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Stationary Random Functions have been successfully applied in geostatistical applications for decades. In some instances, the assumption of a homogeneous spatial dependence structure across the entire domain of interest is unrealistic. A…
This paper studies methods for testing and estimating change-points in the covariance structure of a high-dimensional linear time series. The assumed framework allows for a large class of multivariate linear processes (including vector…
Determining the relevant spatial covariates is one of the most important problems in the analysis of point patterns. Parametric methods may lead to incorrect conclusions, especially when the model of interactions between points is wrong.…
How can we tell whether two neural networks utilize the same internal processes for a particular computation? This question is pertinent for multiple subfields of neuroscience and machine learning, including neuroAI, mechanistic…
Singular spectrum analysis (SSA) is a nonparametric and adaptive spectral decomposition of a time series. The singular value decomposition of the trajectory matrix and the anti-diagonal averaging leads to a time-series decomposition. In…
This paper introduces a local-to-unity/small sigma process for a stationary time series with strong persistence and non-negligible long run risk. This process represents the stationary long run component in an unobserved short- and long-run…
In recent years, active subspace methods (ASMs) have become a popular means of performing subspace sensitivity analysis on black-box functions. Naively applied, however, ASMs require gradient evaluations of the target function. In the event…
Numerous interesting properties in nonlinear systems analysis can be written as polynomial optimization problems with nonconvex sum-of-squares problems. To solve those problems efficiently, we propose a sequential approach of local…
In this paper, we introduce a new method for testing the stationarity of time series, where the test statistic is obtained from measuring and maximising the difference in the second-order structure over pairs of randomly drawn intervals.…
We congratulate the authors for a stimulating and valuable manuscript, providing a careful review of the state-of the-art in cross-sectional and time-series benchmarking procedures for small area estimation. They develop a novel two-stage…
The assumption of separability of the covariance operator for a random image or hypersurface can be of substantial use in applications, especially in situations where the accurate estimation of the full covariance structure is unfeasible,…
This paper presents a test for wide-sense stationarity (WSS) based on the geometry of the covariance function. We estimate local patches of the covariance surface and then check whether the directional derivative in the $(1,1,0)$ direction…
The well-established practice of time series analysis involves estimating deterministic, non-stationary trend and seasonality components followed by learning the residual stochastic, stationary components. Recently, it has been shown that…
Time series foundation models (TSFMs) are widely used as generic feature extractors, yet the notion of non-stationarity in their embedding spaces remains poorly understood. Recent work often conflates non-stationarity with distribution…
Singular Spectrum Analysis (SSA) or Singular Value Decomposition (SVD) are often used to de-noise univariate time series or to study their spectral profile. Both techniques rely on the eigendecomposition of the cor- relation matrix…
Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used for exact or approximate Bayesian learning. In many…
For many stochastic processes there is an underlying coordinate space, $V$, with the process moving from point to point in $V$ or on variables (such as spin configurations) defined with respect to $V$. There is a matrix of transition…
The higher dimensional autoregressive models would describe some of the econometric processes relatively generically if they incorporate the heterogeneity in dependence on times. This paper analyzes the stationarity of an autoregressive…
Many statistical models seek relationship between variables via subspaces of reduced dimensions. For instance, in factor models, variables are roughly distributed around a low dimensional subspace determined by the loading matrix; in mixed…
This paper presents a novel methodology for evaluating the boundedness, stability, and instability of some vector nonlinear systems with multiple time-varying delays and variable coefficients. The proposed technique develops two scalar…