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Long memory in the marginalized time series of a VAR revisited

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  • del Barrio Castro, Tomas
  • Sanso Rossello, Andreu
  • Sibbertsen, Philipp

Abstract

In this paper we find an alternative explanation for the presence of long memory in marginalized time series of an autoregressive system in situations earlier explored by Bauwens, Chevillon and Laurent (2023) and Chevillon, Hecq, and Laurent (2018) which is the near cancellation of the damped trend shared by all the time series of the VAR(1) used in these papers and the MA(1) part of the data generating process followed by the marginalized time series. For a given time dimension T the long memory observed in the marginalized time series will depend on the number of time series in the VAR(1) system but not on the specific value of the main diagonal associated with the matrix of coefficients of the VAR(1) as stated in Chevillon, Hecq, and Laurent (2018) and Bauwens, Chevillon and Laurent (2023). Our results are based on the properties of circulant matrices and the Vector Moving Average representation of the VAR(1) model proposed in the previous two papers. Finally a Monte-Carlo experiment supports our analytical findings.

Suggested Citation

  • del Barrio Castro, Tomas & Sanso Rossello, Andreu & Sibbertsen, Philipp, 2025. "Long memory in the marginalized time series of a VAR revisited," Hannover Economic Papers (HEP) dp-742, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    • Handle: RePEc:han:dpaper:dp-742
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    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables

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