The Price-Volume Relationship of the Shanghai Stock Index: Structural Change and the Threshold Effect of Volatility
Abstract
1. Introduction
2. Literature Review
3. Methodology
3.1. Linear VAR
3.2. Threshold VAR
3.3. Research Design
4. Data
5. Empirical Results and Discussion
5.1. Overall Price-Volume Relationship in China’s Stock Market
5.2. Test of Structural Change
5.2.1. Estimation of Time Thresholds
5.2.2. The structural Change Characteristics of the Price-Volume Relation
5.3. The Threshold Effect of Market Volatility on Price-Volume Relation
5.3.1. Estimation of Volatility Thresholds
5.3.2. The Threshold Effect of Market Volatility on the Price-Volume Relationship
5.4. Robustness Checks
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Variable | Mean | Median | Maximum | Minimum | Std. Dev. | Skewness | Kurtosis | J-B | ADF |
---|---|---|---|---|---|---|---|---|---|
2570.48 | 2574.68 | 6092.06 | 1011.50 | 921.42 | 0.68 | 3.87 | 428.28 *** (0.0000) | −2.00 (0.2858) | |
121.90 | 98.04 | 857.13 | 4.08 | 115.39 | 2.37 | 10.48 | 12,801.70 *** (0.0000) | −3.60 * (0.0058) | |
0.02 | 0.06 | 9.03 | −9.26 | 1.60 | −0.50 | 7.42 | 3357.60 *** (0.0000) | −61.42 *** (0.0001) | |
0.00 | −0.04 | 1.69 | −1.58 | 0.63 | 0.22 | 2.49 | 73.10 *** (0.0000) | −4.9825 *** (0.0000) | |
2.75 | 1.78 | 17.52 | 0.25 | 2.65 | 2.10 | 7.64 | 6389.75 *** (0.0000) | −4.2570 *** (0.0005) |
Null Hypothesis | Alternative Hypothesis | Test Result | |
---|---|---|---|
Volume does not Granger cause price | 12.76 * (0.0471) | Reject | |
Price does not Granger cause volume | 369.25 *** (0.0000) | Reject |
Threshold Variable | Setting the Numberof Threshold Values | Threshold Value Estimate | LR Test | |
---|---|---|---|---|
Equation Ret | Equation Vol | |||
Panel A: sample period 2003/3/4–2019/4/22 | ||||
1 | T = 2015/06/11 | 88.56 *** (0.0000) | 321.76 *** (0.0000) | |
2 | t1 = 2015/06/11 t2 = 2016/03/31 | 88.56 *** (0.0000) | 321.76 *** (0.0000) | |
Panel B: sample period 2003/3/4–2015/06/11 | ||||
1 | t’ =2007/10/15 | 31.71 *** (0.0000) | 157.75 *** (0.0000) | |
2 | t3 =2007/10/15 t4 =2008/11/03 | 31.71 *** (0.0000) | 157.75 *** (0.0000) |
Null Hypothesis | Alternative Hypothesis | Test Result | |
---|---|---|---|
Subsample 1: 2003/3/4–2007/10/15 | |||
Volume does not Granger causes price | 16.88 ** (0.0020) | Reject | |
Price does not Granger causes volume | 94.95 *** (0.0000) | Reject | |
Subsample 2: 2007/10/15–2008/11/03 | |||
Volume does not Granger causes price | 1.39 (0.2392) | Accept | |
Price does not Granger causes volume | 16.64 *** (0.0000) | Reject | |
Subsample 3: 2008/11/03–2015/06/11 | |||
Volume does not Granger causes price | 14.83 (0.0625) | Accept | |
Price does not Granger causes volume | 309.81 *** (0.0000) | Reject | |
Subsample 4: 2015/06/11–2016/03/31 | |||
Volume does not Granger causes price | 3.57 (0.0587) | Accept | |
Price does not Granger causes volume | 0.02 (0.8959) | Accept | |
Subsample 5: 2016/03/31–2019/4/22 | |||
Volume does not Granger causes price | 0.47 (0.9261) | Accept | |
Price does not Granger causes volume | 68.90 *** (0.0000) | Reject |
Threshold Variable | Setting the Numberof Threshold Value | Threshold Estimates | LR test | |
---|---|---|---|---|
Equation ret | Equation vol | |||
1 | = 6.52 | 61.58 *** (0.0000) | 115.32 *** (0.0000) | |
2 | = 3.09 = 6.52 | 61.58 *** (0.0000) | 115.32 *** (0.0000) |
Explanatory Variable | (1) | (2) | (3) | (4) | ||||
