Related papers: On model fitting and estimation of strictly statio…

We define a new multivariate time series model by generalizing the ARMAX process in a multivariate way. We give conditions on stationarity and analyze local dependence and domains of attraction. As a consequence of the obtained result, we…

Producing probabilistic guarantee for several steps of a predicted signal follow a temporal logic defined behavior has its rising importance in monitoring. In this paper, we derive a method to compute the joint probability distribution of…

We discuss simulation schemes for continuous-time autoregressive moving average (CARMA) processes driven by tempered stable L\'evy noises. CARMA processes are the continuous-time analogue of ARMA processes as well as a generalization of…

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…

A wide range of approaches for batch processes monitoring can be found in the literature. This kind of process generates a very peculiar data structure, in which successive measurements of many process variables in each batch run are…

We consider the asymmetric random average process which is a one-dimensional stochastic lattice model with nearest neighbour interaction but continuous and unbounded state variables. First, the explicit functional representations, so-called…

The Model-free Prediction Principle has been successfully applied to general regression problems, as well as problems involving stationary and locally stationary time series. In this paper we demonstrate how Model-Free Prediction can be…

This paper provides a simple method to estimate both univariate and multivariate MA processes. Similar to Durbin's method, it rests on the recursive relation between the parameters of the MA process and those of its AR representation. This…

In this paper we propose a new optimization model for maximum likelihood estimation of causal and invertible ARMA models. Through a set of numerical experiments we show how our proposed model outperforms, both in terms of quality of the…

In this paper, using spectral theory of Hilbertian operators, we study ARMA Gaussian processes indexed by graphs. We extend Whittle maximum likelihood estimation of the parameters for the corresponding spectral density and show their…

In this paper, we introduce the concept of fractional integration for spatial autoregressive models. We show that the range of the dependence can be spatially extended or diminished by introducing a further fractional integration parameter…

This article considers a nonparametric method for detecting change points in non-stationary time series. The proposed method will divide the time series into several segments so that between two adjacent segments, the normalized spectral…

Celestial objects exhibit a wide range of variability in brightness at different wavebands. Surprisingly, the most common methods for characterizing time series in statistics -- parametric autoregressive modeling -- is rarely used to…

This paper considers a simulation-based estimator for a general class of Markovian processes and explores some strong consistency properties of the estimator. The estimation problem is defined over a continuum of invariant distributions…

This paper introduces a new class of robust estimates for ARMA models. They are M-estimates, but the residuals are computed so the effect of one outlier is limited to the period where it occurs. These estimates are closely related to those…

This paper addresses the prediction of stationary functional time series. Existing contributions to this problem have largely focused on the special case of first-order functional autoregressive processes because of their technical…

Given the scarcity of anomalies in real-world applications, the majority of literature has been focusing on modeling normality. The learned representations enable anomaly detection as the normality model is trained to capture certain key…

Dynamic model averaging (DMA) combines the forecasts of a large number of dynamic linear models (DLMs) to predict the future value of a time series. The performance of DMA critically depends on the appropriate choice of two forgetting…

Max-stable processes are natural models for spatial extremes because they provide suitable asymptotic approximations to the distribution of maxima of random fields. In the recent past, several parametric families of stationary max-stable…

The positive link prediction (PLP) problem is formulated in a system identification framework: we consider dynamic graphical models for auto-regressive moving-average (ARMA) Gaussian random processes. For the identification of the…