高频网络波动率矩阵模型构建及其应用

doi:10.16381/j.cnki.issn1003-207x.2023.0115

Abstract

Abstract:

Volatility matrix is the basis and core of quantitative analysis of many high-dimensional financial activities. Multivariate volatility models mainly include multivariate GARCH model， high-frequency volatility matrix model and network volatility model. There are three main difficulties in their modeling process， including the problem of dimensional disaster， meeting the requirements of the mathematical and empirical characteristics of volatility matrix， and the model has a certain economic interpretation. In order to alleviate these three kinds of problems， the integration of two kinds of modeling ideas is realized by utilizing the advantages of high frequency volatility model， which contains rich volatility information and flexible modeling， and the advantages of network volatility model， which has economic significance. Based on the traditional high-frequency CAW model， the conduction structure is presupposed between fluctuations by introducing positive and negative correlation networks with the characteristics of risk accumulation and risk dispersion， and further a two-layer network volatility matrix model （DNVM model） is established based on the heterogeneous market hypothesis. Under this framework， the network effects and spillover effects of asset volatility conduction along different network paths are derived. The model in this paper realizes the structural dimension reduction of parameters and the improvement of the economic significance of the model.The empirical research based on the 50 constituent stocks of Shanghai Stock Exchange in China shows that the correlation between assets is heterogeneous in time dimension， and there is significant positive and negative asymmetry in cross section. The volatility transmission between assets has a significant network effect， and the network effect is stronger in the short term than in the medium and long term. The short-term volatility spillover effect between assets is stronger than that in the medium and long term， and the positive volatility spillover effect is stronger than the negative volatility spillover effect on the whole， and the short-term positive volatility spillover plays a dominant role. Both the statistical prediction effect and the minimum variance portfolio strategy show that the DNVM model is better than the non-network high frequency model and the low frequency multivariate GARCH model such as BEKK model. DNVM model provides a new guidance and research method for the study of high-dimensional volatility matrix prediction of financial market， and also provides a new perspective for the expansion of traditional network econometric model based on vector data to matrix data.

Key words: high-frequency multivariate volatility matrix, network relevance, structural dimension reduction, volatility spillover effect

CLC Number:

F224.0

Shuran Zhao,Jinchen Li,Jie Zhang, et al. Construction and Application of High-frequency Network Volatility Matrix Model[J]. Chinese Journal of Management Science, 2026, 34(3): 122-133.

Figures/Tables 15

—	$w i j, t d$	$w i j, t d +$	$w i j, t d -$	$w i j, t w$	$w i j, t w +$	$w i j, t w -$	$w i j, t d - w i j, t w$
平均值	0.4190	0.4830	-0.1522	0.4315	0.5567	-0.2534	0.2046
最大值	0.9904	0.9904	-1.47×10^-6	0.9970	0.9970	-3.60×10^-6	1.2779
最小值	-0.8141	1.30×10^-6	-0.8141	-0.9179	2.23×10^-5	-0.9179	2.24×10^-7
标准差	0.3009	0.2414	0.1260	0.3845	0.2586	0.1898	0.1686

