Page 57 - Textos de Matemática Vol. 47

-TGARCH MODEL: CAPTURING THE TAYLOR EFFECT 47
Analysing Tables 1 and 2 separately, it appears that increasing values are not favourable to Taylor e↵ect, especially for = 2, which includes the standard GARCH model. Looking at the model kurtosis, it seems that it plays a role in the appearance of the Taylor e↵ect, larger values being preferable, but other factors also seem to be at play. Now comparing both tables regarding the generating process marginal distribution, the leptokurtic Laplace distribution apparently generates more series with this e↵ect than the mesokurtic Gaussian distribution. Although these results do not contradict previous findings, further studies are required to fully support these claims.
Acknowledgments
I would like to thank the referee for helpful comments and suggestions.
I kindly acknowledge the precious comments and revision of Professor Nazar´e Mendes Lopes and Professor Esmeralda Gon¸calves in the development of this theme, as my PhD advisors until 2013. In a broader sense, I am grateful to them for introducing me to time series analysis and for their supreme guidance in so many stages of my academic training. On this occasion, I especially wish to thank Professor Nazar´e Mendes Lopes for sharing her knowledge, insights and uplifting way to approach problems. I have to say... it has been a privilege.
References
[1] F. Black, Studies of stock price volatility changes, in: Proc. of the 1976 Meeting of the Business and Economic Statistics Section, American Statistical Association, 177–181, 1976.
[2] Z. Ding, C. W. J. Granger, and R. F. Engle, A long memory property of stock market returns and a new model, J. Empir. Financ. 1, 83–106, 1993.
[3] R. F. Engle, New frontiers for ARCH models, J. Appl. Econometrics 17, 425–446, 2002.
[4] C. Francq and J. M. Zakoian, GARCH Models: Structure, Statistical Inference and
Financial Applications. John Wiley & Sons, Chichester, UK, 2010.
[5] E. Gonc¸alves, J. Leite, and N. Mendes-Lopes, A mathematical approach to detect the
Taylor property in TARCH processes, Statist. Probab. Lett. 79, 602–610, 2009.
[6] E. Gon¸calves, J. Leite, and N. Mendes-Lopes, On the probabilistic structure of power threshold generalized ARCH stochastic processes, Statist. Probab. Lett. 82, 1597–1609,
2012.
[7] E. Gon¸calves, C. Martins, and N. Mendes-Lopes, The Taylor property in non-negative
bilinear models, REVSTAT (in press), 2015.
[8] E. Gon¸calves, N. Mendes-Lopes, I. Dorotoviˇc, J. M. Fernandes, and A. Garcia, North
and South Hemispheric Solar Activity for Cycles 21-23: Asymmetry and Conditional
Volatility of Plage Regions Areas, Sol. Phys. 289 (6), 2283–2296, 2014.
[9] C. W. J. Granger, The past and future of empirical finance: some personal comments,
J. of Econometrics 129, 35–40, 2005.
[10] C.W.J.GrangerandZ.Ding,Somepropertiesofabsolutereturn:analternativemeasure
of risk, Annales d’E´conomie et de Statistique 40, 67–91, 1995.