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Using a proper model to characterize a time series is crucial in making accurate predictions. In this work we use time-varying autoregressive process (TVAR) to describe non-stationary time series and model it as a mixture of multiple stable…

The detection of the abnormal area from urban data is a significant research problem. However, to the best of our knowledge, previous methods designed on spatio-temporal anomalies are road-based or grid-based, which usually causes the data…

A structural vector autoregressive (SVAR) process is a linear causal model for variables that evolve over a discrete set of time points and between which there may be lagged and instantaneous effects. The qualitative causal structure of an…

Symbolic Regression (SR) aims to discover interpretable equations from observational data, with the potential to reveal underlying principles behind natural phenomena. However, existing approaches often fall into the Pseudo-Equation Trap:…

We propose a multiscale approach to time series autoregression, in which linear regressors for the process in question include features of its own path that live on multiple timescales. We take these multiscale features to be the recent…

Vector autoregressive (VAR) models are widely used for causal discovery and forecasting in multivariate time series analysis. In the high-dimensional setting, which is increasingly common in fields such as neuroscience and econometrics,…

Fitting autoregressive moving average (ARMA) time series models requires model identification before parameter estimation. Model identification involves determining the order of the autoregressive and moving average components which is…

Time series observations are ubiquitous in astronomy, and are generated to distinguish between different types of supernovae, to detect and characterize extrasolar planets and to classify variable stars. These time series are usually…

Structural vector autoregressive (SVAR) models are widely used to analyze the simultaneous relationships between multiple time-dependent data. Various statistical inference methods have been studied to overcome the identification problems…

Errors are prevalent in time series data, such as GPS trajectories or sensor readings. Existing methods focus more on anomaly detection but not on repairing the detected anomalies. By simply filtering out the dirty data via anomaly…

In recent years, autoregressive models have had a profound impact on the description of astronomical time series as the observation of a stochastic process. These methods have advantages compared with common Fourier techniques concerning…

There are a variety of industrial products that possess periodic textures or surfaces, such as carbon fiber textiles and display panels. Traditional image-based quality inspection methods for these products require identifying the periodic…

In chemical processing and bioprocessing, conventional online sensors are limited to measure only basic process variables like pressure and temperature, pH, dissolved O and CO$_2$ and viable cell density (VCD). The concentration of other…

Our goal is to estimate causal interactions in multivariate time series. Using vector autoregressive (VAR) models, these can be defined based on non-vanishing coefficients belonging to respective time-lagged instances. As in most cases a…

Online system identification algorithms are widely used for monitoring, diagnostics and control by continuously adapting to time-varying dynamics. Typically, these algorithms consider a model structure that lacks parsimony and offers…

Temporal networks are commonly used to represent dynamical complex systems like social networks, simultaneous firing of neurons, human mobility or public transportation. Their dynamics may evolve on multiple time scales characterising for…

In this paper, as opposed to the random phase masks, the structured illuminations with a pixel-dependent deterministic phase shift are considered to derandomize the model setup. The RAAR algorithm is modified to adapt to two or more…

Learning representations that clearly distinguish between normal and abnormal data is key to the success of anomaly detection. Most of existing anomaly detection algorithms use activation representations from forward propagation while not…

Performative prediction is a framework accounting for the shift in the data distribution induced by the prediction of a model deployed in the real world. Ensuring rapid convergence to a stable solution where the data distribution remains…

Celestial objects exhibit a wide range of variability in brightness at different wavebands. Surprisingly, the most common methods for characterizing time series in statistics -- parametric autoregressive modeling -- is rarely used to…