股票名称	$β d +$	$β d -$	$β d 0$	$β w +$	$β w -$	$β w 0$
中国建设银行	0.0201^***	-0.2135	0.2578	0.0296^***	0.0842^***	0.6999^***
中国银行	0.0008^***	-0.1634^***	0.5529	0.0501	0.1236	0.6110
中国农业银行	0.0063^***	-0.1426	0.3954^***	0.0187^***	0.0748^***	0.6769
中国交通银行	0.0162	-0.1327^***	0.4274^***	0.0205^***	0.1289	0.6543^***
中国工商银行	0.0125	-0.1482^***	0.3186	0.0329	0.0359^***	0.5171
中国民生银行	0.0176^***	-0.1488^***	0.6813^***	0.0052	0.1530	0.6721^***
太平洋保险	0.0431	-0.1526^***	-0.0161	0.0126^***	0.0150^***	0.6548^***
中国人寿保险	0.0228^***	-0.1661	0.2607^***	0.0118^***	0.0260^***	0.7193^***
海通证券	0.1224	-0.2034	-0.7442	0.0155^***	0.0057^***	0.6268^***
金地集团	0.1376^***	-0.1605	-0.6797^***	0.0358	-0.1050^***	0.3868
上海国际机场	0.0761^***	-0.1146^***	-0.2069^***	-0.0136	0.0134	0.8026^***
大秦铁路	0.0079	-0.1410^***	0.6492^***	-0.0023^***	0.0678	0.7010^***
中国石化	0.0029^***	-0.1419^***	0.4154^***	0.0119	0.0597	0.5285^**
中国石油	0.0126	-0.1416	0.1538	0.0280^***	-0.0591^***	0.5167^***
海油工程	0.0304	-0.1791^***	0.2401^***	-0.0066^***	0.0042	0.7503^***
中国建筑	0.0393	-0.1515	0.3485	-0.0090^***	-0.1449^***	0.6572^***
中国交建	0.0671	-0.3463^***	0.1821	-0.0028	-0.0147	0.7236
北方稀土	0.0479	-0.3364^***	0.1779	-0.0193^***	0.1286	0.7992^***
三一重工	0.0240	-0.1251^***	0.3653^***	-0.0041^***	0.1644^***	0.7139^***
贵州茅台酒	0.0398	-0.0944	0.1232^***	0.0186	0.0473	0.4435
F范数	0.2344	0.8113	1.8477	0.0953	0.4020	2.9159

统计项	Panel A：日度层面			Panel B：周度层面
统计项	平均正向波动溢出 $h a v e, t - 1 + +, d$	平均负向波动溢出 $h a v e, t - 1 - -, d$	合计	平均正向波动溢出 $h a v e, t - 1 + +, w$	平均负向波动溢出 $h a v e, t - 1 - -, w$	合计
均值	0.0114	0.0029	0.0144	0.0029	0.0022	0.0052
标准差	0.0062	0.0047	0.0055	0.0012	0.0028	0.0023
变异系数	0.5431	1.5859	0.3795	0.4146	1.2557	0.4309
占比（%）	79.53	20.47	100	57.13	42.87	100

统计项	$w i j, t d$	$w i j, t d +$	$w i j, t d -$	$w i j, t w$	$w i j, t w +$	$w i j, t w -$	$w i j, t d - w i j, t w$
平均值	0.4197	0.4784	-0.1532	0.4219	0.5464	-0.2473	0.2076
最大值	0.9945	0.9945	-1.26×10^-5	0.9966	0.9966	-1.06×10^-6	1.2377
最小值	-0.8184	1.62×10^-7	-0.8184	-0.9059	1.52×10^-7	-0.9059	6.17×10^-7
标准差	0.2903	0.2329	0.1256	0.3794	0.2562	0.1844	0.1701

—	$β d +$	$β d -$	$β d 0$	$β w +$	$β w -$	$β w 0$
矩阵F分布	0.2212	0.7759	1.8214	0.0581	0.4114	2.8708
Wishart分布	0.2217	0.7763	1.8523	0.0626	0.4220	2.9043

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统计项	总体峰度	方差峰度	协方差峰度	总体偏度	方差偏度	协方差偏度
均值	169.28	112.44	175.26	10.55	8.37	10.79
标准差	76.77	68.79	75.26	2.49	2.51	2.38

统计项	阶数	1	2	3	4	5	10	20
自相关	方差	0.549	0.435	0.437	0.436	0.409	0.251	0.150
自相关	协方差	0.519	0.393	0.412	0.415	0.360	0.194	0.206
偏自相关	方差	0.549	0.183	0.207	0.158	0.097	-0.043	0.010
偏自相关	协方差	0.519	0.158	0.224	0.159	0.058	-0.047	0.037

模型	均方误差 ×10^-3	逆矩阵的均方误差 ×10⁶	均方误差×10^-3		拟似然损失	逆Stein 损失	无穷范数 ×10^-3	2-范数 ×10^-3	系数型参数数量	最优指标	平均排名
模型	均方误差 ×10^-3	逆矩阵的均方误差 ×10⁶	方差	协方差	拟似然损失	逆Stein 损失	无穷范数 ×10^-3	2-范数 ×10^-3	系数型参数数量	最优指标	平均排名
CAW	2.914⁴	2.2564⁴	1.419⁴	2.481³	-157.320⁴	49.599⁴	4.579⁴	2.495⁴	400	0	3.88
HAR-CAW(1,5)	2.900³	2.2506³	1.343³	2.515⁴	-158.349³	48.541³	4.552³	2.493³	800	0	3.13
HAR-CAW(1,5,22)	2.857²	2.2442²	1.321¹	2.475²	-158.751¹	48.099¹	4.507²	2.460²	1200	3	1.63
DNVM	2.829¹	2.2426¹	1.334²	2.433¹	-158.739²	48.113²	4.463¹	2.417¹	120	5	1.38

