Forecasting volatility by using wavelet transform, ARIMA and GARCH models

Forecasting volatility of certain stocks plays an important role for investors as it allows to quantify associated trading risk and thus make right decisions. This work explores econometric alternatives for time series forecasting, such as the ARIMA and GARCH models, which have been widely used in the financial industry. These techniques have the advantage that training the models does not require high computational cost. To improve predictions obtained from ARIMA, the discrete Fourier transform is used as ARIMA pre-processing, resulting in the wavelet ARIMA strategy. Due to the linear nature of ARIMA, non-linear patterns in the volatility time series cannot be captured. To solve this problem, two hybridisation techniques are proposed, combining wavelet ARIMA and GARCH. The advantage of applying this methodology is associated with the ability of each to capture linear and non-linear patterns present in a time series. These two hybridisation techniques are evaluated to verify which provides better prediction. The volatility time series is associated with Tesla stock, which has a highly volatile nature and it is of major interest to many investors today.