A survey of methods for time series change point detection

Samaneh Aminikhanghahi, Diane J. Cook
2016 Knowledge and Information Systems  
Change points are abrupt variations in time series data. Such abrupt changes may represent transitions that occur between states. Detection of change points is useful in modelling and prediction of time series and is found in application areas such as medical condition monitoring, climate change detection, speech and image analysis, and human activity analysis. This survey article enumerates, categorizes, and compares many of the methods that have been proposed to detect change points in time
more » ... ries. The methods examined include both supervised and unsupervised algorithms that have been introduced and evaluated. We introduce several criteria to compare the algorithms. Finally, we present some grand challenges for the community to consider. Definition 1: A time series data stream is an infinite sequence of elements where x i is a d-dimensional data vector arriving at time stamp i [17]. Definition 2: A stationary time series is a finite variance process whose statistical properties are all constant over time [18] . This definition assumes that • The mean value function μ t = E(x t ) is constant and does not depend on time t. • The auto covariance function γ(s, t) = cov(x s , x t ) = E[(x s − μ s )(x t − μ t )] depends on time stamps s and t only through their time difference, or |s -t|. Definition 3: Independent and identically distributed (i.i.d.) variables are mutually independent of each other, and are identically distributed in the sense that they are drawn from the same probability distribution. An i.i.d. time series is a special case of a stationary time series. Definition 4: Given a time series T of fixed length m (a subset of a time series data stream) and x t as a series sample at time t, a matrix WM of all possible subsequences of length k can be built by moving a sliding window of size k across T and placing subsequence X p = {x p , x p+1 , ... , x p+k } (Figure 2) in the p th row of WM. The size of the resulting matrix WM is (m − k + 1) × n [19][20]. Definition 5: In a time series, using sliding window X t as a sample instead of x t , an interval χ t with Hankel matrix {X t , X t+1 , ... , X t+n-1 } as shown in Figure 2 will be a set of n retrospective subsequence samples starting at time t [2][21][22].
doi:10.1007/s10115-016-0987-z pmid:28603327 pmcid:PMC5464762 fatcat:qtjvqsgdkjgwtivwlmjn27xyde