Year of Graduation
Time Series Prediction with Discrete Wavelet Transform and Hybrid Forecasting Models
Forecasting of time series containing transient volatility and structural breaks without proper preprocessing of data is recognized as a significantly complicated task. To resolve it one can use Fourier decomposition or, its more efficient counterpart, - wavelet transform. The latter identifies detailed changes of the series more accurately and can be useful in denoising of data. In the current study wavelet decomposition is used in order to obtain components of high and low frequencies, which presumably represent correspondingly linear (detailed) and nonlinear (approximate) parts of the series. Reconstructed detailed part is estimated via ARIMA and then obtained residuals are summed up with approximate part in order to be estimated with LSTM. Obtained forecasts of the data, preprocessed with three different types of wavelets ("Haar", "Daubechies-2" и "Daubechies-4"), are compared with the forecasts of the sole models consisting of ARIMA or LSTM. Results demonstrated practical use of wavelet transform and showed that there is a single optimal threshold for separation of the series into high and low frequency parts.