阶段	模型	均方误差 ×10^-3	逆矩阵的均方误差×10⁶	均方误差×10^-3		拟似然损失	逆Stein'损失	无穷范数'×10^-3	2-范数'×10^-3	最优'指标	平均排名
阶段	模型	均方误差 ×10^-3	逆矩阵的均方误差×10⁶	方差	协方差	拟似然损失	逆Stein'损失	无穷范数'×10^-3	2-范数'×10^-3	最优'指标	平均排名
繁荣时期	CAW	5.167¹	1.5723⁴	2.403²	4.483¹	-144.690⁴	53.649⁴	7.985¹	4.501¹	4	2.25
	HAR-CAW(1,5)	5.383²	1.5472³	2.324¹	4.774²	-146.248¹	51.694³	8.377²	4.677²	2	2.00
	HAR-CAW(1,5,22)	5.659⁴	1.4433²	2.426³	5.024⁴	-145.680³	51.166²	8.818⁴	4.936⁴	0	3.25
	DNVM	5.521³	1.4278¹	2.470⁴	4.848³	-145.884²	50.740¹	8.670³	4.756³	2	2.50
股灾时期	CAW	7.224³	1.7674⁴	2.954⁴	6.481³	-144.555⁴	55.730⁴	11.465⁴	6.595³	0	3.63
	HAR-CAW(1,5)	6.957²	1.7666²	2.786²	6.282²	-146.862³	53.423³	10.833¹	6.317²	1	2.13
	HAR-CAW(1,5,22)	6.942¹	1.7673³	2.766¹	6.273¹	-147.616¹	52.669¹	10.846²	6.287¹	6	1.38
	DNVM	7.279⁴	1.7659¹	2.877³	6.584⁴	-147.352²	52.933²	11.407³	6.629⁴	1	2.88
恢复时期	CAW	1.592²	2.9351⁴	0.963⁴	1.230²	-162.357⁴	49.246⁴	2.400²	1.266²	0	3.00
	HAR-CAW(1,5)	1.722⁴	2.9323³	0.916³	1.415⁴	-162.994³	48.609³	2.614⁴	1.440⁴	0	3.50
	HAR-CAW(1,5,22)	1.635³	2.9297²	0.879²	1.334³	-163.391¹	48.212¹	2.504³	1.361³	2	2.25
	DNVM	1.426¹	2.9281¹	0.850¹	1.107¹	-163.295²	48.308²	2.193¹	1.136¹	6	1.25
平稳时期	CAW	1.843⁴	2.1889⁴	0.935⁴	1.564⁴	-160.698⁴	47.377⁴	2.831⁴	1.503⁴	0	4.00
	HAR-CAW(1,5)	1.775³	2.1862³	0.869³	1.525³	-161.375³	46.700³	2.765³	1.464³	0	3.00
	HAR-CAW(1,5,22)	1.728²	2.1846²	0.840¹	1.487²	-161.613¹	46.444¹	2.718²	1.431²	3	1.63
	DNVM	1.715¹	2.1831¹	0.849²	1.467¹	-161.621²	46.454²	2.660¹	1.392¹	5	1.38
疫情期间	CAW	1.798⁴	2.5241⁴	0.951⁴	1.491⁴	-163.480⁴	47.769⁴	2.903⁴	1.488⁴	0	4.00
	HAR-CAW(1,5)	1.725³	2.5200³	0.886³	1.448³	-164.281³	46.968³	2.795³	1.434³	0	3.00
	HAR-CAW(1,5,22)	1.674¹	2.5180²	0.859¹	1.404¹	-164.654¹	46.596¹	2.738¹	1.400¹	7	1.13
	DNVM	1.717²	2.5143¹	0.881²	1.440²	-164.598²	46.651²	2.762²	1.420²	1	1.88
后疫情期	CAW	2.234³	2.3119⁴	1.359⁴	1.706²	-159.317⁴	48.299⁴	3.730³	1.817³	0	3.38
	HAR-CAW(1,5)	2.272⁴	2.3085³	1.277³	1.808⁴	-160.242³	47.375³	3.826⁴	1.840⁴	0	3.50
	HAR-CAW(1,5,22)	2.182²	2.3066²	1.255²	1.714³	-160.687¹	46.929¹	3.681²	1.777²	2	1.88
	DNVM	2.060¹	2.3038¹	1.235¹	1.580¹	-160.597²	47.019²	3.467¹	1.664¹	6	1.25

