Deniz Kenan Kılıç, Ph.D.
Department of Financial Mathematics
February 2021
Supervisor: Ömür Uğur (Institute of Applied Mathematics, Middle East Technical University, Ankara)
Abstract
The thesis aims to combine wavelet theory with nonlinear models, particularly neural networks, to find an appropriate time series model structure. Data like financial time series are nonstationary, noisy, and chaotic. Therefore using wavelet analysis helps better modeling in the sense of both frequency and time.
S&P500 (^GSPC) and NASDAQ (^IXIC) data are divided into several components by using multiresolution analysis (MRA). Subsequently, each part is modeled by using a suitable neural network structure. In this step, the design of the model is formed according to the pattern of the subseries. Then predictions of each subseries are combined. The combined prediction result is compared to the original time series' prediction result using only a nonlinear model. Moreover, wavelets are used as an activation function for LSTM networks to form a hybrid LSTM-Wavenet model. Furthermore, the hybrid LSTM-Wavenet model is fused with MRA as a proposed method.
In brief, it is studied whether using MRA and hybrid LSTM-Wavenet model decreases the loss or not for both S&P500 and NASDAQ data. Four different modeling methods are used: LSTM, LSTM+MRA, hybrid LSTM-Wavenet, hybrid LSTM-Wavenet+MRA (the proposed method). Results show that using MRA and wavelets as an activation function together decreases error values the most.
Keywords: nonlinear models, neural networks, LSTM, wavelets, time series analysis, finance, multiresolution analysis, wavelet neural network, wavenet, hybrid models