Related papers: Sliding-Window Signatures for Time Series: Applica…
Short term load forecasting has an essential medium for the reliable, economical and efficient operation of the power system. Most of the existing forecasting approaches utilize fixed statistical models with large historical data for…
Over the past few decades, many applications of physics-based simulations and data-driven techniques (including machine learning and deep learning) have emerged to analyze and predict solar flares. These approaches are pivotal in…
We develop in this paper a theoretical framework for the topological study of time series data. Broadly speaking, we describe geometrical and topological properties of sliding window (or time-delay) embeddings, as seen through the lens of…
Statistical models are an essential tool to model, forecast and understand the hydrological processes in watersheds. In particular, the understanding of time lags associated with the delay between rainfall occurrence and subsequent changes…
We show how to utilize machine learning approaches to improve sliding window algorithms for approximate frequency estimation problems, under the ``algorithms with predictions'' framework. In this dynamic environment, previous…
Many finance, physics, and engineering phenomena are modeled by continuous-time dynamical systems driven by highly irregular (stochastic) inputs. A powerful tool to perform time series analysis in this context is rooted in rough path theory…
The proposed method in this paper is designed to address the problem of time series forecasting. Although some exquisitely designed models achieve excellent prediction performances, how to extract more useful information and make accurate…
Non-stationarity poses significant challenges for multivariate time series forecasting due to the inherent short-term fluctuations and long-term trends that can lead to spurious regressions or obscure essential long-term relationships. Most…
Distribution Regression (DR) on stochastic processes describes the learning task of regression on collections of time series. Path signatures, a technique prevalent in stochastic analysis, have been used to solve the DR problem. Recent…
Modern weather forecasting has increasingly transitioned from numerical weather prediction (NWP) to data-driven machine learning forecasting techniques. While these new models produce probabilistic forecasts to quantify uncertainty, their…
Score-based diffusion models have recently emerged as state-of-the-art generative models for a variety of data modalities. Nonetheless, it remains unclear how to adapt these models to generate long multivariate time series. Viewing a time…
Complex networks represent system dynamics through the interactions of a set of anomalous time series. Consider the problem of computing correlations for highly correlated pairs of time series across sliding windows. Efficiently computing…
Sequential and temporal data arise in many fields of research, such as quantitative finance, medicine, or computer vision. A novel approach for sequential learning, called the signature method and rooted in rough path theory, is considered.…
We introduce a new method of nowcasting using regression on path signatures. Path signatures capture the geometric properties of sequential data. Because signatures embed observations in continuous time, they naturally handle mixed…
Accurate time series forecasting is a fundamental challenge in data science. It is often affected by external covariates such as weather or human intervention, which in many applications, may be predicted with reasonable accuracy. We refer…
This paper introduces a data-driven time embedding method for modeling long-range seasonal dependencies in spatiotemporal forecasting tasks. The proposed approach employs Dynamic Mode Decomposition (DMD) to extract temporal modes directly…
We propose a novel and unified framework for change-point estimation in multivariate time series. The proposed method is fully nonparametric, enjoys effortless tuning and is robust to temporal dependence. One salient and distinct feature of…
At present, state-of-the-art forecasting models are short of the ability to capture spatio-temporal dependency and synthesize global information at the stage of learning. To address this issue, in this paper, through the adaptive fuzzified…
Time Series Forecasting is at the core of many practical applications such as sales forecasting for business, rainfall forecasting for agriculture and many others. Though this problem has been extensively studied for years, it is still…
Complex systems span multiple spatial and temporal scales, making their dynamics challenging to understand and predict. This challenge is especially daunting when one wants to study localized and/or rare events. Advances in dynamical…