经济政策不确定性与中国股市波动率——基于已实现SV-MIDAS模型的实证研究

doi:10.16381/j.cnki.issn1003-207x.2023.1116

摘要/Abstract

摘要：

本文构建了已实现SV-MIDAS（RSV-MIDAS）模型框架，将经济政策不确定性（EPU）引入其中，实证分析了EPU对中国股市波动率的影响以及预测作用。为了估计RSV-MIDAS模型的参数，本文提出基于连续粒子滤波的极大似然估计方法，并利用蒙特卡罗模拟实验验证了该估计方法的有效性。采用月度中国EPU指数和日内高频上证综合指数与深证成分指数价格数据，对引入EPU的RSV-MIDAS（RSV-MIDAS-EPU）模型进行实证研究，结果表明：EPU对中国股市长期波动率具有显著的负向影响，即EPU水平提高，预期中国股市长期波动率会下降；EPU对股市长期波动率的影响相比月度已实现波动率（RV）对股市长期波动率的影响持续时间更长。利用多种损失函数和模型置信集（MCS）检验作为判断准则，实证比较了RSV-MIDAS-EPU模型与其他竞争模型对中国股市波动率的样本外预测能力，结果表明：已实现测度和EPU对于中国股市波动率预测具有重要作用；RSV-MIDAS-EPU模型具有更优越的波动率预测能力。最后，通过波动率择时策略分析发现，RSV-MIDAS-EPU模型能够获得更高的投资组合经济价值。

关键词: 经济政策不确定性, 波动率预测, 已实现SV-MIDAS, 连续粒子滤波, 波动率择时

Abstract:

Modelling and forecasting volatility has attracted a great deal of attention in financial econometrics literature due to the fact that volatility plays an important role in many financial applications， such as portfolio allocation， risk measurement and derivative pricing. It is well known that volatility is time-varying and highly persistent， and many models have been proposed to capture these stylized facts. The stochastic volatility （SV） model is among the most popular model. However， the standard SV model is a single factor model， which ignores important information contained in the high-frequency data and macroeconomic variables.

An alternative approach for modelling volatility is the realized stochastic volatility （RSV） model， which extends the SV model by incorporating the realized volatility measures and produces more accurate volatility forecasts than the SV model. Despite the empirical success of the RSV model， it still fails to capture the impact of macroeconomic variables on stock market volatility. In recent years， the level of economic policy uncertainty （EPU） keeps rising due to a series of major events， such as the Sino-US trade war， the COVID-19 pandemic and the Russia-Ukraine conflict. Chinese stock market is an emerging stock market， which is affected greatly by policy. As a consequence， it can be argued that Chinese stock market is closely related to EPU. The existing literature on the impact of EPU on the stock market volatility is extensive and has not reached consistent conclusions. Moreover， the existing research is mainly based on the GARCH-MIDAS model， which lacks flexibility compared to the SV framework.

Motivated by the above interpretation， the RSV-MIDAS model framework is proposed， which combines the insights of the SV-MIDAS model and the RSV model. The proposed framework exploits the high-frequency intraday information and allows to link macroeconomic variables （such as the EPU） directly to the long-term volatility via the flexible MIDAS structure. By incorporating the EPU into the framework， it aims to investigate the impact and predictive value of the EPU on Chinese stock market volatility. The model is flexible， but has challenges in estimation owing to the lack of a closed-form expression for the likelihood function. To address this issue， a continuous particle filters-based maximum likelihood method is proposed. Monte Carlo simulation results show that the estimation method performs well.

The RSV-MIDAS model incorporating the EPU （hereafter the RSV-MIDAS-EPU model） is applied to the monthly Chinese EPU index and the high-frequency intraday data of the Shanghai Stock Exchange Composite Index and Shenzhen Stock Exchange Component Index. The empirical results show that the EPU has a significantly negative impact on the long-term volatility of Chinese stock market. That is， an increase in the EPU level predicts lower level of the long-run volatility of Chinese stock market. The impact of the EPU on the long-run volatility of Chinese stock market is more persistent than that of the monthly realized volatility （RV）. Using various loss functions and the model confidence set （MCS） test， the out-of-sample forecasting ability of the RSV-MIDAS-EPU model and the competitor models for Chinese stock market volatility are compared. It is observed that the realized measure and EPU play an important role in forecasting Chinese stock market volatility， and the RSV-MIDAS-EPU model achieves the best forecasting performance. Further， extensive robustness analysis shows that the superior predictive ability of the RSV-MIDAS-EPU model is robust. Finally， a volatility timing strategy shows that the RSV-MIDAS-EPU model yields more significant economic value of portfolio compared to other models.

