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Bayesian Inference and Forecasting in the Stationary Bilinear Model


  • Roberto Leon-Gonzalez

    (National Graduate Institute for Policy Studies)

  • Fuyu Yang

    (University of East Anglia)


A stationary bilinear (SB) model can be used to describe processes with a time-varying degree of persistence that depends on past shocks. An example of such a process is inflation. This study develops methods for Bayesian inference, model comparison, and forecasting in the SB model. Using monthly U.K. inflation data, we find that the SB model outperforms the random walk and first order autoregressive AR(1) models in terms of root mean squared forecast errors for both the one-step-ahead and the multi-step-ahead out-of-sample forecast. In addition, the SB model is superior to these two models in terms of predictive likelihood for 208 out of 243 forecast observations. In particular, compared with a lower order autoregressive AR model, the SB model is much better at predicting the inflation observations during the financial crisis and immediately after.

Suggested Citation

  • Roberto Leon-Gonzalez & Fuyu Yang, 2014. "Bayesian Inference and Forecasting in the Stationary Bilinear Model," University of East Anglia Applied and Financial Economics Working Paper Series 055, School of Economics, University of East Anglia, Norwich, UK..
  • Handle: RePEc:uea:aepppr:2012_55

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    References listed on IDEAS

    1. Geweke, John & Amisano, Gianni, 2010. "Comparing and evaluating Bayesian predictive distributions of asset returns," International Journal of Forecasting, Elsevier, vol. 26(2), pages 216-230, April.
    2. Francq, Christian & Makarova, Svetlana & Zakoi[diaeresis]an, Jean-Michel, 2008. "A class of stochastic unit-root bilinear processes: Mixing properties and unit-root test," Journal of Econometrics, Elsevier, vol. 142(1), pages 312-326, January.
    3. Brunner, Allan D. & Hess, Gregory D., 1995. "Potential problems in estimating bilinear time-series models," Journal of Economic Dynamics and Control, Elsevier, vol. 19(4), pages 663-681, May.
    4. Wojciech Charemza & Yuriy Kharin & Vladislav Maevskiy, 2012. "Bilinear forecast risk assessment for non-systematic inflation: Theory and evidence," Discussion Papers in Economics 12/22, Department of Economics, University of Leicester.
    5. Charemza, Wojciech W. & Lifshits, Mikhail & Makarova, Svetlana, 2005. "Conditional testing for unit-root bilinearity in financial time series: some theoretical and empirical results," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 63-96, January.
    6. J. D. Byers & D. A. Peel, 1995. "Bilinear quadratic ARCH and volatility spillovers in inter-war exchange rates," Applied Economics Letters, Taylor & Francis Journals, vol. 2(7), pages 215-219.
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