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Trend and cycle decomposition of Markov switching (co)integrated time series

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  • Maddalena Cavicchioli

    (University of Modena and Reggio Emilia)

Abstract

In this paper we derive the Beveridge–Nelson (BN) decomposition and the state space representation for various multivariate (co)integrated time series subject to Markov switching in regime. Then we provide explicit expressions for the BN trend and cyclical components in terms of the matrices involved in the state space representation of the considered process. Our matrix expressions in closed form improve computational performance since they are readily programmable and greatly reduce the computational cost. Then we develop impulse-response function analysis and represent the BN trend component as a random walk. An empirical application on the world economy illustrates the feasibility of the proposed approach.

Suggested Citation

  • Maddalena Cavicchioli, 2023. "Trend and cycle decomposition of Markov switching (co)integrated time series," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(5), pages 1381-1406, December.
    • Handle: RePEc:spr:stmapp:v:32:y:2023:i:5:d:10.1007_s10260-023-00710-4
    DOI: 10.1007/s10260-023-00710-4
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    More about this item

    Keywords

    Beveridge–Nelson decomposition; Trend and cyclical component; Markov switching (co)integrated processes; Impulse-response function; State space representation;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • 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
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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