C.L. and Rothenberg, T.J. (1995) Generalized least squares with nonnormal errors. In Maddala, G.S., Phillips, P.C.B., and Srinivasan, T.N. (eds.), Advances in Econometrics and Quantitative Economics, Chap. 11. Oxford, UK: Blackwell.Google Scholar
Choi, I. and Saikkonen, P. (2010) Tests for non-linear cointegration. Econometric Theory 26, 682–709.CrossRefGoogle Scholar
Cramér, H. (1946) Mathematical Methods of Statistics. Princeton, NJ: Princeton University Press.Google Scholar
Cuthbertson, K., Hall, S.G., and Taylor, M. (1990) Applied Econometric Techniques. Ann Arbor: University of Michigan Press.Google Scholar
Dolado, J.J., Gonzalo, J., and Marmol, F. (2001) Cointegration. In Baltagi, B.H. (ed.), A Companion to Theoretical Econometrics, Chap. 30. Malden, MA: Blackwell.Google Scholar
Enders, W. (2009) Applied Econometric Techniques. Hoboken, NJ: Wiley.Google Scholar
Engle, R.F. and Granger, C.W.J. (1987) Co-integration and error correction: Representation, estimation, and testing. Econometrica 55 (2), 251–276.CrossRefGoogle Scholar
Gonzalo, J. and Pitarakis, J.Y. (2006) Threshold effects in co-integrating regressions. Oxford Bulletin of Economics and Statistics 68, 813–833.CrossRefGoogle Scholar
Granger, C.W.J. (2008) Nonlinear models: Where do we go next—Time-varying parameter models? Studies in Nonlinear Dynamics and Econometrics 12 (3), 1–9.Google Scholar
Greene, W.H. (2008) Econometric Analysis, 6th ed.Upper Saddle River, NJ: Pearson/Prentice Hall.Google Scholar
Jawadi, F. (2012) Introduction to time-varying modeling with macroeconomic and financial data, Macroeconomic Dynamics 16, 167–175.CrossRefGoogle Scholar
Kanas, A. (2003) Nonlinear cointegration between stock prices and dividends. Applied Economics Letters 10 (7), 401–405.CrossRefGoogle Scholar
Karlsen, H.A., Myklebust, T., and Tjøstheim, D. (2007) Nonparametric estimation in a nonlinear cointegration type model. Annals of Statistics 35 (1), 252–299.CrossRefGoogle Scholar
Kasparis, I. (2008) Detection of functional form misspecification in cointegrating relations. Econometric Theory 24, 1373–1403.CrossRefGoogle Scholar
Kasparis, I. (2011) Functional form misspecification in regressions with a unit root. Econometric Theory 27, 285–311.CrossRefGoogle Scholar
Lee, C.C. (2013) Insurance and real output: The key role of banking activities. Macroeconomic Dynamics 17, 235–260.CrossRefGoogle Scholar
Lehmann, E.L. and Casella, G. (1998) Theory of Point Estimation, 2nd ed.Berlin: Springer-Verlag.Google Scholar
Park, J.Y. and Phillips, P.C.B. (2001) Non-linear regression with integrated time series. Econometrica 69, 117–161.CrossRefGoogle Scholar
Schienle, M. (2011) Nonparametric Nonstationary Regression with Many Covariates. Humboldt-Universität zu Berlin, Discussion paper 076.Google Scholar
Skyrms, B. (1988) Probability and causation. Journal of Econometrics 39 (1/2), 53–68.CrossRefGoogle Scholar
Swamy, P.A.V.B. (1971) Statistical Inference in Random Coefficient Regression Models. New York: Springer-Verlag.CrossRefGoogle Scholar
Swamy, P.A.V.B. (1974) Linear models with random coefficients. In Zarembka, P. (ed.), Frontiers in Econometrics, pp. 143–168. New York: Academic Press.Google Scholar
Swamy, P.A.V.B., Chang, I.L., Mehta, J.S., and Tavlas, G.S. (2003) Correcting for omitted-variable and measurement-error bias in autoregressive model estimation with panel data. Computational Economics 22, 225–253.Google Scholar
Swamy, P.A.V.B. and Mehta, J.S. (1975) Bayesian and non-Bayesian analysis of switching regressions and a random coefficient regression model. Journal of the American Statistical Association 70, 593–602.Google Scholar
Swamy, P.A.V.B., Mehta, J.S., Tavlas, G.S., and Hall, S.G. (2014) Small area estimation with correctly specified linking models, Chap. 10, In Ma, Jun and Wohar, Mark E. (eds.), Recent Advances in Estimating Nonlinear Models, Chap. 10, pp. 193–228. New York: Springer-Verlag.Google Scholar
Swamy, P.A.V.B. and Tavlas, G.S. (2001) Random coefficient models. In Baltagi, B.H. (ed.), A Companion to Theoretical Econometrics, Chap. 19. Malden, MA: Blackwell.Google Scholar
Swamy, P.A.V.B. and Tavlas, G.S. (2006) A note on Muth's rational expectations hypothesis: A time-varying-coefficient interpretation. Macroeconomic Dynamics 10, 415–425.CrossRefGoogle Scholar
Swamy, P.A.V.B., Tavlas, G.S., and Hall, S.G. (in press) Microproduction functions with unique coefficients and errors: A reconsideration and respecification. Macroeconomic Dynamics.Google Scholar
Swamy, P.A.V.B., Tavlas, G.S., Hall, S.G., and Hondroyiannis, G. (2010) Estimation of parameters in the presence of model misspecification and measurement error. Studies in Nonlinear Dynamics and Econometrics 14 (1), 1–33.Google Scholar
Swamy, P.A.V.B., Tavlas, G.S., and Hondroyiannis, G. (2009) The New Keynesian Phillips curve in a time-varying coefficient environment: Some European evidence. Macroeconomic Dynamics 13, 149–166.Google Scholar
Swamy, P.A.V.B. and von zur Muehlen, P. (1988) Further thoughts on testing for causality with econometric models. Journal of Econometrics 39, 105–147.CrossRefGoogle Scholar
Wang, Q. and Phillips, P.C.B. (2009) Structural nonparametric cointegrating regressions. Econometrica 77, 1901–1948.Google Scholar