基于分位数因子模型预测标普500的实证研究

   本文主要研究了基于分位数因子模型进行标普500预测的实证应用问题。考虑到基于一般线性回归模型框架的经典多因子模型在实证研究中往往存在一些局限性，分位数因子模型则在一定程度上有助于改善这些问题，故本文以分位数因子模型为主题探究了其在变量预测方面的优势。分位数因子模型本质上又是基于潜在因子模型的一个创新，即是潜在因子模型与分位数回归模型的一个有机结合。本文从模型结构剖析的角度出发，通过分析其底层的理论模型框架，对潜在因子模型与分位数回归模型做简要介绍，逐步引出本文的研究核心-分位数因子模型，并详细介绍了分位数因子模型的参数估计方法和因子个数选取准则。同时，根据此前相关文献所反映的金融实证研究中存在的一些实际问题，本文也同步考察了将分位数因子模型运用于研究金融中的高维面板数据时，模型中是否存在着动态因子结构的问题，同时考察由分位数因子模型估计得出的分位数因子相比于传统线性回归模型得到的PCA 均值因子是否包含了额外信息，以及这些额外信息是否具有一定的增量预测能力，并以此为导向开展了相关的实证研究。
   本文通过收集美国市场的宏观数据及个股和个股特征数据作为样本数据集展开研究，实证发现分位数因子模型中确实包含着动态因子结构，而这种动态因子结构与分位数有关，即因子结构与分位数之间存在协变性，这与此前的一些相关文献研究结论相一致。而当我们将不同分位点上的分位数因子对PCA 均值因子回
归时，在不同分位点上的回归结果存在着很大差异，暗示了分位数因子提取了更多的关于变量总体的额外信息。此外，当我们将分位数因子用于变量预测时，发现来自于不同样本的分位数因子均能保持一贯的稳健性预测表现，这表明分位数因子有助于预测变量的未来波动。将分位数因子模型应用于个股及个股特征数据的研究并基于IPCA 因子构建的基准预测模型来考察分位数因子的预测能力是本文的一大创新点，本文对分位数因子模型方法论的介绍和相关应用示例的研究，为后续的分位数因子模型在中国市场的应用提供了一个有益的参考。

   This paper mainly studies the empirical application of S&P 500 prediction based on quantile factor model. Considering that the classical multi-factor model is usually based on the general linear regression model framework often has some limitations in empirical research, quantile factor model can help to improve these problems to a certain extent, so this paper centers on the quantile factor model and try to explore it’s advantages in variable prediction. Essentially speaking, quantile factor model is an innovation based on latent factor model, which is an organic combination of potential factor model and quantile regression model. From the perspective of model structure analysis, this paper briefly introduces the potential factor model and quantile regression model by analyzing its underlying theoretical model framework, and eventually leads to the core of our researchquantile factor model, then we detailedly introduce the parameter estimation method and factor number selection criteria of quantile factor model. At the same time, according to some empirical research problems reflected in previous relevant literatures, this paper focuses on the study of whether there is a dynamic factor structure in the quantile factor model when it is applied to study the high-dimensional panel data of finance and economy,and this paper also studies the quantile factors estimated by the quantile factor model
whether it contains additional information when compared with the PCA mean factors obtained by the traditional linear regression model. In addition, this paper also investigate whether the additional information has some incremental predictive ability in variable forecasting. Based on the above questions, we carried out relevant empirical research.
     This paper conducts research by collecting macro variable data , individual stocks and characteristic data of the US market as sample data sets. The empirical results show that the quantile factor model does contain dynamic factor structure, and this dynamic factor structure is related to quantiles, that is, there is co-movement between factor structure and quantiles, which is consistent with the previous study of some relevant literatures. However, when we regressing the quantile factors on the PCA mean factors, there were significant differences in the regression results across quantiles, suggesting that the quantile factor extracted more additional information about the variable population distribution. Furthermore, when the quantile factor is used to predict variable fluctuation, we found that the quantile factors from different samples can maintain consistent robust prediction performance, which indicates that the quantile factors is helpful to predict the future fluctuation of variables.It is a major innovation of this paper to apply the quantile factor model to the analysis of individual stocks and their characteristic data ,and to investigate the prediction ability of the quantile factors based on the benchmark prediction model constructed by IPCA factor.In this paper, the introduction of quantile factor model methodology and the study of relevant application examples provide a useful reference for the subsequent application of quantile factor model in The Chinese market.

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