Financial time series

Overview

Dimitris N. Politis

Published Online: Aug 19 2009 10:29 AM

DOI: 10.1002/wics.24

Free article on Wiley InterScience: HTML | PDF

The evolution of financial markets is a complicated real-world phenomenon that ranks at the top in terms of difficulty of modeling and/or prediction. One reason for this difficulty is the well-documented nonlinearity that is inherent at work. The state-of-the-art on the nonlinear modeling of financial returns is given by the popular auto-regressive conditional heteroscedasticity (ARCH) models and their generalizations but they all have their short-comings. Foregoing the goal of finding the ‘best’ model, it is possible to simply transform the problem into a more manageable setting such as the setting of linearity. The form and properties of such a transformation are given, and the issue of one-step-ahead prediction using the new approach is explicitly addressed. Copyright © 2009 John Wiley & Sons, Inc.

Figure 1.

Daily returns of the S&P500 index spanning the period 8-30-1979 to 8-30-1991.

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Figure 2.

(a) Correlogram of the S&P500 returns. (b) Correlogram of the S&P500 squared returns.

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Figure 3.

Normalized S&P500 returns, i.e., the tranformed V -series, spanning the same period 8-30-1979 to 8-30-1991.

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Figure 4.

Plot of \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$\hat K(w_{1}, w_{2})$\end{document} vs. (w1, w2) for the S&P500 returns.

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Figure 5.

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Figure 6.

QQ-plot of the S&P500 returns.

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Figure 7.

QQ-plot of the normalized S&P500 returns.

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Comments

1 comment

Contributor Epizitone Anabi: Posted on November 04, 2009 | 11:48PM

I do agree the simplicity and linear possibility of arch model makes it attractive, but I am equally worried that, is not convincing enough to shelf the objective of a better prediction model. As a fact, I don't quite have any unique suggestion ,but won't it be more reasonable to overlap various models considering their prediction strenght rather than going with arch for the reason stated?