We develop a heterogeneous spatial arbit and regression coefficients, and heteroscedastic variances, and further establish identification of parameters and asymptotic normality of the conditional QML estimators under some mild conditions. We apply the proposed model to study a real data set of 11 eurozone stock index returns and extend the Fama–French five-factor model to regional stock indices, in which heterogeneous spatial effects and heteroscedastic disturbances are highly significant and they both play very important roles in explaining distinct endogenous effects and distinct risks of the 11 eurozone stock markets. Our empirical results reveal unique characteristics of each of 11 eurozone stock markets and their inner connections.

中文翻译：

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具有异质空间效应和异方差干扰的套利定价

我们开发了异质空间仲裁和回归系数，以及异方差，并进一步建立了在一些温和条件下条件 QML 估计量的参数和渐近正态性的识别。我们将所提出的模型应用到11个欧元区股票指数收益的真实数据集，并将Fama-French五因子模型扩展到区域股票指数，其中异质空间效应和异方差扰动非常显着，它们都发挥着非常重要的作用解释 11 个欧元区股票市场的不同内生效应和不同风险。我们的实证结果揭示了 11 个欧元区股票市场各自的独特特征及其内在联系。