Nonlinear GARCH model and 1/f noise

Aleksejus Kononovicius and Julius Ruseckas

Papers from arXiv.org

Abstract: Auto-regressive conditionally heteroskedastic (ARCH) family models are still used, by practitioners in business and economic policy making, as a conditional volatility forecasting models. Furthermore ARCH models still are attracting an interest of the researchers. In this contribution we consider the well known GARCH(1,1) process and its nonlinear modifications, reminiscent of NGARCH model. We investigate the possibility to reproduce power law statistics, probability density function and power spectral density, using ARCH family models. For this purpose we derive stochastic differential equations from the GARCH processes in consideration. We find the obtained equations to be similar to a general class of stochastic differential equations known to reproduce power law statistics. We show that linear GARCH(1,1) process has power law distribution, but its power spectral density is Brownian noise-like. However, the nonlinear modifications exhibit both power law distribution and power spectral density of the power law form, including 1/f noise.

Date: 2014-12, Revised 2015-02
New Economics Papers: this item is included in nep-ets
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Published in Physica A 427, 2015, pp. 74-81

Downloads: (external link)
http://arxiv.org/pdf/1412.6244 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1412.6244

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().