A normalizing and variance-stabilizing transformation for financial time series

Abstract

This chapter describes a normalizing and variance-stabilizing transformation for financial time series. The well-known ARCH/GARCH models with normal errors can account, only partly, for the degree of heavy tails empirically found in the distribution of financial returns series. In choosing the order and the parameters, the twin goals of normalization and variance-stabilization of the transformed series are taken into account. The target of variance-stabilization is easier and amounts to constructing a local estimator of scale for studentization purposes. It is found that if one wants to ensure that some joint distributions are normalized, then the moment matching criterion of the algorithm can be modified. The time series plot prominently shows the phenomenon of volatility clustering. In addition, the dataset appears quite nonnormal and fat-tailed. It is suggested that simple NoVaS has achieved its objective of normalizing, as well as variance-stabilizing. It is found that the exponential NoVaS algorithm also gave qualitatively similar results. © 2003 Elsevier B.V. All rights reserved.