Abstract
This paper intends, on the example of Urla station, to explore unit root nonstationary behavior of daily mean SP time series driven by infinite variance α-stable white noise. The two complete daily mean SP time series datasets, each of two years long, derived from 10-min digital recordings at the two channels of Urla station are used. It is found that both time series data exhibit a first-order differencing (d = 1) and well can be described by an Autoregressive-Integrated Moving Average (ARIMA(2,1,0)) model. Numerical results of the Autoregressive unit root tests of Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) tests showed that the null hypothesis of a unit root in the SP time series cannot be rejected. This issue is further checked based upon the Modified Log-periodogram Regression (LPR) and Local Whittle (LW) estimators of the differencing parameter d. Non-stability of the SP data is assessed through four diagnostic checking procedures. Stability (or tail) indexes estimated using Nolan’s Maximum Likelihood (ML) procedure were ranging around 1.12–1.13 for the first differences and 1.15–1.16 for the ARIMA(2,1,0) residuals. Numerical results of this study revealed that the SP time series observed at Urla station can be considered as realizations from an order-one integrated autoregressive process driven by nearly symmetrical, infinite variance (α-stable) white noise. It is recommended to take into account for these two crucial properties of the SP time series data in multivariate statistical models where the SP data will be used as a precursory covariate.
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Acknowledgments
The author gratefully acknowledges the Research Fund Council of Dokuz Eylul University for their financial support (project no: 09.KB.FEN.13) and the administration of Izmir Institute of Technology (IZTECH) for their permission and help in installing the SP monitoring station at the northern border of the campus area. The author also would like to thank the referees of the paper for their valuable reviews and suggestions significantly improved the quality of the presented paper.
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Sindirgi, P. On the unit root nonstationary behavior of daily self-potential (SP) time series with infinite variance noise: an example from Urla, Izmir-Turkey. Earth Sci Inform 14, 1185–1196 (2021). https://doi.org/10.1007/s12145-021-00626-1
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DOI: https://doi.org/10.1007/s12145-021-00626-1