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Multi-scale regression based on detrending moving average and its application to seismic data

Author

Listed:
  • Jiaxin Qin

    (School of Mathematical Sciences, Ocean University of China, Qingdao 266100, P. R. China)

  • Min Lin

    (School of Mathematical Sciences, Ocean University of China, Qingdao 266100, P. R. China)

Abstract

We investigate the statistical properties of multi-scale regression model based on detrending moving average (DMA). The performance of the multi-scale regression estimator based on DMA is evaluated by varying the length, distribution and structure for different position parameters. Using different position parameters for the detrending windows in simulation, we find that the variance of the estimated regression coefficients for position parameter θ=0.5 is the smallest. By changing series length, distribution and structure, the estimated regression coefficients are stably near the theoretical values. The method is applied to analyze the dependence of inter-earthquakes time (IET) on inter-earthquakes distances (IED) between consecutive earthquakes in the California region. Results suggest that the cross-correlation between the IET and IED series is statistically significant. Scale-dependent statistic of estimated DMA multi-scale regression coefficient demonstrates significant dependence between IET and IED series.

Suggested Citation

  • Jiaxin Qin & Min Lin, 2023. "Multi-scale regression based on detrending moving average and its application to seismic data," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 34(03), pages 1-20, March.
    • Handle: RePEc:wsi:ijmpcx:v:34:y:2023:i:03:n:s0129183123500304
    DOI: 10.1142/S0129183123500304
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