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Nonparametric Nonlinear Cotrending Analysis, with an Application to Interest and Inflation in the U.S

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  • Bierens, H.J.

    (Tilburg University, Center for Economic Research)

Abstract

Given the assumption that the components of a vector time series are stationary about nonlinear deterministic time trends, nonlinear co-trending is the phenomenon that one or more linear combinations of the time series are stationary about a linear trend, hence the series have common nonlinear deterministic time trends.In this paper we shall develop nonparametric tests for nonlinear co-trending.The tests are based on generalized eigenvalues, where the two matrices involved are constructed nonparametrically on the basis of partial sums.We apply this approach to the federal funds rate and the CPI inflation rate in the U.S., using monthly data.It appears that these series are nonlinearly co-trended, where the nonlinear trend in the inflation rate is positively related to the nonlinear trend in the interest rate.This positive relation between interest and inflation is known in the literature as the price puzzle. Thus, our result suggests that the price puzzle is due to a common nonlinear time trend in the series involved.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 1996-62.

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Date of creation: 1996
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Handle: RePEc:dgr:kubcen:199662

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Web page: http://center.uvt.nl

Related research

Keywords: econometrics; time series; inflation; interest rate; USA;

References

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  1. Perron, Pierre, 1990. "Testing for a Unit Root in a Time Series with a Changing Mean," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 153-62, April.
  2. Bierens, Herman J., 1993. "Higher-order sample autocorrelations and the unit root hypothesis," Journal of Econometrics, Elsevier, vol. 57(1-3), pages 137-160.
  3. Christopher A. Sims, 1992. "Interpreting the Macroeconomic Time Series Facts: The Effects of Monetary Policy," Cowles Foundation Discussion Papers 1011, Cowles Foundation for Research in Economics, Yale University.
  4. Peter C. Schotman & Herman K. van Dijk, 1991. "On Bayesian routes to unit roots," Discussion Paper / Institute for Empirical Macroeconomics 43, Federal Reserve Bank of Minneapolis.
  5. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
  6. Bierens, H.J. & Ploberger, W., 1995. "Asymptotic theory of integrated conditional moment tests," Discussion Paper 1995-124, Tilburg University, Center for Economic Research.
  7. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
  8. Peter C.B. Phillips & Pierre Perron, 1986. "Testing for a Unit Root in Time Series Regression," Cowles Foundation Discussion Papers 795R, Cowles Foundation for Research in Economics, Yale University, revised Sep 1987.
  9. Johansen, Soren & Juselius, Katarina, 1990. "Maximum Likelihood Estimation and Inference on Cointegration--With Applications to the Demand for Money," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 52(2), pages 169-210, May.
  10. 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.
  11. Bierens, H.J., 1995. "Nonparametric cointegration analysis," Discussion Paper 1995-123, Tilburg University, Center for Economic Research.
  12. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  13. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
  14. Bierens, Herman J., 1997. "Testing the unit root with drift hypothesis against nonlinear trend stationarity, with an application to the US price level and interest rate," Journal of Econometrics, Elsevier, vol. 81(1), pages 29-64, November.
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Cited by:
  1. Roberto Ricciuti, 2008. "The quest for a fiscal rule: Italy, 1861–1998," Cliometrica, Journal of Historical Economics and Econometric History, Association Française de Cliométrie (AFC), vol. 2(3), pages 259-274, October.
  2. Fabio C. Bagliano & Claudio Morana, 2006. "International Macroeconomic Dynamics: a Factor Vector Autoregressive Approach," ICER Working Papers 41-2006, ICER - International Centre for Economic Research.
  3. Roberto Tatiwa Ferreira & Ivan Castelar, 2006. "Nonlinearities And Price Puzzle In Brazil," Anais do XXXIV Encontro Nacional de Economia [Proceedings of the 34th Brazilian Economics Meeting] 163, ANPEC - Associação Nacional dos Centros de Pósgraduação em Economia [Brazilian Association of Graduate Programs in Economics].
    • Roberto Tatiwa Ferreira & Ivan Castelar, 2008. "Nonlinearities and Price Puzzle in Brazil," Economia, ANPEC - Associação Nacional dos Centros de Pósgraduação em Economia [Brazilian Association of Graduate Programs in Economics], vol. 9(1), pages 47-62.
  4. Juan Carlos Cuestas, 2007. "Purchasing Power Parity In Central And Eastern European Countries: An Analysis Of Unit Roots And Nonlinearities," Working Papers. Serie AD 2007-22, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  5. Fabio C. Bagliano & Claudio Morana, 2007. "Business Cycle Comovement in the G-7: Common Shocks or Common Transmission Mechanisms?," Carlo Alberto Notebooks 40, Collegio Carlo Alberto.
  6. Bouoiyour, Jamal & Marimoutou, Velayoudoum & Rey, Serge, 2003. "Trends non linéaires et co-trending dans le taux de change réel effectif du dinar tunisien
    [Nonlinear trend and co-trending in the Tunisian real effective exchange rate]
    ," MPRA Paper 30249, University Library of Munich, Germany.
  7. Christian Gourieroux & Joanna Jasiak, 1999. "Nonlinear Persistence and Copersistence," Working Papers 99-63, Centre de Recherche en Economie et Statistique.
  8. Maghyereh, A. & Al-Zoubi, H., 2006. "Does Fisher Effect Apply in Developing Countries: Evidence From a Nonlinear Cotrending Test applied to Argentina, Brazil, Malysia, Mexico, Korea and Turkey," Applied Econometrics and International Development, Euro-American Association of Economic Development, vol. 6(2).
  9. Nuno Cassola & Claudio Morana, 2007. "Comovements in Volatility in the Euro Money Market," ICER Working Papers 7-2007, ICER - International Centre for Economic Research.
  10. HOLMES, Mark J, 2008. "Non-Linear Trend Stationarity And Co-Trending In Latin American Real Exchange Rates," Applied Econometrics and International Development, Euro-American Association of Economic Development, vol. 8(1), pages 107-118.
  11. Roberto Ricciuti, 2004. "Nonlinearity in testing for fiscal sustainability," Money Macro and Finance (MMF) Research Group Conference 2003 80, Money Macro and Finance Research Group.

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