Arbitrage Pricing Theory as a Restricted Nonlinear Multivariate Regression Model Iterated Nonlinear Seemingly Unrelated Regression Estimates
用可观测的宏观经济变量替代因子分析中的未知随机因子，将套利定价理论重新表述为带跨方程约束的多元非线性回归模型，并采用迭代非线性似不相关回归方法估计资产敏感性和风险价格。
By replacing the unknown random factors of factor analysis with observed macroeconomic variables, the arbitrage pricing theory (APT) is recast as a multivariate nonlinear regression model with across-equation restrictions. An explicit theoretical justification for the inclusion of an arbitrary, well-diversified market index is given. Using monthly returns on 70 stocks, iterated nonlinear seemingly unrelated regression techniques are employed to obtain joint estimates of asset sensitivities and their associated APT risk "prices." Without the assumption of normally distributed errors, these estimators are strongly consistent and asymptotically normal. With the additional assumption of normal errors, they are also full-information maximum likelihood estimators. Classical asymptotic nonlinear nested hypothesis tests are supportive of the APT with measured macroeconomic factors.