Page 47 - Textos de Matemática Vol. 47

ON THE ABILITY OF THE POWER THRESHOLD GARCH MODEL TO CAPTURE THE TAYLOR EFFECT
JOANA LEITE
Dedicated to Professor Nazar´e Mendes Lopes on the occasion of her 60th birthday
Abstract. In this paper, we evaluate the capacity that the first order power threshold GARCH ( -TGARCH(1,1)) model has to reproduce the Taylor e↵ect. The Taylor e↵ect is a stylized fact of financial return series which implies that autocorrelations of absolute returns are greater than the ones of squared returns. We firstly consider = 1 and establish the presence of the Taylor property, Taylor e↵ect theoretical counterpart, for a set of model parameters imposing weak conditions on the generating process distribution. We further explore this set considering particular generating process marginal distributions with di↵erent kurtosis, illus- trating that high values of kurtosis seem to favour the appearance of this property. Finally, considering several values for , we present an ex- ploratory simulation study which shows that the models incorporated in the -TGARCH class are not equally favourable to the Taylor e↵ect appearance.
1. Introduction
Empirical regularities shared by a certain time series group are named styl- ized facts and can be used to reveal both strengths and weaknesses of the models proposed for them, as Engle so well summarized in [3].
A class of time series that has been extensively analysed in the pursuit of stylized facts are financial daily return series. Some of the stylized facts un- covered are very well known, like (see, for example, Francq and Zakoian [4] or
Accepted: 17 February 2015.
2010 Mathematics Subject Classification. 62M10, 62P20.
Key words and phrases. Financial time series, autocorrelations, Taylor e↵ect, Taylor pro-
perty, power TGARCH model.
This work was partially supported by the Centre for Mathematics of the Univer-
sity of Coimbra – UID/MAT/00324/2013, funded by the Portuguese Government through FCT/MEC and co-funded by the European Regional Development Fund through the Part- nership Agreement PT2020.
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