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Tests of seasonal integration and cointegration in multivariate unobserved component models

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  • Fabio Busetti

    (Banca d'Italia)

Abstract

The paper considers tests of seasonal integration and cointegration for multivariate time series. The locally best invariant (LBI) test of the null hypothesis of a deterministic seasonal pattern against the alternative of seasonal integration is derived for a model with Gaussian i.i.d. disturbances and deterministic trend. A test of seasonal cointegration is then proposed, which parallels the common trend test of Nyblom and Harvey (2000). The tests are subsequently generalized to account for stochastic trends, weakly dependent errors and unattended unit roots. Asymptotic representations and critical values of the tests are provided, while the finite sample performance is evaluated by Monte Carlo simulation experiments. We apply the tests to the indices of industrial production of the four largest countries of the European Monetary Union. We find evidence that Germany does not cointegrate with the other countries, while there seems to exist a common nonstationary seasonal component between France, Italy and Spain.

Suggested Citation

  • Fabio Busetti, 2004. "Tests of seasonal integration and cointegration in multivariate unobserved component models," Econometrics 0411003, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpem:0411003
    Note: Type of Document - pdf; pages: 35
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    References listed on IDEAS

    as
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    Cited by:

    1. Fabio Busetti, 2006. "Tests of seasonal integration and cointegration in multivariate unobserved component models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(4), pages 419-438.
    2. Webel, Karsten, 2016. "A data-driven selection of an appropriate seasonal adjustment approach," Discussion Papers 07/2016, Deutsche Bundesbank.
    3. Tucker S McElroy & Agnieszka Jach, 2019. "Testing collinearity of vector time series," The Econometrics Journal, Royal Economic Society, vol. 22(2), pages 97-116.
    4. Sauro Mocetti, 2012. "Educational choices and the selection process: before and after compulsory schooling," Education Economics, Taylor & Francis Journals, vol. 20(2), pages 189-209, February.
    5. El Montasser, Ghassen & Boufateh, Talel & Issaoui, Fakhri, 2013. "The seasonal KPSS test when neglecting seasonal dummies: a Monte Carlo analysis," MPRA Paper 46226, University Library of Munich, Germany.
    6. González-Rivera, Gloria & Rodríguez Caballero, Carlos Vladimir, 2023. "Modelling intervals of minimum/maximum temperatures in the Iberian Peninsula," DES - Working Papers. Statistics and Econometrics. WS 37968, Universidad Carlos III de Madrid. Departamento de Estadística.
    7. Fabio Busetti & Silvestro di Sanzo, 2011. "Bootstrap LR tests of stationarity, common trends and cointegration," Temi di discussione (Economic working papers) 799, Bank of Italy, Economic Research and International Relations Area.

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    More about this item

    Keywords

    Common components; Locally best invariant test; Seasonal unit roots;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: 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

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