Page 161 - Special Topic Session (STS) - Volume 4

STS577 Md. Sabiruzzaman et al.

Perfection of volatility prediction with time scale

information using wavelet transformation
Md. Sabiruzzaman, Md. Kamrul Islam
Department of Statistics, University of Rajshahi

Abstract
Volatility of stock market returns is one of the major concerns among
investors, industrialists and policymakers. GARCH family model is a very
popular tool for describing existence of volatility clustering in such time series
data. However, it lacks from interpreting time-scale variation that is an
important issue for different levels of investors. An efficient way of
representing a time series with such complex dynamic is given by wavelet
methodology. With the help of a wavelet basis, the Maximal Overlap Discrete
Wavelet Transform (MODWT) is able to break a time series with respect to a
time scale while preserving the time dimension and energy. Time scale
specification information is necessary if one accepts the view that stock market
consist of heterogeneous investors operating at different time scales. In that
case, considerable more insight in to the volatility dynamic can be gained by
looking at the data at several time scales. Wavelet transformations are also
fast to calculate and are ideally suited for analyzing large data set. This paper
provides an improved alternative to the classical econometric tools in the
financial markets prediction. Forecasting stock market volatility with wavelet
analysis is the central element of this paper. A novel algorithm, where wavelet
transformation is incorporated to an econometric model, is implemented in
order to improve the performance of volatility prediction. On the analyzed
data we showed that our forecasting algorithm has achieved better results
compared with the approach which not using the wavelet transform.

Keywords
Volatility prediction; Wavelet transformation; Time scale variation; Stock index

1. Introduction
In the financial domain of stock market estimation, prediction of the risk
of holding assets is a challenging job. In stock market, there are different level
of investors who are concerned about the market series and volatility on
different time horizon. Therefore, the researcher pays much attention to give
proper information for the different level of investors. They need more time to
collect and analyze the data at different time horizon. For example, if one
wants to estimate the risk for daily, weekly and monthly investor. And he has
a daily data, when the return interval is increased in a given sample period, the
number of sample points will decrease which result in loss of information. It is

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