Detrending-moving-average-based bivariate regression estimator.

Abstract

In this work, a detrending-moving-average- (DMA) based bivariate linear regression analysis method is proposed. The method is combination of detrended moving average analysis and standard regression methodology, which allows us to estimate the scale-dependent regression coefficients for nonstationary and power-law correlated time series. By using synthetic simulations with error of estimation for different position parameter θ of detrending windows, we test our DMA-based bivariate linear regression algorithm and find that the centered detrending technique (θ=0.5) is of best performance, which provides the most accurate estimates. In addition, the estimated regression coefficients are in good agreement with the theoretical values. The center DMA-based bivariate linear regression estimator is applied to analyze the return series of Shanghai stock exchange composite index, the Hong Kong Hangseng index and the NIKKEI 225 index. The dependence among the Asian stock market across timescales is confirmed. Furthermore, two statistics based on the scale-dependent t statistic and the partial detrending-moving-average cross-correlation coefficient are used to demonstrate the significance of the dependence. The scale-dependent evaluation parameters also show that the DMA-based bivariate regression model can provide rich information than standard regression analysis.