Estimation of nonparametric regression function using shrinkage wavelet and different mother functions

Abstract

Wavelet reduction is one of the most widely used methods for removing noise from the signal, primarily financial and banking data, and building a non-parametric regression model that enables us to study the phenomenon accurately. The appropriate choice of the wavelet mother, which results in concentrating the bulk of the signal strength on a few wavelet coefficients, is one of the most determining factors in noise removal and obtaining accurate regression function estimates. Given the importance of studying the price index in Iraq, many mother functions within the wavelet transformation have been studied. To determine which of them is more suitable for such a type of data, which gives accurate estimates of the relationship between trading volume as an independent variable and the Iraq market index as a dependent variable, the best or most appropriate functions were determined through the estimates that have less (MSE). It became clear that the best or relevant parts are (Coif1, Coif5, and rbio1.3).
The study was applied to real data represented by the trading volume and price index data for the Iraqi market for the period from (2008) to April (2022). It became clear that the trading volume significantly affects the price index, but other variables must be studied.