Related papers: Nonparametric risk bounds for time-series forecast…

In this paper, we show that the recent integration of statistical models with deep recurrent neural networks provides a new way of formulating volatility (the degree of variation of time series) models that have been widely used in time…

Developing statistical models for seismic noise is an exercise of high value in seismic data analysis since these models play a critical role in detecting the onset of seismic events. A majority of these models are usually built on certain…

We study in this paper lower bounds for the generalization error of models derived from multi-layer neural networks, in the regime where the size of the layers is commensurate with the number of samples in the training data. We show that…

We study model evaluation and model selection from the perspective of generalization ability (GA): the ability of a model to predict outcomes in new samples from the same population. We believe that GA is one way formally to address…

Stochastic parareal (SParareal) is a probabilistic variant of the popular parallel-in-time algorithm known as parareal. Similarly to parareal, it combines fine- and coarse-grained solutions to an ordinary differential equation (ODE) using a…

In statistical learning theory, generalization error is used to quantify the degree to which a supervised machine learning algorithm may overfit to training data. Recent work [Xu and Raginsky (2017)] has established a bound on the…

In time-series analyses, particularly for finance, generalized autoregressive conditional heteroscedasticity (GARCH) models are widely applied statistical tools for modelling volatility clusters (i.e., periods of increased or decreased…

Multivariate GARCH models are important tools to describe the dynamics of multivariate times series of financial returns. Nevertheless, these models have been much less used in practice due to the lack of reliable software. This paper…

Time series modeling for predictive purpose has been an active research area of machine learning for many years. However, no sufficiently comprehensive and meanwhile substantive survey was offered so far. This survey strives to meet this…

The purpose of this paper is to provide a discussion, with illustrating examples, on Bayesian forecasting for dynamic generalized linear models (DGLMs). Adopting approximate Bayesian analysis, based on conjugate forms and on Bayes linear…

We develop a generalized stability framework for stochastic discrete-time systems, where the generality pertains to the ways in which the distribution of the state energy can be characterized. We use tools from finance and operations…

This study addresses the computational challenges of forecasting volatility in high-dimensional commodity markets. Building on the Network log-ARCH framework, we introduce a novel class of network topologies from GARCH-informed correlation…

We develop a non-parametric multivariate time series model that remains agnostic on the precise relationship between a (possibly) large set of macroeconomic time series and their lagged values. The main building block of our model is a…

We consider the analysis of continuous repeated measurement outcomes that are collected through time, also known as longitudinal data. A standard framework for analysing data of this kind is a linear Gaussian mixed-effects model within…

Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these…

One of the main theoretical challenges in learning dynamical systems from data is providing upper bounds on the generalization error, that is, the difference between the expected prediction error and the empirical prediction error measured…

Stochastic gradient methods enable learning probabilistic models from large amounts of data. While large step-sizes (learning rates) have shown to be best for least-squares (e.g., Gaussian noise) once combined with parameter averaging,…

In order to calculate the unobserved volatility in conditional heteroscedastic time series models, the natural recursive approximation is very often used. Following \cite{StraumannMikosch2006}, we will call the model \emph{invertible} if…

Time-series forecasting models often encounter abrupt changes in a given period of time which generally occur due to unexpected or unknown events. Despite their scarce occurrences in the training set, abrupt changes incur loss that…

Forecasting groups of time series is of increasing practical importance, e.g. forecasting the demand for multiple products offered by a retailer or server loads within a data center. The local approach to this problem considers each time…