This paper discusses the trend modeling for traffic time series. First, we recount two types of definitions for a long-term trend that appeared in previous studies and illustrate their intrinsic differences. We show that, by assuming an implicit temporal connection among the time series observed at different days/locations, the PCA trend brings several advantages to traffic time series analysis. We also describe and define the so-called short-term trend that cannot be characterized by existing definitions. Second, we sequentially review the role that trend modeling plays in four major problems in traffic time series analysis: abnormal data detection, data compression, missing data imputation, and traffic prediction. The relations between these problems are revealed, and the benefit of detrending is explained. For the first three problems, we summarize our findings in the last ten years and try to provide an integrated framework for future study. For traffic prediction problem, we present a new explanation on why prediction accuracy can be improved at data points representing the short-term trends if the traffic information from multiple sensors can be appropriately used. This finding indicates that the trend modeling is not only a technique to specify the temporal pattern but is also related to the spatial relation of traffic time series.
['Li Li', 'Xiaonan Su', 'Yi Zhang', 'Yuetong Lin', 'Zhiheng Li']
Trend Modeling for Traffic Time Series Analysis: An Integrated Study