Switching-regime regression for modeling and predicting a stock market return

It has been observed that certain economic and financial variables commonly exhibit switching behavior depending on their magnitude. This phenomenon in general cannot be naturally captured by the linear regression (LR), which assumes a linear relationship between the dependent and explanatory variables. To decipher investor behavior more appropriately by accounting for this observation, a switching-regime regression (SRR) is proposed and applied to the S&P 500 market return with respect to seven explanatory variables. It is shown that, compared with LR, the new regression results in a significantly improved adjusted $$R^2$$ R 2 , increasing from less than $$4\%$$ 4 % to over $$50\%$$ 50 % . In addition, SRR yields better out-of-sample forecasting performance, besides that the fitted values from the new regression even resemble the dip during the 2008 financial crisis, while those from LR do not. The study thus indicates that the switching-regime regression improves significantly the statistical properties including the goodness of fit as well as conforms more to investor behavior theory.