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Organizations rely heavily on time series metrics to measure and model key aspects of operational and business performance. The ability to reliably detect issues with these metrics is imperative to identifying early indicators of major…

This paper addresses the problem of change-point detection on sequences of high-dimensional and heterogeneous observations, which also possess a periodic temporal structure. Due to the dimensionality problem, when the time between…

A technique is introduced for estimating unknown parameters when time series of only one variable from a multivariate nonlinear dynamical system is given. The technique employs a combination of two different control methods, a linear…

Changes in the timescales at which complex systems evolve are essential to predicting critical transitions and catastrophic failures. Disentangling the timescales of the dynamics governing complex systems remains a key challenge. With this…

We introduce a novel, practically relevant variation of the anomaly detection problem in multi-variate time series: intrinsic anomaly detection. It appears in diverse practical scenarios ranging from DevOps to IoT, where we want to…

Business processes are prone to unexpected changes, as process workers may suddenly or gradually start executing a process differently in order to adjust to changes in workload, season, or other external factors. Early detection of business…

Understanding the dynamics of complex systems is a central task in many different areas ranging form biology via epidemics to economics and engineering. Unexpected behaviour of dynamic systems or even systems failure is sometimes difficult…

In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…

Statistical differentiability of the measure along the reconstructed trajectory is a good candidate to quantify determinism in time series. The procedure is based upon a formula that explicitly shows the sensitivity of the measure to…

This article considers a nonparametric method for detecting change points in non-stationary time series. The proposed method will divide the time series into several segments so that between two adjacent segments, the normalized spectral…

In this paper, we study optimization problems where the cost function contains time-varying parameters that are unmeasurable and evolve according to linear, yet unknown, dynamics. We propose a solution that leverages control theoretic tools…

This paper proposes a flexible framework for inferring large-scale time-varying and time-lagged correlation networks from multivariate or high-dimensional non-stationary time series with piecewise smooth trends. Built on a novel and unified…

We introduce circulance, a scalar measure for classifying time series of dynamical systems. Circulance captures the extent of temporal regularity or irregularity that is encoded in the topology of a directed ordinal pattern transition…

Real world evolves in continuous time but computations are done from finite samples. Therefore, we study algorithms using finite observations in continuous-time linear dynamical systems. We first study the system identification problem, and…

The state space dynamics representation is the most general approach for nonlinear systems and often chosen for system identification. During training, the state trajectory can deform significantly leading to poor data coverage of the state…

We are sometimes forced to use the Interrupted Time Series (ITS) design as an identification strategy for potential policy change, such as when we only have a single treated unit and no comparable controls. For example, with recent county-…

This paper challenges the dominance of stochastic trend models by introducing the Seasonal-Trend-Stationary ARMA (STSA) framework, which represents univariate nonstationary time series as stationary fluctuations around deterministic trend…

The problem of estimating trend and seasonal variation in time-series data has been studied over several decades, although mostly using single time series. This paper studies the problem of estimating these components from functional data,…

The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and…

We present a convex approach to probabilistic segmentation and modeling of time series data. Our approach builds upon recent advances in multivariate total variation regularization, and seeks to learn a separate set of parameters for the…