Can The Wavelet-kernel Methodology Improve Other Kernel Techniques?
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M. Gago & E. Juaristi
Our aim in this paper is to compare different ways of forecasting using the wavelet transform and the kernel regression. We consider that working with block (or segment) of data is richer than working with individual data (as in traditional kernel), as we assume there is some kind of pattern inside each block which will improve the estimation, and therefore the prediction. We choose the wavelet transform because this transform is able to separate components of data in different locations and with different location in time and frequency.To test the performance of the different methodologies we have carried out a Monte Carlo Study in which we have compared the four methodologies: Ordinary Least Square (OLS), Traditional Kernel (TK), Block Kernel (BK) and Wavelet-Kernel (WK). Two real life applications have been realized. On the one hand, volatility smile has been forecast and on the other, the rated temperature of the steel coils’ furnace is predicted. Surprisingly contradictory results had been obtained. Keywords: wavelets, Kernel regression, bandwidth selection, implied volatility, option pricing models, steel coils’ furnace’s rated temperature. 1 Introduction The wavelet transform is a mathematical tool that is very used in several fields such as engineering, mathematics, physics, economics or finance. It allows us to separate data evolving in time in different frequency-time components. This way, we will be able to identify in data its peaks and discontinuities using high scales components and its long-trend or pattern using the low ones, because as it’s known at low scales the wavelet transform has a large time support,whereas at high scales has a small one.
wavelets, Kernel regression, bandwidth selection, implied volatility, option pricing models, steel coils’ furnace’s rated temperature.