Financial Time Series Forecasting with Hybrid ARIMA-Continuous Wavelet Transform

Financial time series analysis often requires both temporal and spectral information. Wavelet transform, which shares fundamental concepts with windowed Fourier transform, introduces the notion of scale to enable simultaneous time-frequency analysis. Continuous Wavelet Transform (CWT), coupling with Morse analytic wavelet function have been chosen to extract frequency information from the residual of ARIMA fitted financial time series. The extracted frequency information was then utilized to perform in-sample forecasting. The hybrid ARIMA+CWT forecasting results were then compared with pure ARIMA forecasting results. Results showed that hybrid ARIMA+CWT forecasting performed better than pure ARIMA forecasting. A conclusion has thus been drawn that additional data can be extracted from the residual of ARIMA using CWT and turned into useful information.