Aue, Alexander and Horvath, Lajos and Pellatt, Daniel (2015): Functional generalized autoregressive conditional heteroskedasticity.

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Abstract
Heteroskedasticity is a common feature of financial time series and is commonly addressed in the model building process through the use of ARCH and GARCH processes. More recently multivariate variants of these processes have been in the focus of research with attention given to methods seeking an efficient and economic estimation of a large number of model parameters. Due to the need for estimation of many parameters, however, these models may not be suitable for modeling now prevalent highfrequency volatility data. One potentially useful way to bypass these issues is to take a functional approach. In this paper, theory is developed for a new functional version of the generalized autoregressive conditionally heteroskedastic process, termed fGARCH. The main results are concerned with the structure of the fGARCH(1,1) process, providing criteria for the existence of a strictly stationary solutions both in the space of squareintegrable and continuous functions. An estimation procedure is introduced and its consistency verified. A small empirical study highlights potential applications to intraday volatility estimation.
Item Type:  MPRA Paper 

Original Title:  Functional generalized autoregressive conditional heteroskedasticity 
English Title:  Functional generalized autoregressive conditional heteroskedasticity 
Language:  English 
Keywords:  Econometrics; Financial time series; Functional data; GARCH processes; Stationary solutions 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics 
Item ID:  67702 
Depositing User:  Professor Lajos Horvath 
Date Deposited:  09. Nov 2015 05:30 
Last Modified:  09. Nov 2015 05:32 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/67702 