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

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 [Formula: see text] 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.

Fractal Analysis of the Centrifuge Vibrograms

“…The detrended moving average (DMA) [22] method is a statistical technique commonly used to estimate the scaling exponent of time series data with long-range correlations, such as EEG time series during a cognitive workload [37], seismic time series [38], financial time series [39], etc. The DMA algorithm is widely applied to evaluate the long-and short-term correlations of one-and high-dimensional time series data, both in temporal and spatial domains.…”