Wavelet Volterra Coupled Models for forecasting of nonlinear and non-stationary time series

• Developed Wavelet based model for nonlinear and non-stationary time series.
• Tested using the tourism time series and other well known time series.
• Wavelet based model performs better than other benchmark models.

This paper provides a simple forecasting framework for nonlinear and non-stationary time series using Wavelet based nonlinear models. The proposed method exploits the ability of wavelets to detect non-stationarities that may be present in a given time series in combination with higher order nonlinear Volterra Models. The utility of the proposed model is verified using two examples: the first based on a synthetically generated times series with nonlinear and non stationary features; the second case study examined in the paper pertains to forecasting of number of pilgrims visiting the well known religious shrine at Katra in the state of Jammu and Kashmir in India. Further, the proposed model was applied to 3 time series from M3 competition. The results show that the proposed models perform better when compared with the performance of some well known benchmark models. The long term predictive capability of the wavelet based nonlinear models has also been studied separately.