Abstract: Economic variables are mostly low-frequency data such as monthly, quarterly or annual types, whereas stock price data can be time intervals of minutes or seconds or less, while stock price data can be high frequency or ultra-high frequency data. In the traditional research, most scholars require the sampling frequency of model variables to be consistent, so most of the previous researchers use low-frequency data such as monthly and quarterly data when studying the relationship between macroeconomics and stock volatility. While many meaningful conclusions are drawn from the studies, there are also obvious shortcomings. For example, the estimation method using low-frequency data loses the valid information embedded in stock market volatility, causes parameter estimation and volatility prediction bias, and fails to assess the combined impact of economic factors on stock market volatility. Therefore, how to incorporate variables into different sampling frequencies in the same model becomes very important. To solve this problem, some scholars have proposed a GARCH-MIDAS model based on mixed frequency data, which decomposes volatility into long-term and short-term components, mainly employs daily return data and monthly (or quarterly) data on economic variables, and uses these two types of mixed-frequency data to capture the impact of low-frequency macroeconomic variables (long-term component) on high-frequency volatility (short-term component). In estimating the long-run volatility component of the GARCH-MIDAS model, the RV estimates are obtained based on intraday high-frequency data. In estimating the high-frequency volatility of the stock market, the higher the sampling frequency of the high-frequency data used, the more significant the effect of noise and jumps on the high-frequency volatility, at which point the RV will no longer be a consistent estimator of the integral volatility. In order to eliminate the effects of noise and jumps, many scholars have proposed new high-frequency volatility estimators, such as the RTSRV estimator, which eliminates the effects of noise and jumps at the same time and improves the estimation efficiency of the realized volatility.
In this paper, on the basis of previous studies, we have done further extended research, and the highlights mainly focus on two aspects: (1)We comprehensively select 15 economic variables that are closely related to stock market volatility, extract the principal components from them and study the different principal components of economic variables from both the level and volatility. (2)In estimating the long-term volatility component τ_t of the GARCH-MIDAS model, we adopt theRTSRV estimator that takes into account the effects of noise and jumps at the same time, and use the MCS test to compare the GARCH-MIDAS model we construct with the traditional GARCH-MIDAS model.
It is found that: the GARCH-MIDAS-RTSRV model constructed in this paper is better than the traditional GARCH-MIDAS model in terms of higher prediction accuracy and higher economic value for investors; the principal components of economic variables and realized volatility have significant effects on stock market volatility, and volatility has a more significant effect on stock market volatility compared to its level value. The effect of volatility on stock market volatility is more significant than its level value.

Key words: GARCH-MIDAS-RTSRV model, mixed frequency data, economic variables, stock market volatility

摘要： 本文对GARCH-MIDAS模型进行了拓展。首先,在估计GARCH-MIDAS模型的长期波动成分时,采用同时考虑噪声和跳跃影响的稳健双频已实现波动估计量RTSRV来代替传统的已实现波动估计量RV。其次,选取了经济变量并从中提取出主成分,从其水平值和波动率两个层面研究不同主成分对股市波动的影响。研究发现:本文构造的GARCH-MIDAS-RTSRV模型优于传统的GARCH-MIDAS模型,其预测精度更高并且可使投资者获得更高的经济价值;经济变量的主成分和已实现波动率均对股市的波动有显著的影响,并且相较于其水平值,波动率对股市波动的影响更为显著。

关键词: GARCH-MIDAS-RTSRV模型, 混频数据, 经济变量, 股市波动