Related papers: Prediction of functional ARMA processes with an ap…
We express the classic ARMA time-series model as a directed graphical model. In doing so, we find that the deterministic relationships in the model make it effectively impossible to use the EM algorithm for learning model parameters. To…
We consider the problem of comparing several samples of stochastic processes with respect to their second-order structure, and describing the main modes of variation in this second order structure, if present. These tasks can be seen as an…
This paper tackles one of the most fundamental goals in functional time series analysis which is to provide reliable predictions for future functions. Existing methods for predicting a complete future functional observation use only…
Subspace methods like canonical variate analysis (CVA) are regression based methods for the estimation of linear dynamic state space models. They have been shown to deliver accurate (consistent and asymptotically equivalent to quasi maximum…
This paper considers both the least squares and quasi-maximum likelihood estimation for the recently proposed scalable ARMA model, a parametric infinite-order vector AR model, and their asymptotic normality is also established. It makes…
This paper presents GAMMA, a general motion prediction model that enables large-scale real-time simulation and planning for autonomous driving. GAMMA models heterogeneous, interactive traffic agents. They operate under diverse road…
We consider the problem of power demand forecasting in residential micro-grids. Several approaches using ARMA models, support vector machines, and recurrent neural networks that perform one-step ahead predictions have been proposed in the…
This paper studies a regression model where both predictor and response variables are random functions. We consider a functional linear model where the conditional mean of the response variable at each time point is given by a linear…
This paper is motivated by modeling the cycle-to-cycle variability associated with the resistive switching operation behind memristors. As the data are by nature curves, functional principal component analysis is a suitable candidate to…
The modeling of time-varying graph signals as stationary time-vertex stochastic processes permits the inference of missing signal values by efficiently employing the correlation patterns of the process across different graph nodes and time…
A new approach for functional data description is proposed in this paper. It consists of a regression model with a discrete hidden logistic process which is adapted for modeling curves with abrupt or smooth regime changes. The model…
Let $(B(t))_{t\in \Theta}$ with $\Theta={\mathbb Z}$ or $\Theta={\mathbb R}$ be a wide sense stationary process with discrete or continuous time. The classical linear prediction problem consists of finding an element in…
We describe a simple and succinct methodology to develop hourly auto-regressive moving average (ARMA) models to forecast power output from a photovoltaic solar generator. We illustrate how to build an ARMA model, to use statistical tests to…
Graph-based techniques emerged as a choice to deal with the dimensionality issues in modeling multivariate time series. However, there is yet no complete understanding of how the underlying structure could be exploited to ease this task.…
Many agent based simulation approaches have been proposed for pedestrian flow. As such models are applied e.g.\ in evacuation studies, the quality and reliability of such models is of vital interest. Pedestrian trajectories are functional…
We address the problem of defining early warning indicators of critical transition. To this purpose, we fit the relevant time series through a class of linear models, known as Auto-Regressive Moving-Average (ARMA(p,q)) models. We define two…
Fitting autoregressive moving average (ARMA) time series models requires model identification before parameter estimation. Model identification involves determining the order of the autoregressive and moving average components which is…
We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…
We present a mathematical model to predict pedestrian motion over a finite horizon, intended for use in collision avoidance algorithms for autonomous driving. The model is based on a road map structure, and assumes a rational pedestrian…
Several applications of the QR-AAA algorithm, a greedy scheme for vector-valued rational approximation, are presented. The focus is on demonstrating the flexibility and practical effectiveness of QR-AAA in a variety of computational…