WEAKLY DEPENDENT CHAINS WITH INFINITE MEMORY

By Paul Doukhan, Olivier Wintenberger. 2007

139 citations recorded by the source corpus.

We prove the existence of a weakly dependent strictly stationary solution of the equation Xt=F(Xt-1,Xt-2,Xt-3,...;[xi]t) called a chain with infinite memory. Here the innovations [xi]t constitute an independent and identically distributed sequence of random variables. The function F takes values in some Banach space and satisfies a Lipschitz-type condition. We also study the interplay between the existence of moments, the rate of decay of the Lipschitz coefficients of the function F and the weak dependence properties. From these weak dependence properties, we derive strong laws of large number, a central limit theorem and a strong invariance principle.

Subfields: Finance, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5285eac9459f19ef006b5b3a9fd0ada0cda9948f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

1. Konstantinos Fokianos
2. V. Christou
3. Olivier Wintenberger
4. Jean‐Marc Bardet
5. William Kengne
6. Paul Doukhan
7. Wei Biao Wu
8. Eric Moulines

In Mathematical Physics

1. Konstantinos Fokianos
2. V. Christou
3. Wei Biao Wu
4. Randal Douc
5. Paul Doukhan
6. Jean‐Marc Bardet
7. Eric Moulines
8. Olivier Wintenberger

In Statistics and Probability

1. Konstantinos Fokianos
2. V. Christou
3. Olivier Wintenberger
4. Jean‐Marc Bardet
5. Eric Moulines
6. William Kengne
7. Randal Douc
8. Wei Biao Wu

Citations in the corpus

• Asymptotic theory for stationary processes (2011, background): “Note that in our setting W (1) = ∑∞ j=1 wj = 1, while W (1) 1 is required in Doukhan and Wintenberger (2008).”
• Stationarity and geometric ergodicity of BEKK multivariate GARCH models (2011, background): “However, one could try to ex tend the idea of [15] where the existence of aτ-weakly dependent strictly stationary solution for a chain w th infinite memory has been shown under a Lipschitz-type condition, but the exp ression of this condition in terms of the matrices appearing in the BEKK representa”
• Ergodicity of observation-driven time series models and consistency of the maximum likelihood estimator (2012, background): “Those authors apply Doukhan and Wintenberger (2008) results; the latter use a contraction argument also adapted to deal with more general infinite memory models which essentially extends on assumptions (13) below relative to the current Markov case.”
• QUASI‐LIKELIHOOD INFERENCE FOR NEGATIVE BINOMIAL TIME SERIES MODELS (2013, methodology): “We verify condition 3.1 of Doukhan and Wintenberger (2008).”
• Multiple breaks detection in general causal time series using penalized quasi-likelihood (2012, background): “MR2450899 [8] Doukhan, P. and Wintenberger, O. Weakly dependent chains with infinite memory.”