Local Semi-linear Regression for River Runoff Forecasting

Time series data such as river runoff and stock prices are important for the human society. Many time series data exhibit a linear property. That is, a sequence of neighboring data points are approximately on one straight line. Consequently, linear regression techniques are developed for the purpose of forecasting, and linear segmentation techniques are developed for the purposes of data compression, exact sequence matching and forecasting. In this paper, we point out that for some real world data the linear property is strong, however quite local, and linear segmentation techniques produce rather short segments. Therefore we consider an extremely simple regression, called local linear regression, which only takes into account the most recent time series change. While applied on the daily runoff data of Mississippi river, this approach performs better than linear regression, higher order polynomial regressions, and even M5 model trees. Also, it gives quite satisfactory results in flood seasons. To further improve the forecasting accuracy, we propose a local semi-linear regression (LSLR) approach by introducing a factor alpha to the runoff changing speed. Experimental results show that our approach can achieve an accuracy of 86.68% while the error tolerance is only plusmn1.5% in flood seasons.