Abstract—In this dissertation the Discrete Wavelet Transform and HHT Transform will be used for pre-treatment of the stock prices of 50 indicative companies in Taiwan 50 Index in order to establish the stationary state time series, and then the AR(2) model will be used for daily prediction of data in the next transaction days. In the end the root mean square error (RMSE) will be used for accuracy comparison, and the K-S test will be used to examine whether or not the predication residual is in normal distribution. The result of prediction has indicated that DWT prediction performs better than HHT prediction in the first week with a share of 31/50, yet HHT prediction performs better than DWT prediction in the second week with a share of 29/50. As for the two-week prediction, the performances of DWT and HHT predictions are similar. The true value will fall within the Wavelet/HHT confidence bands established by DWT or HHT method in the first week, the second week, or during the two-week time span. The scope of occurrence of this regression line can be obtained using the confidence band of this regression line, and the Wavelet/HHT confidence bands of the 50 underlying stocks established by DWT or HHT will all fall within this confidence band.

Index Terms—Discrete wavelet transform, HHT, second-order autoregressive model, wavelet confidence band, Taiwan 50 index.

Hong-Ru Ke, Chi-I Yang, and Kuei-Fang Chang are with Graduate Institute of Applied Mathematics, Feng-Chia University, 40724 Tai-Chung, Taiwan (e-mail: hungru30@hotmail.com, yesheslhamo@gmail.com, kfchang@math.fcu.edu.tw).
Kai-Cheng Wang is with Ph.D. Program in Mechanical and Aeronautical Engineering, Feng-Chia University, 40724 Tai-Chung, Taiwan (e-mail: gtotony98@gmail.com).

Cite: Hong-Ru Ke, Kai-Cheng Wang, Chi-I. Yang, and Kuei-Fang Chang, "Wavelet and Hilbert-Huang Transform Based on Predicting Stock Forecasting in Second-Order Autoregressive Mode," International Journal of Applied Physics and Mathematics vol. 4, no. 1, pp. 9-14, 2014.