Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Studies in Nonlinear Dynamics & Econometrics

Ed. by Mizrach, Bruce

5 Issues per year


IMPACT FACTOR 2017: 0.855

CiteScore 2017: 0.76

SCImago Journal Rank (SJR) 2017: 0.668
Source Normalized Impact per Paper (SNIP) 2017: 0.894

Mathematical Citation Quotient (MCQ) 2017: 0.02

Online
ISSN
1558-3708
See all formats and pricing
More options …
Volume 17, Issue 3

Issues

Common large innovations across nonlinear time series

Philip Hans Franses / Richard Paap
Published Online: 2013-02-16 | DOI: https://doi.org/10.1515/snde-2012-0047

Abstract

We propose a multivariate nonlinear econometric time series model, which can be used to examine if there is common nonlinearity across economic variables. The model is a multivariate censored latent effects autoregression. The key feature of this model is that nonlinearity appears as separate innovation-like variables. Common nonlinearity can then be easily defined as the presence of common innovations. We discuss representation, inference, estimation and diagnostics. We illustrate the model for US and Canadian unemployment and find that US innovation variables have an effect on Canadian unemployment, and not the other way around, and also that there is no common nonlinearity across the unemployment variables.

Keywords: nonlinearity; common features; censored latent effects autoregression

References

  • Anderson, H., and F. Vahid. 1998. “Testing Multiple Equation Systems for Common Nonlinear Components.” Journal of Econometrics 84: 1–36.CrossrefGoogle Scholar

  • Berndt, E., B. Hall, E. Hall, and J. Hausman. 1974. “Estimation and Inference in Non-Linear Structural Models.” Annals of Economic and Social Measurement 3: 653–665.Google Scholar

  • Diebold, F., J. Lee, and G. Weinbach. 1994. “Regime Switching and Endogenous Transition Probablities.” In Nonstationary Time Series Analysis and Cointegration, edited by C. Hargreaves. Oxford: Oxford University Press, chapter 10, 283–302.Google Scholar

  • Diebold, F., and G. Rudebusch. 1996. “Measuring Business Cycles: A Modern Perspective.” Review of Economics and Statistics 78: 67–77.CrossrefGoogle Scholar

  • Franses, P., and R. Paap. 2002. “Censored Latent Effects Autoregression, with An Application to us Unemployment.” Journal of Applied Econometrics 17: 347–366.CrossrefGoogle Scholar

  • Franses, P., and D. van Dijk. 2001. Nonlinear Time Series Models in Empirical Finance. Cambridge: Cambridge University Press.Google Scholar

  • Gourieroux, C., and A. Monfort. 1994. “Testing Non-Nested Hypotheses,” In Handbook of Econometrics, volume IV, edited by R. Engle and D. McFadden. Amsterdam: North-Holland, chapter 44, 2583–2637.Google Scholar

  • Gourieroux, C., and A. Monfort. 1995. Statistics and Econometric Models. volume 2, Cambridge: Cambridge University Press.Google Scholar

  • Granger, C., and T. Teräsvirta. 1993. Modelling Nonlinear Economic Relations. Oxford: Oxford University Press.Google Scholar

  • Johnson, N., and S. Kotz. 1970. Distributions in Statistics: Continuous Univariate Distributions. Boston: Houghton Mifflin.Google Scholar

  • Kim, C.-J., and C. Nelson. 1998. “Business Cycle Turning Points, a New Coincident Index, and Tests of Duration Dependence on a Dynamic Factor Model with Regime Switching.” Review of Economics and Statistics 80: 188–201.CrossrefGoogle Scholar

  • Krolzig, H.-M. 1997. Markov Switching Vector Autoregressions: Modelling, Statistical Inference, and an Application to Business Cycle Inference. Berlin: Springer.Google Scholar

  • Maddala, G. 1983. Limited Dependent and Qualitative Variables in Econometrics, Econometric Society Monographs. volume 3, Cambridge: Cambridge University Press.Google Scholar

  • Philips, K. 1991. “A Two-Country Model for Stochastic Output with Changes in Regime.” Journal of International Economics 31: 121–142.CrossrefGoogle Scholar

  • Rosenbaum, S. 1961. “Moments of a Truncated Bivariate Normal Distribution.” Journal of the Royal Statistical Society B 23: 405–408.Web of ScienceGoogle Scholar

  • Santos Silva, J. 2001. “A Score Test for Non-Nested Hypotheses with Applications to Discrete Data Models.” Journal of Applied Econometrics 16: 577–597.CrossrefGoogle Scholar

  • Vuong, Q. 1989. “Likelihood Ratio Tests for Model Selection and Non-Nested Hypotheses.” Econometrica 57: 307–333.CrossrefGoogle Scholar

  • Wolak, F. 1989. “Local and Global Testing of Linear and Nonlinear Inequality Constraints in Nonlinear Econometric Models.” Econometric Theory 5: 1–35.CrossrefGoogle Scholar

About the article

Corresponding author: Philip Hans Franses, Erasmus University of Rotterdam, Burgemeester Oudlaan 50, 3062 PA Rotterdam, The Netherlands, Phone: +3110 4081273, Fax: +3110 4089162


Published Online: 2013-02-16

Published in Print: 2013-05-01


It is easy to see that σu12 is not identified if either v1t or v2t is positive. Hence, if one wants to allow for correlation between u1t and u2t its identification will be based on observations where both v1t and v2t are zero in which case there is limited information about the values of u1t and u2t Unreported estimation results show that the covariance is empirically badly identified. Therefore we opt for σu12.


Citation Information: Studies in Nonlinear Dynamics and Econometrics, Volume 17, Issue 3, Pages 251–263, ISSN (Online) 1558-3708, ISSN (Print) 1081-1826, DOI: https://doi.org/10.1515/snde-2012-0047.

Export Citation

©2013 by Walter de Gruyter Berlin Boston.Get Permission

Comments (0)

Please log in or register to comment.
Log in