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IMA Journal of Management Mathematics Advance Access originally published online on May 24, 2007
IMA Journal of Management Mathematics 2007 18(4):395-412; doi:10.1093/imaman/dpm024
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© The authors 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Modelling financial time series with SEMIFAR–GARCH model

Yuanhua Feng

Department of Actuarial Mathematics and Statistics, Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, UK

Jan Beran

Department of Mathematics and Statistics, University of Konstanz, Konstanz, Germany

Keming Yu{dagger}

Department of Mathematical Sciences, Brunel University, Uxbridge, UK

{dagger} Email: keming.yu{at}brunel.ac.uk

Received on 16 November 2006. Accepted on 20 March 2007.

A class of semiparametric fractional autoregressive models with generalized autoregressive conditional heteroskedastic (GARCH) errors, which includes deterministic trends, difference stationarity and stationarity with short- and long-range dependence and heteroskedastic model errors, is very powerful for modelling financial time series. This paper discusses the model fitting, including an efficient algorithm and parameter estimation of GARCH error term, so that the model can be applied in practice. We then illustrate the model and estimation methods with a few of different finance data sets.

Keywords: financial time series; GARCH model; SEMIFAR model; parameter estimation; kernel estimation; asymptotic property


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