A FUNCTIONAL VERSION OF THE ARCH MODEL

By Siegfried Hormann, Lajos Horv'ath, Ron Reeder. Econometric Theory, 2011

103 citations recorded by the source corpus.

Improvements in data acquisition and processing techniques have led to an almost continuous flow of information for financial data. High-resolution tick data are available and can be quite conveniently described by a continuous-time process. It is therefore natural to ask for possible extensions of financial time series models to a functional setup. In this paper we propose a functional version of the popular autoregressive conditional heteroskedasticity model. We will establish conditions for the existence of a strictly stationary solution, derive weak dependence and moment conditions, show consistency of the estimators, and perform a small empirical study demonstrating how our model matches with real data.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/09a35db291902a2a92fa2da899e1721d82facec8

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Citations in the corpus

Convolutional autoregressive models for functional time series (2016, unknown): “The consistency of such estimators has been proved (Bosq, 2000; Hörmann et al., 2013).”
Asymptotic normality of the principal components of functional time series (2013, background): “[16] discuss examples which include bilinear and ARCH-type functional processes.”
Locally Stationary Functional Time Series (2016, methodology): “Similar to Hörmann et al. (2015), we exploit that the linearity of the autoregressive operator implies the first k Fourier coefficients, for k large, approximately satisfy a VAR(1) equation.”
Testing stationarity of functional time series (2014, background): “…recent research has considered functional time series which have nonlinear dependence structure, see Hörmann and Kokoszka (2010), Gabrys et al. (2010), Horváth et al. (2013), Hörmann et al. (2013), as well as the review of Hörmann and Kokoszka (2012) and Chapter 16 of Horváth and Kokoszka (2012).”
White Noise Testing and Model Diagnostic Checking for Functional Time Series (2016, background): “For example, a functional ARCH(1) process (FARCH(1)) is a functional white noise but is dependent (Hörmann et al., 2013).”