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A Long-Run Relationship between Daily Prices on Two Markets: The Bayesian VAR(2)–MSF-SBEKK Model


  • Krzysztof Osiewalski


  • Jacek Osiewalski

    () (Cracow University of Economics)


We develop a fully Bayesian framework for analysis and comparison of two competing approaches to modelling daily prices on different markets. The first approach, prevailing in financial econometrics, amounts to assuming that logarithms of prices behave like a multivariate random walk; this approach describes logarithmic returns most often by the VAR(1) model with MGARCH (or sometimes MSV) disturbances. In the second approach, considered here, it is assumed that daily price levels are linked together and, thus, the error correction term is added to the usual VAR(1)–MGARCH or VAR(1)–MSV model for logarithmic returns, leading to a reduced rank VAR(2) specification for logarithms of prices. The model proposed in the paper uses a hybrid MSVMGARCH structure for VAR(2) disturbances. In order to keep cointegration modelling as simple as possible, we restrict to the case of two prices representing two different markets. The aim of the paper is to show how to check if a long-run relationship between daily prices exists and whether taking it into account influences our inference on volatility and short-run relations between returns on different markets. In the empirical example the daily values of the S&P500 index and the WTI oil price in the period 19.12.2005 – 30.09.2011 are jointly modelled. It is shown that, although the logarithms of the values of S&P500 and WTI oil price seem to be cointegrated, neglecting the error correction term leads to practically the same conclusions on volatility and conditional correlation as keeping it in the model.

Suggested Citation

  • Krzysztof Osiewalski & Jacek Osiewalski, 2013. "A Long-Run Relationship between Daily Prices on Two Markets: The Bayesian VAR(2)–MSF-SBEKK Model," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 5(1), pages 65-83, March.
  • Handle: RePEc:psc:journl:v:5:y:2013:i:1:p:65-83

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    References listed on IDEAS

    1. Strachan, Rodney W, 2003. "Valid Bayesian Estimation of the Cointegrating Error Correction Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 185-195, January.
    2. Jacek Osiewalski & Anna Pajor, 2009. "Bayesian Analysis for Hybrid MSF-SBEKK Models of Multivariate Volatility," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 1(2), pages 179-202, November.
    3. Bekiros, Stelios D. & Diks, Cees G.H., 2008. "The relationship between crude oil spot and futures prices: Cointegration, linear and nonlinear causality," Energy Economics, Elsevier, vol. 30(5), pages 2673-2685, September.
    4. Anna Pajor, 2011. "A Bayesian Analysis of Exogeneity in Models with Latent Variables," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 3(2), pages 49-73, June.
    5. Chang, Chiao-Yi & Lai, Jing-Yi & Chuang, I-Yuan, 2010. "Futures hedging effectiveness under the segmentation of bear/bull energy markets," Energy Economics, Elsevier, vol. 32(2), pages 442-449, March.
    6. Gary Koop & Roberto León-González & Rodney W. Strachan, 2010. "Efficient Posterior Simulation for Cointegrated Models with Priors on the Cointegration Space," Econometric Reviews, Taylor & Francis Journals, vol. 29(2), pages 224-242, April.
    7. Mahadevan, Renuka & Suardi, Sandy, 2011. "The effects of uncertainty dynamics on exports, imports and productivity growth," Journal of Asian Economics, Elsevier, vol. 22(2), pages 174-188, April.
    8. Krzysztof Osiewalski & Jacek Osiewalski, 2012. "Missing observations in daily returns - Bayesian inference within the MSF-SBEKK model," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 4(3), pages 169-197, September.
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    Cited by:

    1. Jacek Osiewalski & Krzysztof Osiewalski, 2016. "Hybrid MSV-MGARCH Models – General Remarks and the GMSF-SBEKK Specification," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 8(4), pages 241-271, December.
    2. repec:eee:ecmode:v:72:y:2018:i:c:p:296-305 is not listed on IDEAS
    3. Kamil Makieła, 2014. "Bayesian Stochastic Frontier Analysis of Economic Growth and Productivity Change in the EU, USA, Japan and Switzerland," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 6(3), pages 193-216, September.
    4. repec:psc:journl:v:9:y:2017:i:3:p:243-273 is not listed on IDEAS

    More about this item


    Bayesian econometrics; vector error correction model; hybrid MGARCH-MSV processes; financial markets; commodity markets;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics


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