Tree-Structured Nonlinear Regression

Tree algorithms have been widely developed for regression problems. One of the good features of a regression tree is the flexibility of fitting because it can correctly capture the nonlinearity of data well. Especially, data with sudden structural breaks such as the price of oil and exchange rates could be fitted well with a simple mixture of a few piecewise linear regression models. Now that split points are determined by chi-squared statistics related with residuals from fitting piecewise linear models and the split variable is chosen by an objective criterion, we can get a quite reasonable fitting result which goes in line with the visual interpretation of data. The piecewise linear regression by a regression tree can be used as a good fitting method, and can be applied to a dataset with much fluctuation.