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Periodic and seasonal (co-)integration in the state space framework

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  • Bauer, Dietmar

Abstract

In this paper (multivariate) periodic and seasonally integrated autoregressive (moving average) processes are investigated by embedding the linear dynamic models for vectors of all observations within a year into the state space framework. In the case of quarterly data this corresponds to models for the vector of quarters (VQ) process. In the general case this may be called a vector of seasons (VS) process. It is demonstrated that this combination of the VS and the state space representation makes the relations between the various series transparent and thus helps in identifying cointegration properties both between as well as within the seasons. The setting is more revealing than the generally used periodic autoregressive (PAR) or seasonally integrated autoregressive moving average (SARIMA) framework.

Suggested Citation

  • Bauer, Dietmar, 2019. "Periodic and seasonal (co-)integration in the state space framework," Economics Letters, Elsevier, vol. 174(C), pages 165-168.
    • Handle: RePEc:eee:ecolet:v:174:y:2019:i:c:p:165-168
    DOI: 10.1016/j.econlet.2018.11.018
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    References listed on IDEAS

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    1. del Barrio Castro, Tomás & Osborn, Denise R., 2008. "Cointegration For Periodically Integrated Processes," Econometric Theory, Cambridge University Press, vol. 24(1), pages 109-142, February.
    2. Cubadda, Gianluca & Omtzigt, Pieter, 2005. "Small-sample improvements in the statistical analysis of seasonally cointegrated systems," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 333-348, April.
    3. Franses, Philip Hans, 1996. "Periodicity and Stochastic Trends in Economic Time Series," OUP Catalogue, Oxford University Press, number 9780198774549, Decembrie.
    4. Koopman, Siem Jan & Ooms, Marius, 2006. "Forecasting daily time series using periodic unobserved components time series models," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 885-903, November.
    5. Tomás del Barrio Castro & Denise R. Osborn, 2012. "Non‐parametric testing for seasonally and periodically integrated processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(3), pages 424-437, May.
    6. Hylleberg, S. & Engle, R. F. & Granger, C. W. J. & Yoo, B. S., 1990. "Seasonal integration and cointegration," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 215-238.
    7. Rodrigues, Paulo M. M. & Taylor, A. M. Robert, 2004. "Alternative estimators and unit root tests for seasonal autoregressive processes," Journal of Econometrics, Elsevier, vol. 120(1), pages 35-73, May.
    8. Breitung, Jörg & Franses, Philip Hans, 1998. "On Phillips–Perron-Type Tests For Seasonal Unit Roots," Econometric Theory, Cambridge University Press, vol. 14(2), pages 200-221, April.
    9. Rodrigues, Paulo M.M. & Taylor, A.M. Robert, 2007. "Efficient tests of the seasonal unit root hypothesis," Journal of Econometrics, Elsevier, vol. 141(2), pages 548-573, December.
    10. Castro, Tomás del Barrio & Osborn, Denise R. & Taylor, A.M. Robert, 2012. "On Augmented Hegy Tests For Seasonal Unit Roots," Econometric Theory, Cambridge University Press, vol. 28(5), pages 1121-1143, October.
    11. Bauer, Dietmar & Wagner, Martin, 2012. "A State Space Canonical Form For Unit Root Processes," Econometric Theory, Cambridge University Press, vol. 28(6), pages 1313-1349, December.
    12. Franses, Philip Hans, 1994. "A multivariate approach to modeling univariate seasonal time series," Journal of Econometrics, Elsevier, vol. 63(1), pages 133-151, July.
    13. Gregoir, Stéphane, 2010. "Fully Modified Estimation Of Seasonally Cointegrated Processes," Econometric Theory, Cambridge University Press, vol. 26(5), pages 1491-1528, October.
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    More about this item

    Keywords

    Unit roots; Cointegration; Seasonal integration; Periodic processes;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: 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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