Key words: economic policy uncertainty, volatility forecasting, realized SV-MIDAS, continuous particle filters, volatility timing

中图分类号:

F830

吴鑫育,朱志田,马超群. 经济政策不确定性与中国股市波动率——基于已实现SV-MIDAS模型的实证研究[J]. 中国管理科学, 2026, 34(1): 28-40.

Xinyu Wu,Zhitian Zhu,Chaoqun Ma. Economic Policy Uncertainty and Chinese Stock Market Volatility: A Realized SV-MIDAS Approach[J]. Chinese Journal of Management Science, 2026, 34(1): 28-40.

图/表 8

图1

图2

图3

表1

描述性统计量"

观测变量	均值	最小值	最大值	标准差	偏度	峰度	Jarque-Bera	Q(10)
	SSEC（日度）
$r i, t$	0.0002	-0.0926	0.0903	0.0155	-0.5808	7.9211	4658.4755	37.6847
$R V i, t$	0.0002	0.0000	0.0039	0.0003	6.0055	58.6474	590517.3214	10586.6970
$l o g R V i, t$	-9.3737	-12.0260	-5.5450	1.0262	0.5530	3.0746	223.8753	23189.0082
SZSEC（日度）
$r i, t$	0.0003	-0.0975	0.0916	0.0180	-0.5045	6.1537	1997.2329	33.1335
$R V i, t$	0.0002	0.0000	0.0053	0.0003	5.7511	56.7239	549880.496	8780.2091
$l o g R V i, t$	-8.9776	-11.8412	-5.2414	0.9506	0.3732	3.1590	106.0759	20829.5662
EPU（月度）
$E P U t$	300.8117	26.1441	970.8299	259.1049	1.0299	2.8242	38.4605	1431.2967

表1

表2

模型参数估计结果：SSEC"

参数	SV	SV-MIDAS	SV-MIDAS-EPU	RSV	RSV-MIDAS	SV-MIDAS-EPU
$μ$	0.0004 (0.0002)	0.0004 (0.0002)	0.0004 (0.0002)	0.0006 (0.0002)	0.0007 (0.0002)	0.0007 (0.0002)
$β$	0.9812 (0.0022)	0.7423 (0.0095)	0.7197 (0.0121)	0.9597 (0.0020)	0.8909 (0.0026)	0.8810 (0.0027)
$ρ$	-0.1340 (0.0021)	-0.2802 (0.0132)	-0.2837 (0.0142)	-0.1236 (0.0030)	-0.1249 (0.0033)	-0.1370 (0.0044)
$σ η 2$	0.0345 (0.0021)	0.2638 (0.0111)	0.2888 (0.0113)	0.0758 (0.0016)	0.0947 (0.0019)	0.0983 (0.0026)
$ξ$				-0.4878 (0.0023)	-0.4793 (0.0038)	-0.4807 (0.0034)
$σ u 2$				0.1475 (0.0014)	0.1352 (0.0019)	0.1324 (0.0023)
$m$	-8.7572 (0.0319)	-3.8344 (0.0387)	-3.4867 (0.0362)	-8.8387 (0.0187)	-3.8623 (0.0105)	-3.3634 (0.0154)
$θ 1$		0.8168 (0.0077)	0.7751 (0.0079)		0.8069 (0.0031)	0.7327 (0.0034)
$γ 1$		50.3629 (0.5494)	53.5083 (0.8811)		11.9543 (0.0438)	13.4135 (0.0679)
$θ 2$			-0.1182 (0.0096)			-0.1865 (0.0041)
$γ 2$			1.7496 (0.0294)			2.6286 (0.0124)
LL	12837.8280	12873.8355	12877.2411	9722.1722	9764.2776	9769.4491
AIC	-25665.6560	-25733.6710	-25736.4821	-19430.3445	-19510.5552	-19516.8982
VR		0.5720	0.5828		0.3566	0.3782

