Wang F, Chen Y. Detrending-moving-average-based multivariate regression model for nonstationary series.
Phys Rev E 2022;
105:054129. [PMID:
35706188 DOI:
10.1103/physreve.105.054129]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2022] [Accepted: 05/03/2022] [Indexed: 06/15/2023]
Abstract
Dependency between a response variable and the explanatory variables is a relationship of universal concern in various real-world problems. Multivariate linear regression (MLR) is a well-known method to focus on this issue. However, it is limited to dealing with stationary variables. In this work, we develop a MLR framework based on detrending moving average (DMA) analysis to reveal the actual dependency among variables with nonstationary measures. The DMA-based MLR can generate multiscale regression coefficients, which characterize different dependent behavior at different timescales. Artificial tests show that the DMA-MLR model can successfully resist the impact of trends on the studied series and produce more accurate regression coefficients with multiscale. Furthermore, some scale-dependent statistics are developed to deduce some important relationships in three typical DMA-based MLR models, which help us to deeply understand the DMA-MLR models in theory. The application of the proposed DMA-MLR framework to Beijing's air quality index system demonstrates that fine particulate matter with diameter ≤2.5μm (PM_{2.5}) is the dominant pollutant affecting the air quality of Beijing in recent years.
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