Hilbert valued fractionally integrated autoregressive moving average processes with long memory operators

10/09/2020
by   Amaury Durand, et al.
0

Fractionally integrated autoregressive moving average processes have been widely and successfully used to model univariate time series exhibiting long range dependence. Vector and functional extensions of these processes have also been considered more recently. Here we rely on a spectral domain approach to extend this class of models in the form of a general Hilbert valued processes. In this framework, the usual univariate long memory parameter d is replaced by a long memory operator D acting on the Hilbert space. Our approach is compared to processes defined in the time domain that were previously introduced for modeling long range dependence in the context of functional time series.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

03/13/2021

Statistical inference for ARTFIMA time series with stable innovations

Autoregressive tempered fractionally integrated moving average with stab...
03/17/2020

A comparison of Hurst exponent estimators in long-range dependent curve time series

The Hurst exponent is the simplest numerical summary of self-similar lon...
01/08/2020

Spectral estimation for non-linear long range dependent discrete time trawl processes

Discrete time trawl processes constitute a large class of time series pa...
12/15/2019

Spectral analysis and parameter estimation of Gaussian functional time series

This paper contributes with some asymptotic results to the spectral anal...
04/05/2021

Spectral Subsampling MCMC for Stationary Multivariate Time Series

Spectral subsampling MCMC was recently proposed to speed up Markov chain...
07/04/2020

The maximum of the periodogram of Hilbert space valued time series

We are interested to detect periodic signals in Hilbert space valued tim...
This week in AI

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