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Spectral based methods to identify common trends and common cycles

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  • Camba-Méndez, Gonzalo
  • Kapetanios, George
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    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

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    Bibliographic Info

    Paper provided by European Central Bank in its series Working Paper Series with number 0062.

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    Date of creation: Apr 2001
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    Handle: RePEc:ecb:ecbwps:20010062

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    1. Mario Forni & Marc Hallin & Lucrezia Reichlin & Marco Lippi, 2000. "The generalised dynamic factor model: identification and estimation," ULB Institutional Repository 2013/10143, ULB -- Universite Libre de Bruxelles.
    2. Engle, Robert F. & Issler, Joao Victor, 1995. "Estimating common sectoral cycles," Journal of Monetary Economics, Elsevier, vol. 35(1), pages 83-113, February.
    3. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
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    Cited by:
    1. Patrick Crowley, 2005. "An intuitive guide to wavelets for economists," Econometrics 0503017, EconWPA.
    2. Crowley , Patrick & Maraun , Douglas & Mayes , David, 2006. "How hard is the euro are core? An evaluation of growth cycles using wavelet analysis," Research Discussion Papers 18/2006, Bank of Finland.

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