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Modeling the U.S. Short-Term Interest Rate by Mixture Autoregressive Processes

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  • Markku Lanne
  • Pentti Saikkonen

Abstract

A new kind of mixture autoregressive model with GARCH errors is introduced and applied to the U.S. short-term interest rate. According to the diagnostic tests developed in the article and further informal checks, the model is capable of capturing both of the typical characteristics of the short-term interest rate: volatility persistence and the dependence of volatility on the level of the interest rate. The model also allows for regime switches whose presence has been a third central result emerging from the recent empirical literature on the U.S. short-term interest rate. Realizations generated from the estimated model seem stable and their properties resemble those of the observed series closely. The drift and diffusion functions implied by the new model are in accordance with the results in much of the literature on continuous-time diffusion models for the short-term interest rate, and the term structure implications agree with historically observed patterns. , .

Suggested Citation

  • Markku Lanne & Pentti Saikkonen, 2003. "Modeling the U.S. Short-Term Interest Rate by Mixture Autoregressive Processes," Journal of Financial Econometrics, Oxford University Press, vol. 1(1), pages 96-125.
  • Handle: RePEc:oup:jfinec:v:1:y:2003:i:1:p:96-125
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    Cited by:

    1. Leena Kalliovirta & Mika Meitz & Pentti Saikkonen, 2015. "A Gaussian Mixture Autoregressive Model for Univariate Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(2), pages 247-266, March.
    2. Maheu, John M. & Yang, Qiao, 2016. "An infinite hidden Markov model for short-term interest rates," Journal of Empirical Finance, Elsevier, vol. 38(PA), pages 202-220.
    3. Badescu Alex & Kulperger Reg & Lazar Emese, 2008. "Option Valuation with Normal Mixture GARCH Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(2), pages 1-42, May.
    4. Haas, Markus & Mittnik, Stefan & Mizrach, Bruce, 2006. "Assessing central bank credibility during the ERM crises: Comparing option and spot market-based forecasts," Journal of Financial Stability, Elsevier, vol. 2(1), pages 28-54, April.
    5. Mohamed Saidane & Christian Lavergne, 2009. "Optimal Prediction with Conditionally Heteroskedastic Factor Analysed Hidden Markov Models," Computational Economics, Springer;Society for Computational Economics, vol. 34(4), pages 323-364, November.
    6. Massimo Guidolin, 2011. "Markov Switching Models in Empirical Finance," Advances in Econometrics, in: Missing Data Methods: Time-Series Methods and Applications, pages 1-86, Emerald Group Publishing Limited.
    7. Abakah, Emmanuel Joel Aikins & Tiwari, Aviral Kumar & Alagidede, Imhotep Paul & Gil-Alana, Luis Alberiko, 2022. "Re-examination of risk-return dynamics in international equity markets and the role of policy uncertainty, geopolitical risk and VIX: Evidence using Markov-switching copulas," Finance Research Letters, Elsevier, vol. 47(PA).
    8. Arie Preminger & Uri Ben-zion & David Wettstein, 2007. "The extended switching regression model: allowing for multiple latent state variables," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 26(7), pages 457-473.
    9. Mandler, Martin, 2007. "The Taylor rule and interest rate uncertainty in the U.S. 1955-2006," MPRA Paper 2340, University Library of Munich, Germany.
    10. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    11. Arash Nademi & Rahman Farnoosh, 2014. "Mixtures of autoregressive-autoregressive conditionally heteroscedastic models: semi-parametric approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(2), pages 275-293, February.
    12. Luc Bauwens & Arie Preminger & Jeroen V.K. Rombouts, 2006. "Regime switching GARCH models," Cahiers de recherche 06-08, HEC Montréal, Institut d'économie appliquée.
    13. Hubert Gabrisch, 2021. "GARCH Analyses of Risk and Uncertainty in the Theories of the Interest Rate of Keynes and Kalecki," wiiw Working Papers 191, The Vienna Institute for International Economic Studies, wiiw.
    14. Markku Lanne, 2006. "Nonlinear dynamics of interest rate and inflation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(8), pages 1157-1168, December.
    15. Carol Alexander & Emese Lazar, 2009. "Modelling Regime‐Specific Stock Price Volatility," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(6), pages 761-797, December.
    16. repec:bgu:wpaper:0605 is not listed on IDEAS
    17. Meitz, Mika & Saikkonen, Pentti, 2021. "Testing for observation-dependent regime switching in mixture autoregressive models," Journal of Econometrics, Elsevier, vol. 222(1), pages 601-624.
    18. Nyberg, Henri, 2010. "QR-GARCH-M Model for Risk-Return Tradeoff in U.S. Stock Returns and Business Cycles," MPRA Paper 23724, University Library of Munich, Germany.
    19. Lanne, Markku & Ahoniemi, Katja, 2008. "Implied Volatility with Time-Varying Regime Probabilities," MPRA Paper 23721, University Library of Munich, Germany.
    20. Tom Pak-wing Fong & Chun-shan Wong, 2008. "Stress Testing Banks' Credit Risk Using Mixture Vector Autoregressive Models," Working Papers 0813, Hong Kong Monetary Authority.
    21. Saikkonen, Pentti, 2005. "Stability results for nonlinear error correction models," Journal of Econometrics, Elsevier, vol. 127(1), pages 69-81, July.
    22. Giannikis, D. & Vrontos, I.D. & Dellaportas, P., 2008. "Modelling nonlinearities and heavy tails via threshold normal mixture GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1549-1571, January.
    23. Carvalho, Alexandre & Skoulakis, Georgios, 2005. "Ergodicity and existence of moments for local mixtures of linear autoregressions," Statistics & Probability Letters, Elsevier, vol. 71(4), pages 313-322, March.
    24. Mandler, Martin, 2012. "Decomposing Federal Funds Rate forecast uncertainty using time-varying Taylor rules and real-time data," The North American Journal of Economics and Finance, Elsevier, vol. 23(2), pages 228-245.

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