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Generally, the presented approach can be applied to the qualitative analyses of the relationships between two time series whenever appropriate control time series are available.
Coherence function as a fundamental measure of the degree of relationship between two time series has numerous applications in diversified fields such as financial economics, stochastic simulation and signal processing.
In this study, the magnitude-squared coherence function which enables one to identify frequency-domain correlation between two time series is revisited with a view towards extracting natural frequencies directly for dynamic structural systems.
Two traffic flow patterns (two time series of traffic flows arising from two different days) are said to be "similar" if the distance between them is small; similarity thus depends on how the metric or distance between two time series of traffic flows is defined.
Cosine distance can be defined as a similarity measure between two time series objects that measures the cosine of angle between two time series objects.
Correlation distance [19] is a measure of statistical dependence between two time series objects.
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This algorithm calculates the minimum aligned distance between two time-series using using the following recursive equation: (1).
Figure 1 illustrates the difference between the two distance metrics in matching among points to calculate the distance between two time-series sequences C and Q.
To explore results at a finer geographical level, we estimated the difference between two time-series: the mean of connection counts per zone after and before the launch of the game by separating observations between business days and weekends.
Dynamic Time Warping (DTW) is an algorithm for measuring similarity between two time-series in the situation that both have similar shapes but they vary in time step or speed rate.
The XWT technique transforms the time series of predictions and corresponding observations into a two-dimensional time-scale space and provides information on scale- and time-dependent timing differences between the two time series.
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