Functional Generalized Autoregressive Conditional Heteroskedasticity

Aue, Alexander; Horváth, Lajos; Pellatt, Daniel F.

doi:10.1111/jtsa.12192

Cited by 65 publications

(90 citation statements)

References 26 publications

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“…() and Bosq ()) and functional generalized auto‐regressive conditional heteroscedastic processes (see Aue et al . ()). It is assumed that the underlying error innovations

({italicϵ}_{i} : i \in Z)

are elements of an arbitrary measurable space S .…”

Section: Resultsmentioning

confidence: 94%

Detecting and Dating Structural Breaks in Functional Data Without Dimension Reduction

Aue

Rice

Sönmez

2017

Journal of the Royal Statistical Society Series B: Statistical Methodology

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158

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Summary Methodology is proposed to uncover structural breaks in functional data that is ‘fully functional’ in the sense that it does not rely on dimension reduction techniques. A thorough asymptotic theory is developed for a fully functional break detection procedure as well as for a break date estimator, assuming a fixed break size and a shrinking break size. The latter result is utilized to derive confidence intervals for the unknown break date. The main results highlight that the fully functional procedures perform best under conditions when analogous estimators based on functional principal component analysis are at their worst, namely when the feature of interest is orthogonal to the leading principal components of the data. The theoretical findings are confirmed by means of a Monte Carlo simulation study in finite samples. An application to annual temperature curves illustrates the practical relevance of the procedures proposed.

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“…() and Bosq ()) and functional generalized auto‐regressive conditional heteroscedastic processes (see Aue et al . ()). It is assumed that the underlying error innovations

({italicϵ}_{i} : i \in Z)

are elements of an arbitrary measurable space S .…”

Section: Resultsmentioning

confidence: 94%

Detecting and Dating Structural Breaks in Functional Data Without Dimension Reduction

Aue

Rice

Sönmez

2017

Journal of the Royal Statistical Society Series B: Statistical Methodology

Self Cite

158

View full text Add to dashboard Cite

show abstract

“…From a semi-parametric viewpoint, [4] put forward a semi-functional partial linear model that combines both parametric and nonparametric models, and this model allows us to consider additive covariates and to use a continuous path in the past to predict future values of a stochastic process. Apart from the estimation of a conditional mean, [20] considered a functional autoregressive conditional heteroskedasticity model for modeling conditional variance, while [5] considered a functional generalized autoregressive conditional heteroskedasticity model. [27] considered a portmanteau test for testing autocorrelation under a functional analog of generalized autoregressive conditional heteroskedasticity model.…”

Section: Introductionmentioning

confidence: 99%

High-dimensional functional time series forecasting: An application to age-specific mortality rates

Gao

Shang

Yang

2019

Journal of Multivariate Analysis

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We address the problem of forecasting high-dimensional functional time series through a two-fold dimension reduction procedure. The difficulty of forecasting high-dimensional functional time series lies in the curse of dimensionality. In this paper, we propose a novel method to solve this problem. Dynamic functional principal component analysis is first applied to reduce each functional time series to a vector. We then use the factor model as a further dimension reduction technique so that only a small number of latent factors are preserved. Classic time series models can be used to forecast the factors and conditional forecasts of the functions can be constructed. Asymptotic properties of the approximated functions are established, including both estimation error and forecast error. The proposed method is easy to implement especially when the dimension of the functional time series is large. We show the superiority of our approach by both simulation studies and an application to Japanese age-specific mortality rates.

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“…The first attempt to generalise GARCH models to functional time series was made in Hörmann et al (2013), where a functional version of the ARCH(1) was proposed. Later, this model was extended in Aue et al (2016) to a functional GARCH(1,1). Both models rely on recurrence equations with unknown operators and curves.…”

Section: Introductionmentioning

confidence: 99%

Functional GARCH models: The quasi-likelihood approach and its applications

Cerovecki

Francq

Hörmann

et al. 2019

Journal of Econometrics

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The increasing availability of high frequency data has initiated many new research areas in statistics. Functional data analysis (FDA) is one such innovative approach towards modelling time series data. In FDA, densely observed data are transformed into curves and then each (random) curve is considered as one data object. A natural, but still relatively unexplored, context for FDA methods is related to financial data, where high-frequency trading currently takes a significant proportion of trading volumes. Recently, articles on functional versions of the famous ARCH and GARCH models have appeared. Due to their technical complexity, existing estimators of the underlying functional parameters are moment based-an approach which is known to be relatively inefficient in this context. In this paper, we promote an alternative quasi-likelihood approach, for which we derive consistency and asymptotic normality results. We support the relevance of our approach by simulations and illustrate its use by forecasting realised volatility of the S&P100 Index.

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Functional Generalized Autoregressive Conditional Heteroskedasticity

Cited by 65 publications

References 26 publications

Detecting and Dating Structural Breaks in Functional Data Without Dimension Reduction

Detecting and Dating Structural Breaks in Functional Data Without Dimension Reduction

High-dimensional functional time series forecasting: An application to age-specific mortality rates

Functional GARCH models: The quasi-likelihood approach and its applications

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