Related papers: A Statistical Simulation Method for Joint Time Ser…
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…
An emerging number of modern applications involve forecasting time series data that exhibit both short-time dynamics and long-time seasonality. Specifically, time series with multiple seasonality is a difficult task with comparatively fewer…
The common approach to inertial sensor calibration for navigation purposes has been to model the stochastic error signals of individual sensors independently, whether as components of a single inertial measurement unit (IMU) in different…
Reliable estimates of sea level return levels are crucial for coastal flooding risk assessments and for coastal flood defence design. We describe a novel method for estimating extreme sea levels that is the first to capture seasonality,…
We study sample average approximations (SAA) of chance constrained programs. SAA methods typically approximate the actual distribution in the chance constraint using an empirical distribution constructed from random samples assumed to be…
A data-driven methodology is proposed to model the distribution of multivariate stochastic trajectories from an observed sample. As a first step, each trajectory in the sample is reduced to a vector of features by means of Functional…
We describe a proof-of-concept development and application of a phase averaging technique to the nonlinear rotating shallow water equations on the sphere, discretised using compatible finite element methods. Phase averaging consists of…
Probabilistic forecasting of multivariate time series is essential for various downstream tasks. Most existing approaches rely on the sequences being uniformly spaced and aligned across all variables. However, real-world multivariate time…
An empirical algorithm is used here to study the stochastic and multifractal nature of nonlinear time series. A parameter can be defined to quantitatively measure the deviation of the time series from a Wiener process so that the…
Cartesian-grid methods with Adaptive Mesh Refinement (AMR) are ideally suited for simulating the breaking of waves, the formation of spray, and the entrainment of air around ships. As a result of the cartesian-grid formulation, minimal…
Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…
This paper characterizes the impact of covariate serial dependence on the non-asymptotic estimation error bound of penalized regressions (PRs). Focusing on the direct relationship between the degree of cross-correlation between covariates…
This article introduces a nonparametric approach to spectral analysis of a high-dimensional multivariate nonstationary time series. The procedure is based on a novel frequency-domain factor model that provides a flexible yet parsimonious…
Compositional time series frequently exhibit structural breaks due to external shocks, policy changes, or market disruptions. Standard methods either ignore such breaks or handle them through fixed effects that cannot extrapolate beyond the…
Linear time series modelling is dominated by the use of purely autoregressive models even though incorporating moving average components can greatly improve parsimony. We present a convex formulation for vector-ARMA system identification…
Recent studies have shown that, in coastal waters where water depth decreases significantly due to rapid bathymetric changes, the non-equilibrium dynamics (NED) substantially increases the occurrence probability of extreme (rogue) waves.…
Many problems in the geophysical sciences demand the ability to calibrate the parameters and predict the time evolution of complex dynamical models using sequentially-collected data. Here we introduce a general methodology for the joint…
Waves traveling through random media exhibit random focusing that leads to extremely high wave intensities even in the absence of nonlinearities. Although such extreme events are present in a wide variety of physical systems and the…
Stochastic optimization naturally arises in machine learning. Efficient algorithms with provable guarantees, however, are still largely missing, when the objective function is nonconvex and the data points are dependent. This paper studies…
Modelling a large bundle of curves arises in a broad spectrum of real applications. However, existing literature relies primarily on the critical assumption of independent curve observations. In this paper, we provide a general theory for…