On the Gaussian Process for Stationary and Non-stationary Time Series Prediction for the Qatar Stock Market

In this paper, we adopt a Gaussian prediction model for non-stationary time series, then we discuss four transformation techniques: Generalized Optimal Wavelet Decomposition Algorithm (GOWDA), Hilbert Huang transform (HHT), Detrending based on Echo State Networks (DESN), and Kolmogorov-Zurbenco (KZ) filter. GOWDA is an algorithm that runs the continuous wavelet transform (CWT) several times using different mother wavelet functions, maximal levels, and thresholding techniques. It chooses a combination with minimal error. While HHT combines echo state networks (ESNs), which decomposes the time series into intrinsic mode functions (IMFs), the Hilbert spectral analysis is applied to the IMFs before reconstructing the denoised signal. DESN is a neural network algorithm with minimal assumptions. KZ filter is a moving average algorithm that is easy to understand and implement. When comparing the performance of these methods with the Gaussian prediction model, it was found that the HHT reconstructed before prediction gave the best results.