Wavelet as a Viable Alternative for Time Series Forecasting

Abstract

Analysis of financial data is always challenging due to the non-linear and non-stationary characteristics of the time series which is further complicated by volatility clustering effect and sudden changes such as jump, steep slopes and valleys. Classical regression based analysis techniques often entail rigorous mathematical treatments albeit with little success in exploiting the differing frequency characteristics to uncover hidden but valuable trending information. Wavelet, on the other hand provides an efficient way to represent time series with such complex dynamics by decomposing it into time-frequency space and at the same time preserve both temporal and spectral information. This property enables analysts to identify the dominant modes (spectral information) of a time series and observe how those modes vary over time (temporal information). Most importantly, wavelet transform is computationally efficient, only a small number of wavelet coefficients are needed to describe complicated signals. This paper seeks to establish cases for the use of wavelets as viable tools in time series forecasting. Two time series, Kijang Emas Daily Index and Bit Coin Daily Price with differing characteristics are used as subjects of study. Out-of-sample dynamic forecasting of 20 points is made using best-fit ARIMA and prior-point imitation follow by wavelet de-noising methods (imitate-wavelet). Comparisons made with MAPE measurements of ARIMA and imitate-wavelet methods indicated comparable forecasting performance between the simpler imitate-wavelet techniques and ARIMA model.