title: Transmission of linear regression patterns between time series: from relationship in time series to complex networks.
abstract: The linear regression parameters between two time series can be different under different lengths of observation period. If we study the whole period by the sliding window of a short period, the change of the linear regression parameters is a process of dynamic transmission over time. We tackle fundamental research that presents a simple and efficient computational scheme: a linear regression patterns transmission algorithm, which transforms linear regression patterns into directed and weighted networks. The linear regression patterns (nodes) are defined by the combination of intervals of the linear regression parameters and the results of the significance testing under different sizes of the sliding window. The transmissions between adjacent patterns are defined as edges, and the weights of the edges are the frequency of the transmissions. The major patterns, the distance, and the medium in the process of the transmission can be captured. The statistical results of weighted out-degree and betweenness centrality are mapped on timelines, which shows the features of the distribution of the results. Many measurements in different areas that involve two related time series variables could take advantage of this algorithm to characterize the dynamic relationships between the time series from a new perspective.
authors.affiliation: School of Humanities and Economic Management, China University of Geosciences, Beijing 100083, China and Key Laboratory of Carrying Capacity Assessment for Resource and Environment, Ministry of Land and Resources (Chinese Academy of Land and Resource Economics, China University of Geosciences Beijing), Beijing 100083, China and Lab of Resources and Environmental Management, China University of Geosciences, Beijing 100083, China and Department of Earth and Environmental Sciences, University of Waterloo, ON, Canada N2L 3G1.
authors.forename: Xiangyun
authors.initials: X
authors.lastname: Gao
authors.affiliation: School of Humanities and Economic Management, China University of Geosciences, Beijing 100083, China and Key Laboratory of Carrying Capacity Assessment for Resource and Environment, Ministry of Land and Resources (Chinese Academy of Land and Resource Economics, China University of Geosciences Beijing), Beijing 100083, China and Lab of Resources and Environmental Management, China University of Geosciences, Beijing 100083, China.
authors.forename: Haizhong
authors.initials: H
authors.lastname: An
authors.affiliation: School of Humanities and Economic Management, China University of Geosciences, Beijing 100083, China and Key Laboratory of Carrying Capacity Assessment for Resource and Environment, Ministry of Land and Resources (Chinese Academy of Land and Resource Economics, China University of Geosciences Beijing), Beijing 100083, China and Lab of Resources and Environmental Management, China University of Geosciences, Beijing 100083, China.
authors.forename: Wei
authors.initials: W
authors.lastname: Fang
authors.affiliation: School of Humanities and Economic Management, China University of Geosciences, Beijing 100083, China and Key Laboratory of Carrying Capacity Assessment for Resource and Environment, Ministry of Land and Resources (Chinese Academy of Land and Resource Economics, China University of Geosciences Beijing), Beijing 100083, China.
authors.forename: Xuan
authors.initials: X
authors.lastname: Huang
authors.affiliation: School of Humanities and Economic Management, China University of Geosciences, Beijing 100083, China and Key Laboratory of Carrying Capacity Assessment for Resource and Environment, Ministry of Land and Resources (Chinese Academy of Land and Resource Economics, China University of Geosciences Beijing), Beijing 100083, China.
authors.forename: Huajiao
authors.initials: H
authors.lastname: Li
authors.affiliation: School of Humanities and Economic Management, China University of Geosciences, Beijing 100083, China and Key Laboratory of Carrying Capacity Assessment for Resource and Environment, Ministry of Land and Resources (Chinese Academy of Land and Resource Economics, China University of Geosciences Beijing), Beijing 100083, China.
authors.forename: Weiqiong
authors.initials: W
authors.lastname: Zhong
authors.affiliation: School of Humanities and Economic Management, China University of Geosciences, Beijing 100083, China and Key Laboratory of Carrying Capacity Assessment for Resource and Environment, Ministry of Land and Resources (Chinese Academy of Land and Resource Economics, China University of Geosciences Beijing), Beijing 100083, China and Lab of Resources and Environmental Management, China University of Geosciences, Beijing 100083, China.
authors.forename: Yinghui
authors.initials: Y
authors.lastname: Ding
mesh_terms: D000465:Algorithms; D016014:Linear Models; D010363:Pattern Recognition, Automated / Q000379:methods*; D013997:Time Factors