De-noising and Prediction of Time Series Based on the Wavelet Algorithm and Chaos Theory (Case Study: SPI Drought Monitoring Index of Tabriz City)

Natural phenomena usually seem irregular at the first glance, however, with changing the scale and the noise they can become regular and therefore it is possible to predict their behaviors. This idea is the main base of the Chaos Theory that deals with studying of unstable and non-periodic behavior of nonlinear and swinging dynamic systems. The time series of drought, as a major natural disaster, has a dynamic nature. and therefore the Chaos Thero can play a significant role in capturing the detailed changes. Refinement of the indicators, standardized precipitation index (SPI) is now widely used in the world. The obtained SPI data are noisy, and therefore the predictions made based on this data are not very accurate. Wavelet algorithm is able to describe a signal in time and frequency domain and also analyze a signal locally. Hence in this study, it is used in order to de-noise time series of SPI of Tabriz city for the past 40 years. The nature of the chaotic time series was evaluated using the Lyapunov exponent and correlation dimension parameters. The results indicated a very chaotic time series behavior for the studied data. The behavior of the system is non-random, and then the time series are not portion of the stochastic and the noise process. To predict the SPI values by the Chaos Theory, the algorithm of the false nearest neighbors is used. Validation of the results indicated the high accuracy of the predictions of the Chaos Theory. According to the proposed method the severity of the droughts and the SPI of the Tabriz city are predicted for the next 3 years.