The functional central limit theorem for a family of GARCH observations with applications

Berkes, István; Hörmann, Siegfried; Horváth, Lajos

doi:10.1016/j.spl.2008.03.021

Cited by 27 publications

(22 citation statements)

References 25 publications

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“…One may also extend the weak convergence result to linear processes with GARCH innovations by making use of the weak convergence result for GARCH processes; see Berkes, Hormann, and Horvath (2008). It is possible to extend the results to be developed in this paper to these other processes.…”

Section: New Unit Root Testsmentioning

confidence: 89%

Unit Root Tests With Wavelets

2010

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This paper develops a wavelet (spectral) approach to testing the presence of a unit root in a stochastic process. The wavelet approach is appealing, since it is based directly on the different behavior of the spectra of a unit root process and that of a short memory stationary process. By decomposing the variance (energy) of the underlying process into the variance of its low frequency components and that of its high frequency components via the discrete wavelet transformation (DWT), we design unit root tests against near unit root alternatives. Since DWT is an energy preserving transformation and able to disbalance energy across high and low frequency components of a series, it is possible to isolate the most persistent component of a series in a small number of scaling coefficients. We demonstrate the size and power properties of our tests through Monte Carlo simulations.

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Section: New Unit Root Testsmentioning

confidence: 89%

Unit Root Tests With Wavelets

2010

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“…For simplicity, we consider here the case of an augmented GARCH(1,1) sequence (with

double-struckS = R

), defined by

Y_{k} = ε_{k} σ_{k - 1}, k \in Z

with

normalΛ ((), σ_{k}^{2}) = c ((), ε_{k}) normalΛ ((), σ_{k - 1}^{2}) + g ((), ε_{k}),

where Λ(·), c (·) and g (·) are real‐valued measurable functions such that Λ −1 (·) exists. Extensions can be readily obtained by following Berkes and Hörmann ). Berkes and Hörmann (), Duan () gave necessary and sufficient conditions for the existence of a unique, strictly stationary solution of ( and .…”

Section: Examplesmentioning

confidence: 99%

Optimal Rate of Convergence for Empirical Quantiles and Distribution Functions for Time Series

Jirak

2016

Journal Time Series Analysis

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Given a stationary sequence ¹X k º k2Z , we are interested in the rate of convergence in the central limit theorem of the empirical quantiles and the empirical distribution function. Under a general notion of weak dependence, we show a Berry-Esseen result with optimal rate n 1=2 . The setup includes many prominent time series models, such as functions of ARMA or (augmented) GARCH processes. In this context, optimal Berry-Esseen rates for empirical quantiles appear to be novel.

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“…La convergencia débil ha sido estudiada en investigaciones más recientes (Bradley, 2007;Dedecker et al, 2007;Wu, 2007), que en general hacen uso de las estimaciones de la varianza de largo plazo, como las descritas por Liu y Wu (2010). Las condiciones que garantizan la aplicación de estos resultados, en el caso de los segundos momentos, se pueden encontrar en Berkes et al (2008). Para el presente estudio, el estadístico de prueba fue calculado en 4.6945, a 1% de significancia se rechaza la hipótesis nula.…”

Section: Prueba De Quiebre Estructural En La Varianzaunclassified

Regímenes de volatilidad del tipo de cambio en Colombia e intervenciones de política

Uribe¹,

Restrepo²,

Fernández³

2015

Investigación Económica

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ResumenEn este documento se explora la evolución reciente de la volatilidad del tipo de cambio nominal (peso-dólar) en Colombia. Se identifican algunas de las características del proceso que la describe, separando la evolución de la volatilidad condicional y la volatilidad no condicional, a la cual se le permite transitar entre regímenes, utilizando un modelo ARCH con cambios de régimen (SWARCH). Al comparar los regímenes de volatilidad, se concluye que las intervenciones del Banco de la República en el mercado cambiario no han sido efectivas para inducir un cambio de régimen en la volatilidad de la serie. Palabras clave: política cambiaria Colombia, SWARCH, intervenciones, volatilidad tipo de cambio países emergentes. Clasificación JEL: C58, E42, E58, E61. AbstractIn this document, we explore the dynamics of the volatility of the Colombian exchange rate (USA dollar-Colombia peso). Some features of the stochastic process describing the exchange rate volatility are identified. Special attention is given to the distinction between conditional and unconditional moments. We use an ARCH model with regimen switching (SWARCH) to perform this task. From the comparison of the volatility regimes we conclude that the interventions of the Colombia Central Bank have been ineffective to induce a regimen change in the market. . Los autores agradecen el apoyo de la Universidad del Valle y del Centro de Investigaciones y Documentación Socioeconómica (CIDSE) en tiempo y recursos, así como la excelente asistencia de investigación de Karol Carbonell y las discusiones con los integrantes del grupo de Macroeconomía Aplicada y Economía Financiera (MAEF) de su institución de adscripción, en especial los comentarios de Inés María Ulloa. Además, agradecen los comentarios realizados por los pares académicos anónimos de la revista. Las opiniones expresadas en este documento son responsabilidad de los autores, así como los errores u omisiones que se pudieren presentar.

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The functional central limit theorem for a family of GARCH observations with applications

Cited by 27 publications

References 25 publications

Unit Root Tests With Wavelets

Unit Root Tests With Wavelets

Optimal Rate of Convergence for Empirical Quantiles and Distribution Functions for Time Series

Regímenes de volatilidad del tipo de cambio en Colombia e intervenciones de política

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