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 \(R^2\), increasing from less than \(4\%\) to over \(50\%\). 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.

中文翻译：

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切换区域回归模型和预测股票市场收益

已经观察到，某些经济和金融变量通常根据其大小表现出转换行为。通常，线性回归（LR）不能自然地捕获此现象，因为线性回归假定因变量和解释变量之间存在线性关系。为了通过解释这一观察结果更恰当地破译投资者行为，提出了一种转换制度回归（SRR），并针对七个解释变量将其应用于标准普尔500指数市场回报。结果表明，与LR相比，新的回归导致调整后的\（R ^ 2 \）显着提高，从小于\（4 \％\）增加到大于\（50 \％\）。此外，SRR可以提供更好的样本外预测性能，此外，新回归的拟合值甚至类似于2008年金融危机期间的下跌，而LR则没有。因此，该研究表明，转换制度回归显着改善了统计性质，包括拟合优度，并且更符合投资者行为理论。