表2

表3

模型参数估计结果：SZSEC"

参数	SV	SV-MIDAS	SV-MIDAS-EPU	RSV	RSV-MIDAS	SV-MIDAS-EPU
$μ$	0.0004 (0.0002)	0.0004 (0.0002)	0.0004 (0.0002)	0.0007 (0.0002)	0.0008 (0.0002)	0.0008 (0.0002)
$β$	0.9780 (0.0022)	0.7933 (0.0106)	0.7886 (0.0090)	0.9509 (0.0009)	0.8894 (0.0028)	0.8831 (0.0031)
$ρ$	-0.2187 (0.0028)	-0.3246 (0.0138)	-0.3326 (0.0152)	-0.1012 (0.0023)	-0.1484 (0.0033)	-0.1614 (0.0053)
$σ η 2$	0.0295 (0.0022)	0.1705 (0.0105	0.1742 (0.0112)	0.0693 (0.0011)	0.0880 (0.0020)	0.0888 (0.0024)
$ξ$				-0.5231 (0.0025)	-0.5183 (0.0031)	-0.5104 (0.0028)
$σ u 2$				0.1543 (0.0017)	0.1384 (0.0022)	0.1375 (0.0025)
$m$	-8.3673 (0.0229)	-4.2103 (0.0428)	-3.9153 (0.0369)	-8.4585 (0.0156)	-3.2414 (0.0090)	-3.1236 (0.0123)
$θ 1$		0.7275 (0.0078)	0.6788 (0.0081)		0.8907 (0.0032)	0.7942 (0.0028)
$γ 1$		50.9761 (0.6597)	57.3567 (0.6863)		10.7585 (0.0406)	12.9766 (0.0585)
$θ 2$			-0.1121 (0.0091)			-0.1348 (0.0031)
$γ 2$			1.5078 (0.0300)			1.0430 (0.0036)
LL	11933.3740	11965.1096	11967.4208	8843.6231	8882.9981	8888.5138
AIC	-23856.7479	-23916.2193	-23916.8416	-17673.2461	-17747.9962	-17755.0275
VR		0.5221	0.5290		0.4337	0.4262

表3

表4

表5

投资组合的业绩表现（年化基点费用）"

模型	SSEC			SZSEC
模型	$A = 3$	$A = 6$	$A = 9$	$A = 3$	$A = 6$	$A = 9$
SV-MIDAS	11.5929	5.7936	3.8605	49.1700	24.5819	16.3858
SV-MIDAS-EPU	107.7203	53.8616	35.9088	163.1659	81.5837	54.3897
RSV	199.9720	99.9863	66.6577	92.8914	46.4480	30.9669
RSV-MIDAS	222.1463	111.0729	74.0485	130.0143	65.0071	43.3380
RSV-MIDAS-EPU	257.7694	128.8857	85.9245	177.0980	88.5499	59.0339

