Time Series Forecasting Using Wavelet Denoising an Application to Saudi Stock Index

Abstract

In recent years, wavelet transform has become very popular in many application areas such as physics, engineering, biomedical, signal processing, mathematics, and statistics. In this paper, we present the role of wavelet transform in time series analysis. Saudi Stock Index (SSI) time series was used as a vehicle to highlight the benefits of wavelet transform usage in time series analysis in general and in time series denoising, in particular. SSI was modeled as a deterministic function plus random noise (white or colored). Different denoising techniques were considered with Haar, Daubechies’, and Biorthogonal wavelets. Several Forecasting models of SSI were developed for original and denoised series. Namely, Linear Regression (LR), Simple Moving Average (SMA), Exponential Smoothing (ES), Autoregressive (AR), and Autoregressive Moving Average (ARMA). Computational results have shown that more information could be exploited from SSI when it is decomposed into several series with different resolutions using wavelet transform. Moreover, forecasting errors of SSI can be substantially reduced when the index was first denoised using soft thresholding with white noise assumption. Keywords: Wavelet transform, denoising, forecasting