Related papers: Limits to consistent on-line forecasting for ergod…

Researchers in empirical software engineering often make claims based on observable data such as defect reports. Unfortunately, in many cases, these claims are generalized beyond the data sets that have been evaluated. Will the researcher's…

A well known problem with EOP prediction is that a prediction strategy proved to be the best for some testing period and prediction length may not remain as such for other period of time. In this paper we consider possible strategies to…

We consider the problem of uncertainty quantification for prediction in a time series: if we use past data to forecast the next time point, can we provide valid prediction intervals around our forecasts? To avoid placing distributional…

The study of complex systems has attracted widespread attention from researchers in the fields of natural sciences, social sciences, and engineering. Prediction is one of the central issues in this field. Although most related studies have…

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…

This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely…

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…

This short review describes mathematical techniques for statistical analysis and prediction in dynamical systems. Two problems are discussed, namely (i) the supervised learning problem of forecasting the time evolution of an observable…

This paper proposes a model predictive controller for discrete-time linear systems with additive, possibly unbounded, stochastic disturbances and subject to chance constraints. By computing a polytopic probabilistic positively invariant set…

The paper presents sufficient conditions of predictability for continuous time processes in deterministic setting. We found that processes with exponential decay on energy for higher frequencies are predictable in some weak sense on some…

Invertibility conditions for observation-driven time series models often fail to be guaranteed in empirical applications. As a result, the asymptotic theory of maximum likelihood and quasi-maximum likelihood estimators may be compromised.…

We present data-dependent learning bounds for the general scenario of non-stationary non-mixing stochastic processes. Our learning guarantees are expressed in terms of a data-dependent measure of sequential complexity and a discrepancy…

Time series prediction underpins a broad range of downstream tasks across many scientific domains. Recent advances and increasing adoption of black-box machine learning models for time series prediction highlight the critical need for…

We study the limit behaviour of upper and lower bounds on expected time averages in imprecise Markov chains; a generalised type of Markov chain where the local dynamics, traditionally characterised by transition probabilities, are now…

Let $\{(X_i,Y_i)\}$ be a stationary ergodic time series with $(X,Y)$ values in the product space $\R^d\bigotimes \R .$ This study offers what is believed to be the first strongly consistent (with respect to pointwise, least-squares, and…

This letter raises the possibility that ergodicity concerns might have some bearing on the signal-to-noise paradox. This is explored by applying the ergodic theorem to the theory behind ensemble weather forecasting and the ensemble mean.…

In the transformative landscape of smart cities, the integration of the cutting-edge web technologies into time series forecasting presents a pivotal opportunity to enhance urban planning, sustainability, and economic growth. The…

Probabilistic time series forecasting has played critical role in decision-making processes due to its capability to quantify uncertainties. Deep forecasting models, however, could be prone to input perturbations, and the notion of such…

Predictability is an emerging metric that quantifies the highest possible prediction accuracy for a given time series, being widely utilized in assessing known prediction algorithms and characterizing intrinsic regularities in human…

The setting is a stationary, ergodic time series. The challenge is to construct a sequence of functions, each based on only finite segments of the past, which together provide a strongly consistent estimator for the conditional probability…