Approximating Financial Time Series with Wavelets

Abstract

Financial time series show many characteristic properties including the phenomenon of clustering of variance, fat-tail distribution, and negative correlation between the rates of return and the volatility of their variance. These facts often render standard methods of parameter estimation and forecasting ineffective. An important feature of financial time series is that they can be characterized by long samples. This causes the models used for their estimation to potentially be more extensive.The aim of the article is to use wavelets to approximate and predict a series. The article describes the author's model for financial time forecasting and provides basic information about wavelets necessary for proper understanding of the proposed wavelet algorithm. The algorithm uses a Daubechies wavelet.

Nonlinear Alleviation of Edge Effects in the Context of Minimizing Prediction Errors

“…An important advantage of this simplest wavelet system is the ease of demonstrating the idea of a discrete wavelet transform using it. The second of the selected wavelet families are the Daubechies wavelets (Daubechies, 1992;Hadaś-Dyduch, 2017;2017b). The further two families -also constructed by Daubechies - …”