Nonlinear Adjustment in US Bond Yields: an Empirical Analysis with Conditional Heteroskedasticity

Lucchetti, Riccardo and Palomba, Giulio (2008): Nonlinear Adjustment in US Bond Yields: an Empirical Analysis with Conditional Heteroskedasticity.

Abstract

Starting from the work by Campbell and Shiller (1987), empirical analysis of interest rates has been conducted in the framework of cointegration. However, parts of this approach have been questioned recently, as the adjustment mechanism may not follow a simple linear rule; another line of criticism points out that stationarity of the spreads is difficult to maintain empirically. In this paper, we analyse data on US bond yields by means of an augmented VAR specification which approximates a generic nonlinear adjustment model. We argue that nonlinearity captures macro information via the shape of the yield curve and thus provides an alternative explanation for some findings recently appeared in the literature. Moreover, we show how conditional heteroskedasticity can be taken into account via GARCH specifications for the conditional variance, either univariate and multivariate.

• Item Type: MPRA Paper
• Language: English
• Keywords: interest rates, cointegration, nonlinear adjustment, conditional heteroskedasticity
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C32 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models; E - Macroeconomics and Monetary Economics > E4 - Money and Interest Rates > E43 - Interest Rates: Determination, Term Structure, and Effects

References

Alexander, C. and A. Chibumba (1996): “Multivariate orthogonal factor GARCH,” Discussion Paper in mathematics, University of Sussex.

Andrews, D. W. K. and J. C. Monahan (1992): “An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator,” Econometrica, 60, 953–966.

Ang, A. and M. Piazzesi (2003): “A no-arbitrage vector autoregression of term structure dynamics with macroeconomic and latent variables,” Journal of Monetary Economics, 50.

Balcombe, K. G. (2006): “Bayesian estimation of cointegrating thresholds in the term structure of interest rates,” Empirical Economics, 31, 277–289.

Balke, N. and T. Fomby (1997): “Threshold cointegration,” International Economic Review, 38, 627–645.

Bollerslev, T., R. F. Engle, and J. M. Wooldridge (1988): “A capital asset pricing model with time varying covariances,” Journal of Political Economy, 96, 116–131.

Bollerslev, T. and J. M. Wooldridge (1992): “Quasi maximum likelihood estimation and inference in dynamic models with time varying covariances,” Economic Review, 11, 143–172.

Campbell, J. Y. and R. J. Shiller (1987): “Cointegration and tests of present value models,” Journal of Political Economy, 95, 1062–1088.

Clements, M. P. (2005): Evaluating Econometric Forecasts Of Economic And Financial Variables, Palgrave Macmillan.

Diebold, F. X. and R. M. Mariano (1995): “Comparing predictive accuracy,” Journal of Business and Economic Statistics, 13, 253–263.

Elliott, G., T. Rothenberg, and J. Stock (1996): “Efficient tests for an autoregressive unit root,” Econometrica, 64, 813–836.

Engle, R. F. (1982): “Autoregressive conditional heteroskedasticity with estimates of the U.K. inflation,” Econometrica, 50, 987–1008.

Engle, R. F. (2002): “Dynamic conditional correlation - A simple class of multivariate GARCH models,” Journal of Business and Economic Statistics, 20, 339–350.

Engle, R. F. and K. F. Kroner (1995): “Multivariate simultaneous generalized ARCH,” Econometric Theory, 11, 122–150.

Engle, R. F. and V. K. Ng (1993): “Measuring and testing the the impact of news on volatility,” Journal of Finance, 48, 1749–1778.

Escribano, A. (2004): “Nonlinear Error Correction: the Case of Money Demand in the United Kingdom (1878–2000),” Macroeconomic Dynamics, 8, 76–116.

Escribano, A. and S. M. Navarro (2002): “Nonlinear Error Correction Models,” Journal of Time Series Analysis, 23, 509–522.

