Analytic Hessian Matrices and the Computation of FIGARCH Estimates
AbstractLong memory in conditional variance is one of the empirical features of most financial time series. One class of models that was suggested to capture this behavior refers to the so-called Fractionally Integrated GARCH processes (Baillie, Bollerslev and Mikkelsen 1996) in which the ideas of fractional integration originally introduced by Granger (1980) and Hosking (1981) for processes for the mean are applied to a GARCH framework. In this paper we derive analytic expressions for the second-order derivatives of the log-likelihood function of FIGARCH processes with a view to the advantages that can be gained in computational speed and estimation accuracy. The comparison is computationally intensive given the typical sample size of the time series involved and the way the likelihood function is built. An illustration is provided on exchange rate and stock index data.
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Bibliographic InfoPaper provided by Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti" in its series Econometrics Working Papers Archive with number wp2002_03.
Length: 21 pages
Date of creation: 11 Feb 2002
Date of revision:
Long Memory; Volatility Modelling; FIGARCH Processes.;
Find related papers by JEL classification:
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
- C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2002-06-13 (All new papers)
- NEP-ECM-2002-06-13 (Econometrics)
- NEP-ETS-2002-06-13 (Econometric Time Series)
- NEP-IFN-2002-06-13 (International Finance)
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