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Spectral based methods to identify common trends and common cycles

Author

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  • Camba-Méndez, Gonzalo
  • Kapetanios, George

Abstract

The rank of the spectral density matrix conveys relevant information in a variety of modelling scenarios. Phillips (1986) showed that a necessary condition for cointegration is that the spectral density matrix of the innovation sequence at frequency zero is of a reduced rank. In a recent paper Forni and Reichlin (1998) suggested the use of generalized dynamic factor model to explain the dynamics of a large set of macroeconomic series. Their method relied also on the computation of the rank of the spectral density matrix. This paper provides formal tests to estimate the rank of the spectral density matrix at any given frequency. The tests of rank at frequency zero are tests of the null of 'cointegration', complementary to those suggested by Phillips and Ouliaris (1988) which test the null of 'no cointegration'. JEL Classification: C12, C15, C32

Suggested Citation

  • Camba-Méndez, Gonzalo & Kapetanios, George, 2001. "Spectral based methods to identify common trends and common cycles," Working Paper Series 62, European Central Bank.
  • Handle: RePEc:ecb:ecbwps:200162
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    Citations

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    Cited by:

    1. repec:zbw:bofrdp:2010_006 is not listed on IDEAS
    2. Crowley, Patrick M., 2010. "Long cycles in growth : explorations using new frequency domain techniques with US data," Research Discussion Papers 6/2010, Bank of Finland.
    3. Patrick Crowley, 2005. "An intuitive guide to wavelets for economists," Econometrics 0503017, University Library of Munich, Germany.
    4. Crowley, Patrick M. & Maraun, Douglas & Mayes, David, 2006. "How hard is the euro area core? : an evaluation of growth cycles using wavelet analysis," Research Discussion Papers 18/2006, Bank of Finland.
    5. Patrick M. Crowley, 2007. "A Guide To Wavelets For Economists," Journal of Economic Surveys, Wiley Blackwell, vol. 21(2), pages 207-267, April.
    6. Crowley, Patrick M., 2010. "Long cycles in growth: explorations using new frequency domain techniques with US data," Bank of Finland Research Discussion Papers 6/2010, Bank of Finland.
    7. Crowley, Patrick M. & Maraun, Douglas & Mayes, David, 2006. "How hard is the euro area core? An evaluation of growth cycles using wavelet analysis," Bank of Finland Research Discussion Papers 18/2006, Bank of Finland.
    8. repec:zbw:bofrdp:2005_001 is not listed on IDEAS
    9. Pami Dua & Vineeta Sharma, 2013. "Measurement And Patterns Of International Synchronization-- A Spectral Approach," Working papers 224, Centre for Development Economics, Delhi School of Economics.
    10. Patrick Crowley, 2005. "An intuitive guide to wavelets for economists," Econometrics 0503017, University Library of Munich, Germany.
    11. repec:zbw:bofrdp:2006_018 is not listed on IDEAS

    More about this item

    Keywords

    canonical correlations; spectral density matrix; test of rank;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: 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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