Ghysels, E., A. C. Harvey, and E. Renault (1996): Stochastic volatility, in G.S. Maddala & C.R. Rao (eds.), Handbook of Statistics, vol. 14, Statistical Methods in Finance, Elsevier, North Holland.

Giese, J. (2006): “Level, slope, curvature: The yield curve’s derivatives and their relations to macro variables,” Paper presented at the European Economic Association and the Econometric Society European Meeting (EEA-ESEM), Vienna, August.

Hall, A. (1994): “Testing for a unit root in time series with pretest data-based model selection,” Journal of Business and Economic Statistics, 12, 461–469.

Hannan, E. J. and B. G. Quinn (1979): “The determination of the order of an autoregression,” Journal of the Royal Statistical Society (B), 41, 190–195.

Hansen, B. and B. Seo (2002): “Testing for two-regime threshold cointegration in vector error correction models,” Journal of Econometrics, 110, 293–318.

Johansen, S. (1996): Likelihood-Based Inference in Cointegrated Vector Autoregressive Models, Oxford University Press.

Kapetanios, G., Y. Shin, and A. Snell (2003): “Testing for a unit root in the nonlinear STAR framework,” Journal of Econometrics, 112, 359–379.

Kilian, L. and M. P. Taylor (2003): “Why is it so difficult to beat the random walk forecast of exchange rates?” Journal of International Economics, 60, 85–107.

Krishnakumar, J. and D. Neto (2005): “Testing unit root in threshold cointegration,” Cahiers du Département d’Econom ́trie, Faculté des sciences économiques et Sociales, Université de Genève, 4.

Kwiatkowski, D., P. C. B. Phillips, P. Schmidt, and Y. Shin (1992): “Testing the null hypothesis of stationarity against the alternative of a unit root,” Journal of Econometrics, 54, 159–178.

Lanne, M. and P. Saikkonen (2007): “A multivariate generalized orthogonal factor GARCH model,” Journal of Business and Economic Statistic, 25, 61–75.

Laurent, S., L. Bauwens, and J. V. K. Rombouts (2006): “Multivariate GARCH models: a survey,” Journal of Applied Econometrics, 21, 79–109.

Ling, S., W. Li, and M. McAleer (2003): “Estimation and testing for unit root processes with GARCH (1, 1) errors: Theory and monte carlo evidence,” Econometric Reviews, 22, 179–202.

Liu, J., S. Wu, and J. V. Zidek (1997): “On segmented multivariate regressions,” Statistica Sinica, 7, 497–525.

Lo, M. C. and E. Zivot (2001): “Threshold cointegration and nonlinear adjustment to the law of one price,” Macroeconomic Dynamics, 5, 533–76.

Lucchetti, R. (2002): “Analytical score for multivariate GARCH models,” Computational Economics, 19, 133–143.

MacKinnon, J. G. (1996): “Numerical distribution functions for unit root and cointegration tests,” Journal of Applied Econometrics, 11, 601–618.

Magnus, J. R. and H. Neudecker (1988): Matrix Differential Calculus with Applications in Statistics and Econometrics, John Wiley & Sons.

Meyn, S. P. and R. L. Tweedie (1993): Markov Chains and Stochastic Stability, Springer.

Saikkonen, P. (2005): “Stability results for nonlinear error correction models,” Journal of Econometrics, 127, 69–81.

Thornton, D. L. (2005): “When did the FOMC begin targeting the federal funds rate? what the verbatim transcripts tell us,” Working Papers 2004–015, Federal Reserve Bank of St. Louis.

Unal, H., A. Demirgüc-Kunt, and K.-W. Leung (1993): “The Brady Plan, 1989 Mexican debt-reduction agreement, and bank stock returns in United States and Japan,” Journal of Money, Credit and Banking, 25, 410–29.

Van der Weide, R. (2002): “GO-GARCH: a multivariate generalized orthogonal GARCH model,” Journal of Applied Econometrics, 17, 549–564.