表5

参考文献 44

[1]	Bollerslev T. Generalized autoregressive conditional heteroskedasticity［J］. Journal of Econometrics， 1986， 31（3）： 307-327.
[2]	Taylor S J. Modeling stochastic volatility： A review and comparative study［J］. Mathematical Finance， 1994， 4（2）： 183-204.
[3]	Yu J. On leverage in a stochastic volatility model［J］. Journal of Econometrics， 2005， 127（2）： 165-178.
[4]	Andersen T G， Bollerslev T， Diebold F X， et al. The distribution of realized stock return volatility［J］. Journal of Financial Economics， 2001， 61（1）： 43-76.
[5]	刘广应，包悦妍，林金官. 基于金融高频数据的LASSO-CDRD协方差矩阵预测模型［J］. 统计研究， 2022， 39（9）： 145-160.
	Liu G Y， Bao Y Y， Lin J G. LASSO-CDRD covariance matrix prediction model based on high frequency financial data［J］. Statistical Research， 2022， 39（9）： 145-160.
[6]	Barndorff-Nielsen O E， Shephard N. Econometric analysis of realized volatility and its use in estimating stochastic volatility models［J］. Journal of the Royal Statistical Society Series B （Statistical Methodology）， 2002， 64（2）： 253-280.
[7]	Takahashi M， Omori Y， Watanabe T. Estimating stochastic volatility models using daily returns and realized volatility simultaneously［J］. Computational Statistics & Data Analysis， 2009， 53（6）： 2404-2426.
[8]	吴鑫育，周海林. 基于已实现SV模型的动态VaR测度研究［J］. 管理工程学报， 2018， 32（2）： 144-150.
	Wu X Y， Zhou H L. Study on dynamic VaR measures based on realized SV model［J］. Journal of Industrial Engineering and Engineering Management， 2018， 32（2）： 144-150.
[9]	吴鑫育，李心丹，马超群. 双因子非对称已实现SV模型及其实证研究［J］. 中国管理科学， 2018， 26（2）： 1-13.
	Wu X Y， Li X D， Ma C Q. Two-factor asymmetric realized SV model and its empirical test［J］. Chinese Journal of Management Science， 2018， 26（2）： 1-13.
[10]	吴鑫育，李心丹，马超群. 混合正态双因子已实现SV模型及其实证研究［J］. 管理科学， 2019， 32（2）： 148-160.
	Wu X Y， Li X D， Ma C Q. Two-factor realized SV model with mixture of normals and its empirical research［J］. Journal of Management Science， 2019， 32（2）： 148-160.
[11]	Wu X， Wang X. Forecasting volatility using realized stochastic volatility model with time-varying leverage effect［J］. Finance Research Letters， 2020， 34： 101271.
[12]	Zhang Z， Zhao R. Improving the asymmetric stochastic volatility model with ex-post volatility： The identification of the asymmetry［J］. Quantitative Finance， 2023， 23（1）： 35-51.
[13]	张波，蒋远营. 基于中国股票高频交易数据的随机波动建模与应用［J］. 统计研究， 2017， 34（3）： 107-117.
	Zhang B， Jiang Y Y. Stochastic volatility modeling based on high-frequency Chinese stock-market transaction data and applications［J］. Statistical Research， 2017， 34（3）： 107-117.
[14]	Asai M， Chang C L， McAleer M. Realized matrix-exponential stochastic volatility with asymmetry， long memory and higher-moment spillovers［J］. Journal of Econometrics， 2022， 227（1）： 285-304.
[15]	Baker S R， Bloom N， Davis S J. Measuring economic policy uncertainty［J］. The Quarterly Journal of Economics， 2016， 131（4）： 1593-1636.
[16]	杨子晖，陈里璇，陈雨恬. 经济政策不确定性与系统性金融风险的跨市场传染——基于非线性网络关联的研究［J］. 经济研究， 2020， 55（1）： 65-81.
	Yang Z H， Chen L X， Chen Y T. Cross-market contagion of economic policy uncertainty and systemic financial risk： A nonlinear network connectedness analysis［J］. Economic Research Journal， 2020， 55（1）： 65-81.
[17]	钟婉玲，李海奇. 国际油价、宏观经济变量与中国股市的尾部风险溢出效应研究［J］. 中国管理科学， 2022， 30（2）： 27-37.
	Zhong W L， Li H Q. Tail risk spillover effects among crude oil price， macroeconomic variables and China’s stock market［J］. Chinese Journal of Management Science， 2022， 30（2）： 27-37.
[18]	王正新，姚培毅. 中国经济政策不确定性的跨国动态溢出效应［J］. 中国管理科学， 2019， 27（5）： 78-85.
	Wang Z X， Yao P Y. Dynamic spillovers effects of economic policy uncertainty of China［J］. Chinese Journal of Management Science， 2019， 27（5）： 78-85.
[19]	张喜艳，陈乐一. 经济政策不确定性的溢出效应及形成机理研究［J］. 统计研究， 2019， 36（1）： 115-128.
	Zhang X Y， Chen L Y. A study on the spillover effect and its formation mechanism of economic policy uncertainty［J］. Statistical Research， 2019， 36（1）： 115-128.
[20]	胡成春，陈迅. 经济政策不确定性、宏观经济与资产价格波动——基于TVAR模型及溢出指数的实证分析［J］. 中国管理科学， 2020， 28（11）： 61-70.
	Hu C C， Chen X. Economic policy uncertainty， macroeconomic and asset price fluctuation： Based on TVAR model and spillover index［J］. Chinese Journal of Management Science， 2020， 28（11）： 61-70.
[21]	吴鑫育，谢海滨，马超群. 经济政策不确定性与人民币汇率波动率——基于CARR-MIDAS模型的实证研究［J］. 中国管理科学， 2024，32（8）：1-14.
	Wu X Y， Xie H B， Ma C Q. Economic policy uncertainty and renminbi exchange rate volatility： Evidence from CARR-MIDAS model［J］. Chinese Journal of Management Science， 2024，32（8）：1-14.
