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Likelihood Analysis of Seasonal Cointegration

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Author Info
Johansen, S.
Schaumburg, E.

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Abstract

The vector autoregressive model for seasonal cointegration is analysed. The general error correction model is discussed and conditions are found under which the process is integrated of order 1 at seasonal frequency and exhibits cointegration. Under these conditions a representation theorem for the solution is given expressed in terms of seasonal random walks. Finally the asymptotic properties of the likelihood ratio test for cointegrating rank is given, and it is shown that the estimated cointegrating vectors are asymptotically mixed Gaussian. The results resemble the result for cointegration at zero frequency but expressed in terms of a complex Brownian motion. Tables are provided for asymptotic inference under various assumptions on the deterministic terms.

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Publisher Info
Paper provided by European University Institute in its series Economics Working Papers with number eco97/16.

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Length: 39 pages
Date of creation: 1997
Date of revision:
Handle: RePEc:eui:euiwps:eco97/16

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Keywords: ECONOMETRICS;

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C00 - Mathematical and Quantitative Methods - - General - - - General

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  1. Cubadda, Gianluca & Omtzigt, Pieter, 2003. "Small Sample Improvements in the Statistical Analysis of Seasonally Cointegrated Systems," Economics & Statistics Discussion Papers esdp03012, University of Molise, Dept. SEGeS. [Downloadable!]
    Other versions:
  2. Peter Hansen, 2000. "The Johansen-Granger Representation Theorem: An Explicit Expression for I(1) Processes," University of California at San Diego, Economics Working Paper Series 2000-17, Department of Economics, UC San Diego. [Downloadable!]
  3. Gustavsson, Patrik & Nordström, Jonas, 1999. "The Impact of Seasonal Unit Roots and Vector ARMA Modeling on Forecasting Monthly Tourism Flows," Working Paper Series 150, Trade Union Institute for Economic Research, revised 01 Jul 2000. [Downloadable!]
  4. Philip Kostov & John Lingard, 2005. "Seasonally specific model analysis of UK cereals prices," Econometrics 0507014, EconWPA. [Downloadable!]
  5. Dietmar Bauer & Martin Wagner, 2003. "A Canonical Form for Unit Root Processes in the State Space Framework," Diskussionsschriften dp0312, Universitaet Bern, Departement Volkswirtschaft. [Downloadable!]
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  6. Dietmar Bauer & Martin Wagner, 2002. "Asymptotic Properties of Pseudo Maximum Likelihood Estimates for Multiple Frequency I(1) Processes," Diskussionsschriften dp0205, Universitaet Bern, Departement Volkswirtschaft. [Downloadable!]
  7. Kirstin Hubrich & Helmut Lütkepohl & Pentti Saikkonen, 2001. "A Review Of Systems Cointegration Tests," Econometric Reviews, Taylor and Francis Journals, vol. 20(3), pages 247-318. [Downloadable!] (restricted)
    Other versions:
  8. Pami Dua & Lokendra Kumawat, 2005. "Modelling and Forecasting Seasonality in Indian Macroeconomic Time Series," Working papers 136, Centre for Development Economics, Delhi School of Economics. [Downloadable!]
  9. H. Peter Boswijk & Jurgen Doornik, 2003. "Identifying, Estimating and Testing Restricted Cointegrated Systems: An Overview," Economics Papers 2003-W10, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
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  10. Dietmar Bauer & Martin Wagner, 2003. "On Polynomial Cointegration in the State Space Framework," Diskussionsschriften dp0313, Universitaet Bern, Departement Volkswirtschaft. [Downloadable!]
  11. Antonio Rubia, 2001. "Testing For Weekly Seasonal Unit Roots In Daily Electricity Demand: Evidence From Deregulated Markets," Working Papers. Serie EC 2001-21, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
  12. Johan Lyhagen, 2006. "The seasonal KPSS statistic," Economics Bulletin, Economics Bulletin, vol. 3(13), pages 1-9. [Downloadable!]
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  13. Gianluca Cubadda, 2000. "Complex Reduced Rank Models for Seasonally Cointegrated Time Series," Econometric Society World Congress 2000 Contributed Papers 0092, Econometric Society. [Downloadable!]
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  14. Svend Hylleberg, 2006. "Seasonal Adjustment," Economics Working Papers 2006-04, School of Economics and Management, University of Aarhus. [Downloadable!]
  15. Raimundo Soto & Matías Tapia, 2001. "Seasonal cointegration and the stability of the demand for money," Working Papers Central Bank of Chile 103, Central Bank of Chile. [Downloadable!]
  16. Raimundo Soto, 2000. "Ajuste Estacional e Integración en Variables Macroeconómicas," Working Papers Central Bank of Chile 73, Central Bank of Chile. [Downloadable!]
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  17. Gianluca Cubadda, 2001. "Common Features In Time Series With Both Deterministic And Stochastic Seasonality," Econometric Reviews, Taylor and Francis Journals, vol. 20(2), pages 201-216. [Downloadable!] (restricted)
  18. Bent Nielsen, 2005. "Analysis of co-explosive processes," Economics Papers 2005-W08, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
  19. Peter Reinhard Hansen, . "The Johansen-Granger Representation Theorem: A Closed Form Expression for I(1)Processes Creation-Date: 2000," Working Papers 2000-19, Brown University, Department of Economics. [Downloadable!]
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