模型	收益率	波动率	夏普率	M2	Δ₁	Δ₅	Δ₁₀	SR
CCC	0.1634	17.2353	-.1356	-	-	-	-	-
DCC	2.7685	17.1275	.0157	260.684	261.441	262.058	262.199	49.98
DECO	2.7291	21.9635	.0109	225.464	198.552	178.476	173.914	48.09
BEKK	3.4110	19.9412	.0462	292.923	288.267	282.364	281.023	51.46
CAW	4.1480	18.1776	.0907	368.405	366.378	360.863	359.609	50.50
HAR-CAW(1,5)	3.6231	17.5028	.0642	354.728	354.076	352.722	352.414	51.80
HAR-CAW(1,5,22)	4.6646	17.8792	.1211	463.994	466.006	462.568	461.787	51.35
DNVM	5.1631	16.9077	.1575	522.151	518.877	521.154	521.673	51.82
纠偏DNVM	7.2451	17.8552	.2658	692.428	702.197	698.980	698.249	52.37

Construction and Application of High-frequency Network Volatility Matrix Model

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模型	均方误差 ×10^-3	逆矩阵的均方误差×10⁶	均方误差×10^-3		拟似然损失	逆Stein 损失	无穷范数 ×10^-3	2-范数 ×10^-3	系数型参数数量	最优指标	平均排名
模型	均方误差 ×10^-3	逆矩阵的均方误差×10⁶	方差	协方差	拟似然损失	逆Stein 损失	无穷范数 ×10^-3	2-范数 ×10^-3	系数型参数数量	最优指标	平均排名
CAF	2.616⁴	2.2860⁴	1.320⁴	2.197²	-156.903⁴	50.575⁴	4.161⁴	2.270⁴	400	0	3.75
HAR-CAF(1,5)	2.590³	2.2771³	1.219³	2.229⁴	-158.284³	49.170³	4.157³	2.231³	800	0	3.13
HAR-CAF(1,5,22)	2.573²	2.2727²	1.216²	2.211³	-158.649²	48.775²	4.125²	2.224²	1200	0	2.13
DNVM-F	2.526¹	2.2707¹	1.212¹	2.157¹	-158.706¹	48.722¹	4.068¹	2.169¹	120	6	1

模型	收益率	波动率	夏普率	M2	Δ₁	Δ₅	Δ₁₀	SR
CAF	6.486	17.467	0.228	332.938	282.493	307.322	312.965	51.94
HAR-CAF(1,5)	6.010	17.154	0.205	286.856	241.591	268.358	274.441	50.95
HAR-CAF(1,5,22)	6.808	17.020	0.253	458.664	390.321	418.133	424.454	51.02
DNVM-F	6.822	16.905	0.256	481.187	409.588	438.132	444.619	50.96
纠偏DNVM-F	7.579	18.570	0.274	501.511	452.737	471.429	475.678	52.16

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[2]	XIONG Zheng-de, WEN Hui, XIONG Yi-peng. Empirical Research on Spillover Effect between Foreign Exchange Market and Stock Market by Wavelet Multi-resolution Analysis and Multivariate BEKK-GARCH(1,1) Model [J]. Chinese Journal of Management Science, 2015, 23(4): 30-38.
[3]	XIONG Zheng de, HAN Li jun. An Empirical Study on the Volatility Spillover Effect between Financial Markets——GC-MSV Model and Application [J]. Chinese Journal of Management Science, 2013, (2): 32-41.