[22]	张宗新，林弘毅，李欣越. 经济政策不确定性如何影响金融市场间的流动性协同运动？——基于中国金融周期的视角［J］. 统计研究， 2020， 37（2）： 37-51.
	Zhang Z X， Lin H Y， Li X Y. How economic policy uncertainty affects liquidity co-movements among financial markets：From the perspective of China’s financial cycle［J］. Statistical Research， 2020， 37（2）： 37-51.
[23]	Ghysels E， Sinko A， Valkanov R. MIDAS regressions： Further results and new directions［J］. Econometric Reviews， 2007， 26（1）： 53-90.
[24]	Engle R F， Ghysels E， Sohn B. Stock market volatility and macroeconomic fundamentals［J］. The Review of Economics and Statistics， 2013， 95（3）： 776-797.
[25]	雷立坤，余江，魏宇，等. 经济政策不确定性与我国股市波动率预测研究［J］. 管理科学学报， 2018， 21（6）： 88-98.
	Lei L K， Yu J， Wei Y， et al. Forecasting volatility of Chinese stock market with economic policy uncertainty［J］. Journal of Management Sciences in China， 2018， 21（6）： 88-98.
[26]	夏婷，闻岳春. 经济不确定性是股市波动的因子吗？——基于GARCH-MIDAS模型的分析［J］. 中国管理科学， 2018， 26（12）： 1-11.
	Xia T， Wen Y C. Does economic uncertainty matter for stock market Volatility？ An analysis based on GARCH-MIDAS［J］. Chinese Journal of Management Science， 2018， 26（12）： 1-11.
[27]	张一锋，雷立坤，魏宇. 羊群效应的新测度指数及其对我国股市波动的预测作用研究［J］. 系统工程理论与实践， 2020， 40（11）： 2810-2824.
	Zhang Y F， Lei L K， Wei Y. A new herd index and volatility forecasting of China’s stock market［J］. Systems Engineering-Theory & Practice， 2020， 40（11）： 2810-2824.
[28]	Shang Y， Liu L. An extension of stochastic volatility model with mixed frequency information［J］. Economics Letters， 2017， 155： 144-148.
[29]	吴鑫育，周海林，汪寿阳，等. 双杠杆门限随机波动率模型及其实证研究［J］. 管理科学学报， 2014， 17（7）： 63-81.
	Wu X Y， Zhou H L， Wang S Y， et al. A threshold stochastic volatility model with double leverage and its empirical test［J］. Journal of Management Sciences in China， 2014， 17（7）： 63-81.
[30]	苑慧玲，徐路，周勇. 带有市场交易信息和随机微观噪声下的杠杆效应研究［J］. 中国管理科学， 2020， 28（9）： 12-22.
	Yuan H L， Xu L， Zhou Y. Leverage effect combining trading information with stochastic microstructure noise［J］. Chinese Journal of Management Science， 2020， 28（9）： 12-22.
[31]	刘小军，汪寿阳，谢海滨. 已实现波动率预测：非对称二次滑动平均模型［J］. 计量经济学报， 2022， 2（4）： 930-945.
	Liu X J， Wang S Y， Xie H B. Realized volatility forecasting： An asymmetric double moving average model［J］. China Journal of Econometrics， 2022， 2（4）： 930-945.
[32]	Shang Y， Zheng T. Mixed-frequency SV model for stock volatility and macroeconomics［J］. Economic Modelling， 2021， 95： 462-472.
[33]	Li T， Ma F， Zhang X， et al. Economic policy uncertainty and the Chinese stock market volatility： Novel evidence［J］. Economic Modelling， 2020， 87： 24-33.
[34]	李木易，方颖. 动态混合HGARCH模型的估计和预测［J］. 管理科学学报， 2020， 23（5）： 1-12.
	Li M Y， Fang Y. Estimation and forecasting of mixture HGARCH model［J］. Journal of Management Sciences in China， 2020， 23（5）： 1-12.
[35]	Malik S， Pitt M K. Particle filters for continuous likelihood evaluation and maximisation［J］. Journal of Econometrics， 2011， 165（2）： 190-209.
[36]	Patton A J. Volatility forecast comparison using imperfect volatility proxies［J］. Journal of Econometrics， 2011， 160（1）： 246-256.
[37]	Hansen P R， Lunde A， Nason J M. The model confidence set［J］. Econometrica， 2011， 79（02）： 453-497.
[38]	Conrad C， Loch K. Anticipating long-term stock market volatility［J］. Journal of Applied Econometrics， 2015， 30（7）： 1090-1114.
[39]	Wang X， Luo Y， Wang Z， et al. The impact of economic policy uncertainty on volatility of China’s financial stocks： An empirical analysis［J］. Finance Research Letters， 2021， 39： 101650.
[40]	Fleming J， Kirby C， Ostdiek B. The economic value of volatility timing using “realized” volatility［J］. Journal of Financial Economics， 2003， 67（3）： 473-509.
[41]	Huang Y， Luk P. Measuring economic policy uncertainty in China［J］. China Economic Review， 2020， 59： 101367.
[42]	邢艳春，廖晗. 经济政策不确定性对中国股市波动率的影响［J］. 统计与信息论坛， 2023， 38（1）： 71-80.
	Xing Y C， Liao H. The impact of economic policy uncertainty on China’s stock market volatility［J］. Journal of Statistics and Information， 2023， 38（1）： 71-80.
[43]	Chen Z， Zhang L， Weng C. Does climate policy uncertainty affect Chinese stock market volatility？［J］. International Review of Economics & Finance， 2023， 84： 369-381.
[44]	Campbell J Y， Thompson S B. Predicting excess stock returns out of sample： Can anything beat the historical average？［J］. The Review of Financial Studies， 2008， 21（4）： 1509-1531.

