License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/OASIcs.SCOR.2014.34
URN: urn:nbn:de:0030-drops-46683
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2014/4668/
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Katsiampa, Paraskevi

A new approach to modelling nonlinear time series: Introducing the ExpAR-ARCH and ExpAR-GARCH models and applications

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Abstract

The analysis of time series has long been the subject of interest in different fields. For decades time series were analysed with linear models. Nevertheless, an issue that has been raised is whether there exist other models that can explain and fit real data better than linear ones. In this paper, new nonlinear time series models are proposed (namely the ExpAR-ARCH and the ExpAR-GARCH), which are combinations of a nonlinear model in the conditional mean and a nonlinear model in the conditional variance and have the potential of explaining observed data in various fields. Simulated data of these models are presented, while different algorithms (the Nelder-Mead simplex direct search method, the Quasi-Newton line search algorithm, the Active-Set algorithm, the Sequential Quadratic Programming algorithm, the Interior Point algorithm and a Genetic Algorithm) are used and compared in order to check their estimation performance when it comes to these suggested nonlinear models. Moreover, an application to the Dow Jones data is considered, showing that the new models can explain real data better than the AR-ARCH and AR-GARCH models.

BibTeX - Entry

@InProceedings{katsiampa:OASIcs:2014:4668,
  author =	{Paraskevi Katsiampa},
  title =	{{A new approach to modelling nonlinear time series: Introducing the ExpAR-ARCH and ExpAR-GARCH models and applications}},
  booktitle =	{4th Student Conference on Operational Research},
  pages =	{34--51},
  series =	{OpenAccess Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-67-5},
  ISSN =	{2190-6807},
  year =	{2014},
  volume =	{37},
  editor =	{Pedro Crespo Del Granado and Martim Joyce-Moniz and Stefan Ravizza},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2014/4668},
  URN =		{urn:nbn:de:0030-drops-46683},
  doi =		{10.4230/OASIcs.SCOR.2014.34},
  annote =	{Keywords: Nonlinear time series, ExpAR-ARCH model, ExpAR-GARCH model}
}

Keywords: Nonlinear time series, ExpAR-ARCH model, ExpAR-GARCH model
Collection: 4th Student Conference on Operational Research
Issue Date: 2014
Date of publication: 06.08.2014

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