The ARMA Point Process and its Estimation

06/26/2018
by   Spencer Wheatley, et al.
0

We introduce the ARMA (autoregressive-moving-average) point process, which is a Hawkes process driven by a Neyman-Scott process with Poisson immigration. It contains both the Hawkes and Neyman-Scott process as special cases and naturally combines self-exciting and shot-noise cluster mechanisms, useful in a variety of applications. The name ARMA is used because the ARMA point process is an appropriate analogue of the ARMA time series model for integer-valued series. As such, the ARMA point process framework accommodates a flexible family of models sharing methodological and mathematical similarities with ARMA time series. We derive an estimation procedure for ARMA point processes, as well as the integer ARMA models, based on an MCEM (Monte Carlo Expectation Maximization) algorithm. This powerful framework for estimation accommodates trends in immigration, multiple parametric specifications of excitement functions, as well as cases where marks and immigrants are not observed.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

11/29/2017

Extended Poisson INAR(1) processes with equidispersion, underdispersion and overdispersion

Real count data time series often show the phenomenon of the underdisper...
06/05/2019

A copula-based bivariate integer-valued autoregressive process with application

A bivariate integer-valued autoregressive process of order 1 (BINAR(1)) ...
01/26/2019

Clustering Discrete Valued Time Series

There is a need for the development of models that are able to account f...
02/04/2022

First-order integer-valued autoregressive processes with Generalized Katz innovations

A new integer-valued autoregressive process (INAR) with Generalised Lagr...
12/08/2021

Determinantal shot noise Cox processes

We present a new class of cluster point process models, which we call de...
08/29/2019

A robust approach for testing parameter change in Poisson autoregressive models

Parameter change test has been an important issue in time series analysi...
11/29/2017

Fractional approaches for the distribution of innovation sequence of INAR(1) processes

In this paper, we present a fractional decomposition of the probability ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.