损失函数	SV	SV-MIDAS	SV-MIDAS-EPU	RSV	RSV-MIDAS	RSV-MIDAS-EPU
SSEC
MSE	1.6594e-05	1.3307e-05	9.1665e-06	1.1129e-05	9.3453e-06	8.0625e-06
MAE	3.3818e-03	3.0173e-03	2.3635e-03	2.6873e-03	2.5091e-03	2.2914e-03
HMSE	1.2140e-01	1.2499e-01	1.1270e-01	9.1588e-02	8.7407e-02	8.0637e-02
HMAE	3.0959e-01	3.0058e-01	2.6582e-01	2.6351e-01	2.5608e-01	2.4177e-01
QLIKE	-3.8486e+00	-3.8547e+00	-3.8743e+00	-3.8735e+00	-3.8775e+00	-3.8836e+00
SZSEC
MSE	2.7298e-05	2.3157e-05	1.5792e-05	1.8786e-05	1.5599e-05	1.4257e-05
MAE	4.4718e-03	4.1064e-03	3.1944e-03	3.5499e-03	3.2899e-03	3.1104e-03
HMSE	1.1776e-01	1.1978e-01	1.0253e-01	8.7319e-02	8.2955e-02	7.8664e-02
HMAE	3.0849e-01	3.0179e-01	2.5989e-01	2.5971e-01	2.5127e-01	2.4204e-01
QLIKE	-3.5551e+00	-3.5592e+00	-3.5791e+00	-3.5792e+00	-3.5834e+00	-3.5870e+00