利用样本新息对三因子Fama-French回归模型的新认识
A New Look to Three-Factor Fama-French Regression Model using Sample Innovations
摘要：
Fama-French模型被广泛用于评估投资组合与市场回报相比的表现。在Fama-French模型中，所有因子都是时间序列数据。横截面数据与时间序列数据略有不同。时间序列回归的一个明显问题是，时间序列回归中的R平方通常非常高，特别是与横截面数据的典型R平方相比。R平方的高值可能会导致误解，即回归模型很好地拟合了观测数据，并且自变量很好地解释了因变量的方差。因此，为了进行回归分析，并克服序列相关和波动率聚集，我们使用标准的计量经济学时间序列模型来获得样本创新。在这项研究中，我们重新审视和验证的Fama-French模型在两个不同的方式：使用Fama-French模型中的因素和资产收益率，并考虑样本创新的Fama-French模型，而不是研究因素。比较本研究中考虑的两种方法，我们建议Fama-French模型应考虑重尾分布，因为尾部行为在Fama-French模型中是相关的，包括金融数据，QQ图不能验证选择正态分布作为模型中噪声的理论分布。
英文摘要：
The Fama-French model is widely used in assessing the portfolio's performance compared to market returns. In Fama-French models, all factors are time-series data. The cross-sectional data are slightly different from the time series data. A distinct problem with time-series regressions is that R-squared in time series regressions is usually very high, especially compared with typical R-squared for cross-sectional data. The high value of R-squared may cause misinterpretation that the regression model fits the observed data well, and the variance in the dependent variable is explained well by the independent variables. Thus, to do regression analysis, and overcome with the serial dependence and volatility clustering, we use standard econometrics time series models to derive sample innovations. In this study, we revisit and validate the Fama-French models in two different ways: using the factors and asset returns in the Fama-French model and considering the sample innovations in the Fama-French model instead of studying the factors. Comparing the two methods considered in this study, we suggest the Fama-French model should be considered with heavy tail distributions as the tail behavior is relevant in Fama-French models, including financial data, and the QQ plot does not validate that the choice of the normal distribution as the theoretical distribution for the noise in the model.
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