Detrending-moving-average-based bivariate regression estimator.

Area of Science:

• Time Series Analysis
• Econometrics
• Statistical Modeling

Background:

• Nonstationary and power-law correlated time series present challenges for standard regression analysis.
• Scale-dependent relationships are crucial for understanding complex systems like financial markets.
• Existing methods may not adequately capture the nuances of time series dependence across different timescales.

Purpose of the Study:

• To propose a novel detrending-moving-average (DMA)-based bivariate linear regression method.
• To estimate scale-dependent regression coefficients for nonstationary and power-law correlated time series.
• To assess the performance of the DMA method, particularly the centered detrending technique.

Main Methods:

• Development of a DMA-based bivariate linear regression analysis.
• Utilizing synthetic simulations to test the algorithm with varying position parameters (θ) for detrending windows.
• Application of the centered DMA-based regression estimator to analyze Asian stock market return series (Shanghai, Hong Kong, NIKKEI 225).
• Employing scale-dependent t statistics and partial detrending-moving-average cross-correlation coefficients to demonstrate dependence significance.

Main Results:

• The centered detrending technique (θ=0.5) demonstrated the best performance, yielding the most accurate regression coefficient estimates.
• Estimated regression coefficients showed good agreement with theoretical values.
• The analysis confirmed significant dependence among the Shanghai, Hong Kong, and NIKKEI 225 stock market return series across various timescales.
• Scale-dependent evaluation parameters revealed that the DMA-based model provides richer information compared to standard regression analysis.

Conclusions:

• The proposed DMA-based bivariate linear regression is an effective method for analyzing nonstationary time series.
• Centered detrending is optimal for improving the accuracy of regression coefficient estimation.
• The DMA method successfully reveals and quantifies scale-dependent interdependencies within financial markets.
• This approach offers a more comprehensive understanding of market dynamics than traditional regression techniques.