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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.
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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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