Using Hybrid Regression Tree and ARIMA Model with Wavelet Transforms for Evaporation Time Series Forecasting
Abstract
Forecasting accuracy of evaporation time series is an importance to control environmental impacts, damages, and risks affecting especially plant life and growth, and thus that impact on human and animal life. Evaporation data are considered from climate time series, which are characterized by its nature a non-linearity data, as they suffer from the problem of heterogeneity because they contain many seasonal and periodic components, and necessarily that complexity may lead to inaccurate forecasts. The time stratified method will be used in this study with the proposed forecasting methods to achieve greater homogeneity and less complex temporal behavior. Two forecasting methods will be used, represented by the regression tree (RT) method and the integrated autoregressive and moving average (ARIMA)model, and it is proposed to hybridize them with a method that combines both within the hybrid ARIMA-RT model as a way to improve forecasting results by dealing more accurately with the non-linearity data. The effect of wavelet transformations (WT) will also be tested with both the ARIMA model and the hybrid ARIMA-RT model, and whether it will have a role in improving forecasting results. A time series modeling structure will be adopted to determine the input structure of the RT model within the proposed hybrid approach by using multiplicative seasonal ARIMA. Also, the use of WT will be limited to filtering a random errors series (residuals), which the rest of its time lags depended on, represented by the moving average variables process. The forecasting results of the proposed methods might comparisons with the traditional forecasting method. This study was concerned with investigating various methods for forecasting evaporation time series for an agricultural meteorological station in the city of Mosul, Iraq for hot and cold seasons. The results of this study reflected the superiority of the hybrid method compared to the traditional ARIMA model. The results also included that forecasts were clearly affected by the use of WT. it can be concluded that the ARIMA-RT hybrid model has a clear role in improving the accuracy of forecast results through this study. Using WT leads to a slight improvement in the accuracy of forecasts, and it may vary according to the data and its nature and homogeneity.
References
- Alada, E., Forecasting of particulate matter with a hybrid ARIMA model based on wavelet transformation and seasonal adjustment. Urban Climate, 2021. 39: p. 100930.
- Chan, N.H., Time Series Applications to Finance. 2002, John Wiley & Sons, Inc.
- Choubin, B., et al., Precipitation forecasting using classification and regression trees (CART) model: a comparative study of different approaches. Environmental earth sciences, 2018. 77(8): p. 1-13.
- Das, R.C., Forecasting incidences of COVID-19 using Box-Jenkins method for the period July 12-Septembert 11, 2020: A study on highly affected countries. Chaos, Solitons & Fractals, 2020. 140: p. 110248.
- Donoho, D.L. and I.M. Johnstone, Adapting to unknown smoothness via wavelet shrinkage. Journal of the american statistical association, 1995. 90(432): p. 1200-1224.
- Eymen, A. and . Kyl, Seasonal trend analysis and ARIMA modeling of relative humidity and wind speed time series around Yamula Dam. Meteorology and Atmospheric Physics, 2019. 131: p. 601-612.
- Gupta, A. and A. Kumar. Mid term daily load forecasting using ARIMA, wavelet-ARIMA and machine learning. in 2020 IEEE International Conference on Environment and Electrical Engineering and 2020 IEEE Industrial and Commercial Power Systems Europe (EEEIC/I&CPS Europe). 2020. IEEE.
- Hyndman, R.J. and A.B. Koehler, Another look at measures of forecast accuracy. International journal of forecasting, 2006. 22(4): p. 679-688.
- Jaishi, H.P., et al., Comparing wavelet-based artificial neural network, multiple linear regression, and ARIMA models for detecting genuine radon anomalies associated with seismic events. Proceedings of the Indian National Science Academy, 2024: p. 1-15.
- Liu, L.-M., Time Series Analysis and Forecasting. 2nd ed. 2006. 578.
- Loh, W.-Y., Classification and regression tree methods. Encyclopedia of statistics in quality and reliability, 2008. 1: p. 315-323.
- Loh, W.Y., Classification and regression trees. Wiley interdisciplinary reviews: data mining and knowledge discovery, 2011. 1(1): p. 14-23.
- Mallat, S.G., A theory for multiresolution signal decomposition: the wavelet representation. IEEE transactions on pattern analysis and machine intelligence, 1989. 11(7): p. 674-693.
- Palma, W., Long-memory time series: theory and methods. Vol. 662. 2007: John Wiley & Sons.
- Pham, B.T., I. Prakash, and D.T. Bui, Spatial prediction of landslides using a hybrid machine learning approach based on random subspace and classification and regression trees. Geomorphology, 2018. 303: p. 256-270.
- Rutkowski, L., et al., The CART decision tree for mining data streams. Information Sciences, 2014. 266: p. 1-15.
- Shukur, O.B. and M.H. Lee, Daily wind speed forecasting through hybrid KF-ANN model based on ARIMA. Renewable Energy, 2015. 76: p. 637-647.
- Wei, W.W.S., Time series analysis : univariate and multivariate methods. 2nd ed ed. 2006: Pearson Addison Wesley.
- Zhang, J., et al., A hybrid approach of wavelet transform, ARIMA and LSTM model for the share price index futures forecasting. The North American Journal of Economics and Finance, 2024. 69: p. 102022.
