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Modelling interest rates with a cointegrated VAR-GARCH model

Author

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  • BAUWENS, Luc

    (Center for Operations Research and Econometrics (CORE), Université catholique de Louvain (UCL), Louvain la Neuve, Belgium)

  • DEPRINS, Dominique

    (Facultés Universitaires Saint-Louis, Brussels, and Institut de Statistique, Université catholique de Louvain (UCL), Louvain la Neuve, Belgium)

  • VANDEUREN, Jean-Pierre

    (Département de Mathématique, Université catholique de Louvain (UCL), Louvain la Neuve, Belgium)

Abstract

We use a bivariate VAR model to model and predict the joint evolution of short term and long term interest rates. We introduce a GARCH effect on the innovations of the model in order to account for the changing volatility of the series. We test the cointegration of the two interest rates, which is implied by a present value relation between the rates. The cointegration test is done both with and without taking account of the GARCH effect. The empirical results for five countries (Belgium, Germany, France, Great Britain and the USA) point to the same conclusions: i) the incorporation of the GARCH part allows to conclude more clearly that a cointegration relation exists; ii) GARCH effects are quite present; and iii) the models are useful for short term predictions of interest rates.

Suggested Citation

  • BAUWENS, Luc & DEPRINS, Dominique & VANDEUREN, Jean-Pierre, 1997. "Modelling interest rates with a cointegrated VAR-GARCH model," LIDAM Discussion Papers CORE 1997080, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:1997080
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    References listed on IDEAS

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    1. BAUWENS, Luc & VANDEUREN, Jean-Pierre, 1995. "On the Weak Consistency of the Quasi-Maximum Likelihood Estimator in VAR Models with BEKK-GARCH(1,q) Errors," LIDAM Discussion Papers CORE 1995038, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Kim, Kiwhan & Schmidt, Peter, 1993. "Unit root tests with conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 59(3), pages 287-300, October.
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    4. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    5. Pantula, Sastry G & Gonzalez-Farias, Graciela & Fuller, Wayne A, 1994. "A Comparison of Unit-Root Test Criteria," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 449-459, October.
    6. Campbell, John Y & Shiller, Robert J, 1987. "Cointegration and Tests of Present Value Models," Journal of Political Economy, University of Chicago Press, vol. 95(5), pages 1062-1088, October.
    7. Sargent, Thomas J., 1979. "A note on maximum likelihood estimation of the rational expectations model of the term structure," Journal of Monetary Economics, Elsevier, vol. 5(1), pages 133-143, January.
    8. Cheung, Yin-Wong & Lai, Kon S, 1993. "Finite-Sample Sizes of Johansen's Likelihood Ration Tests for Conintegration," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 55(3), pages 313-328, August.
    9. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Cited by:

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    2. Röthig, Andreas, 2004. "Currency Futures and Currency Crises," Darmstadt Discussion Papers in Economics 136, Darmstadt University of Technology, Department of Law and Economics.
    3. Lengwiler, Yvan & Lenz, Carlos, 2010. "Intelligible factors for the yield curve," Journal of Econometrics, Elsevier, vol. 157(2), pages 481-491, August.
    4. Chang, Yoosoon & Miller, J. Isaac & Park, Joon Y., 2005. "Extracting a Common Stochastic Trend: Theories with Some Applications," Working Papers 2005-06, Rice University, Department of Economics.
    5. Ge, Yuanlong & Wang, H. Holly & Ahn, Sung K., 2008. "Implication of Cotton Price Behavior on Market Integration," 2008 Conference, April 21-22, 2008, St. Louis, Missouri 37623, NCCC-134 Conference on Applied Commodity Price Analysis, Forecasting, and Market Risk Management.
    6. Hui, Cho-Hoi & Fong, Tom Pak-Wing, 2015. "Price cointegration between sovereign CDS and currency option markets in the financial crises of 2007–2013," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 174-190.
    7. Röthig, Andreas, 2004. "Currency futures and currency crises," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 4022, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    8. Chang, Yoosoon & Isaac Miller, J. & Park, Joon Y., 2009. "Extracting a common stochastic trend: Theory with some applications," Journal of Econometrics, Elsevier, vol. 150(2), pages 231-247, June.

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