Koopman-theoretic Approach for Identification of Exogenous Anomalies in Nonstationary Time-series Data

Traditional statistical methods include the time-domain Time-series analysis is used to extracting meaningful methods, such as the family of autoregressive (AR) models statistics and characteristics of temporal sequences and their many variants, including ARMA (AR moving of data [1], and is among the most ubiquitous mathematical average), ARIMA (AR integrated moving average), methods. Indeed, time-series are universal for SARIMA (seasonal ARIMA), etc. [1]. Such models use a signal processing methods and in pattern recognition applications, diversity of optimization techniques to estimate parameters dominating characterization of econometrics of a linear model with its history dependence. Traditional and finance along with almost any scientific and engineering frequency-domain methods use the properties of application. Time-series methods can be broadly short-time Fourier transforms [9] and/or wavelet transforms divided into time-domain and frequency-domain methods, [10] in order to characterize the signal in a joint the former of which uses a variety of statistical techniques time-frequency representation. More recently, there have to characterize a sequence, and the latter of which been efforts to model time-series data as from a dynamical uses spectral (e.g.