Pseudo-maximum likelihood estimation of ARCH(∞) models

By Peter M. Robinson, Paolo Zaffaroni. 2005

95 citations recorded by the source corpus.

Strong consistency and asymptotic normality of the Gaussian pseudo-maximum likelihood estimate of the parameters in a wide class of ARCH(∞) processes are established. We require the ARCH weights to decay at least hyperbolically, with a faster rate needed for the central limit theorem than for the law of large numbers. Various rates are illustrated in examples of particular parameteriza- tions in which our conditions are shown to be satisfied.

Subfields: Economics and Econometrics, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/dd59ccc63cd3d8ec71d7ec3c81d07aac8eed8cee

How researchers see this paper

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

In Economics and Econometrics

1. Piotr Fryzlewicz
2. Francisco Blasques
3. William Kengne
4. Olivier Wintenberger
5. S. J. Koopman
6. Jean‐Marc Bardet
7. S. Rao
8. Paolo Gorgi

In Finance

1. Francisco Blasques
2. S. J. Koopman
3. Piotr Fryzlewicz
4. William Kengne
5. Olivier Wintenberger
6. Jean‐Marc Bardet
7. Paolo Gorgi
8. S. Rao

In Statistics and Probability

1. Francisco Blasques
2. William Kengne
3. Olivier Wintenberger
4. Jean‐Marc Bardet
5. S. J. Koopman
6. Piotr Fryzlewicz
7. S. Rao
8. Paolo Gorgi

Citations in the corpus

• QUASI-MAXIMUM LIKELIHOOD ESTIMATION OF SEMI-STRONG GARCH MODELS (2009, unknown): “See also Berkes and Horváth (2003, 2004), Hall and Yao (2003), and Robinson and Zaffaroni (2006).”
• Multiple breaks detection in general causal time series using penalized quasi-likelihood (2012, background): “MR0072412 [21] Robinson, P., and Zaffaroni, P. Pseudo-maximum likelihood estimation of ARCH(∞) models.”
• ASYMPTOTIC NORMALITY OF THE QUASI MAXIMUM LIKELIHOOD ESTIMATOR FOR MULTIDIMENSIONAL CAUSAL PROCESSES (2007, methodology): “There are no such conditions in Proposition 2, and assumption (Id′) seems to be more general and easier used than assumption A(r), F(1) and G of [24].”
• Feasible invertibility conditions and maximum likelihood estimation for observation-driven models (2018, result): “Among others, [22] and [39] weaken the conditions for consistency and asymptotic normality and extend the results to a larger class of models.”
• GARCH Models (2010, unknown): “The condition for the existence of a strictly stationary ARCH(∞) process was established by Robinson and Zaffaroni (2006) and Douc, Roueff and Soulier (2008).”
• Mixing properties of ARCH and time-varying ARCH processes (2011, background): “It is worth mentioning that the GARCH(p, q) process has an ARCH(∞) representation, where the aj decay geometrically with j. Giraitis and Robinson [19], Robinson and Zaffaroni [34] and Subba Rao [37] consider parameter estimation for the ARCH(∞) process.”