Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/333581 
Year of Publication: 
2025
Series/Report no.: 
Hannover Economic Papers (HEP) No. 742
Publisher: 
Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät, Hannover
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.
Subjects: 
Long Memory
Marginalized Time Series
Damped Trend
JEL: 
C3
Document Type: 
Working Paper

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