Related papers: The ARMA Point Process and its Estimation

Generally, anomaly detection has a great importance particularly in applied statistical signal processing. Here we provide a general framework in order to detect anomaly through the statistical modeling. In this paper, it is assumed that a…

In this paper, we propose a novel and efficient two-stage variable selection approach for sparse GLARMA models, which are pervasive for modeling discrete-valued time series. Our approach consists in iteratively combining the estimation of…

By a random process with immigration at random times we mean a shot noise process with a random response function (response process) in which shots occur at arbitrary random times. The so defined random processes generalize random processes…

We develop a canonical framework for the study of the problem of registration of multiple point processes subjected to warping, known as the problem of separation of amplitude and phase variation. The amplitude variation of a real random…

It is an important task in the literature to check whether a fitted autoregressive moving average (ARMA) model is adequate, while the currently used tests may suffer from the size distortion problem when the underlying autoregressive models…

Evidence Accumulation Models (EAMs) have been widely used to investigate speeded decision-making processes, but they have largely neglected the role of predictive processes emphasized by theories of the predictive brain. In this paper, we…

The problem of estimating ARMA models is computationally interesting due to the nonconcavity of the log-likelihood function. Recent results were based on the convex minimization. Joint model selection using penalization by a convex norm,…

This paper introduces and studies a new model of computation called an Alternating Automatic Register Machine (AARM). An AARM possesses the basic features of a conventional register machine and an alternating Turing machine, but can carry…

This paper proves the consistency property for the regularized maximum likelihood estimators (MLEs) of multivariate Hawkes processes (MHPs). It also develops an alternating minimization type algorithm (AA-iPALM) to compute the MLEs with…

This paper presents a comparative study of two Bayesian approaches - Markov Chain Monte Carlo (MCMC) and Approximate Bayesian Computation (ABC) - for estimating the parameters of autoregressive fractionally-integrated moving average…

We introduce a nonlinear modification of the classical Hawkes process, which allows inhibitory couplings between units without restrictions. The resulting system of interacting point processes provides a useful mathematical model for…

In this paper, we address the problem of adaptive learning for autoregressive moving average (ARMA) model in the quaternion domain. By transforming the original learning problem into a full information optimization task without explicit…

Estimation in GARMA models has traditionally been carried out under the frequentist approach. To date, Bayesian approaches for such estimation have been relatively limited. In the context of GARMA models for count time series, Bayesian…

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 article we study multivariate continuous-time autoregressive moving-average (MCARMA) processes with values in convex cones. More specifically, we introduce matrix-valued MCARMA processes with L\'evy noise and present necessary and…

We develop a new family of marked point processes by focusing the characteristic properties of marked Hawkes processes exclusively to the space of marks, providing the freedom to specify a different model for the occurrence times. This is…

In this paper we discuss dynamic ARMA-type regression models for time series taking values in $(0,\infty)$. In the proposed model, the conditional mean is modeled by a dynamic structure containing autoregressive and moving average terms,…

An extension of the Hawkes model where the productivity is variable is considered. In particular, the case is considered where each point may have its own productivity and a simple analytic formula is derived for the maximum likelihood…

The class of multivariate L\'{e}vy-driven autoregressive moving average (MCARMA) processes, the continuous-time analogs of the classical vector ARMA processes, is shown to be equivalent to the class of continuous-time state space models.…

In this paper, we design a nonparametric online algorithm for estimating the triggering functions of multivariate Hawkes processes. Unlike parametric estimation, where evolutionary dynamics can be exploited for fast computation of the…