---|---|---|---|---|---|---|---|---|
Equation ret | Equation vol | Equation ret | Equation vol | Equation ret | Equation vol | Equation ret | Equation vol | |
ret(-1) | 0.0088 (0.0197) | 0.0433 *** (0.0023) | 0.0066 (0.0258) | 0.0515 *** (0.0030) | 0.0122 (0.0310) | 0.0328 *** (0.0036) | 0.0181 (0.0307) | 0.0199 *** (0.0036) |
ret(-2) | −0.0506 * (0.0223) | 0.0076 ** (0.0026) | −0.0316 (0.0297) | 0.0075 * (0.0034) | −0.0796 * (0.0350) | 0.0078 (0.0040) | −0.0370 (0.0280) | −0.0045 (0.0032) |
ret(-3) | 0.0717 ** (0.0224) | 0.0092 *** (0.0026) | 0.0427 (0.0294) | 0.0068 * (0.0034) | 0.1286 *** (0.0361) | 0.0130 ** (0.0042) | −0.0719 ** (0.0274) | −0.0005 (0.0032) |
ret(-4) | −0.0102 (0.0225) | −0.0003 (0.0026) | −0.0026 (0.0293) | 0.0029 (0.0034) | −0.0169 (0.0369) | −0.0052 (0.0043) | 0.1051 *** (0.0271) | 0.0003 (0.0031) |
ret(-5) | 0.0152 (0.0223) | −0.0013 (0.0026) | −0.0096 (0.0289) | 0.0012 (0.0033) | 0.0519 (0.0368) | −0.0028 (0.0043) | −0.0351 (0.0269) | −0.0028 (0.0031) |
ret(-6) | −0.0525 * (0.0214) | −0.0083 *** (0.0025) | −0.0551 * (0.0278) | −0.0067 * (0.0032) | −0.0370 (0.0350) | −0.0088 * (0.0041) | −0.0919 *** (0.0263) | −0.0050 (0.0031) |
vol(-1) | 0.3953 ** (0.1522) | 0.5873 *** (0.0177) | 0.3205 (0.1688) | 0.5712 *** (0.0195) | 0.7927 * (0.3695) | 0.6383 *** (0.0428) | −0.2316 (0.4221) | 0.6234 *** (0.0489) |
vol(-2) | 0.0046 (0.1777) | 0.1112 *** (0.0206) | 0.2036 (0.1946) | 0.1338 *** (0.0225) | −1.0370 * (0.4515) | 0.0108 (0.0523) | 0.7211 (0.4611) | 0.1568 ** (0.0535) |
vol(-3) | −0.1071 (0.1786) | 0.0821 *** (0.0207) | −0.1237 (0.1963) | 0.0577 * (0.0227) | 0.1943 (0.4513) | 0.2063 *** (0.0522) | 0.2895 (0.4541) | 0.0267 (0.0527) |
vol(-4) | −0.1183 (0.1795) | 0.0683 ** (0.0208) | −0.1965 (0.1963) | 0.0732 ** (0.0227) | 0.2009 (0.4632) | 0.0085 (0.0536) | −0.6416 (0.4381) | 0.0595 (0.0508) |
vol(-5) | 0.0173 (0.1782) | 0.0586 ** (0.0207) | 0.1213 (0.1946) | 0.0713 ** (0.0225) | −0.4300 (0.4637) | 0.0150 (0.0537) | −0.5812 (0.4432) | −0.0035 (0.0514) |
vol(-6) | −0.0645 (0.1514) | 0.0590 *** (0.0176) | −0.2183 (0.1673) | 0.0524 ** (0.0194) | 0.5397 (0.3694) | 0.0906 * (0.0428) | 0.4553 (0.3719) | 0.0616 (0.0431) |
Constant | 0.0508 (0.0272) | −0.0014 (0.0032) | 0.0527 (0.0325) | −0.0047 (0.0038) | −0.0683 (0.0929) | 0.0055 (0.0108) | −0.2337 (0.1246) | 0.0222 (0.0145) |
Explanatory Variable | (1) | (2) | (3) | (4) | ||||
---|---|---|---|---|---|---|---|---|
Equation ret | Equation vol | Equation ret | Equation vol | Equation ret | Equation vol | Equation ret | Equation vol | |
ret(-1) | 0.0256 (0.0272) | 0.0560 *** (0.0031) | 0.0619 (0.0345) | 0.0620 *** (0.0040) | −0.0730 (0.0513) | 0.0463 *** (0.0059) | −0.0084 (0.0213) | 0.0238 *** (0.0024) |
ret(-2) | −0.0581 * (0.0239) | 0.0052 (0.0027) | −0.0813 ** (0.0290) | 0.0034 (0.0033) | 0.0152 (0.0514) | 0.0076 (0.0059) | −0.0388 (0.0264) | 0.0001 (0.0030) |
ret(-3) | 0.0141 (0.0226) | 0.0080 ** (0.0026) | 0.0248 (0.0270) | 0.0054 (0.0031) | 0.0005 (0.0449) | 0.0127 * (0.0052) | 0.0337 (0.0272) | 0.0026 (0.0031) |
ret(-4) | −0.0120 (0.0218) | 0.0034 (0.0025) | −0.0172 (0.0263) | 0.0047 (0.0030) | 0.0249 (0.0439) | −0.0026 (0.0051) | 0.1187 *** (0.0273) | −0.0028 (0.0031) |
ret(-5) | −0.0208 (0.0221) | 0.0008 (0.0025) | −0.0374 (0.0259) | 0.0002 (0.0030) | 0.0484 (0.0469) | 0.0006 (0.0054) | 0.0176 (0.0265) | −0.0059 (0.0031) |
ret(-6) | −0.0580 ** (0.0200) | −0.0062 ** (0.0023) | −0.0753 ** (0.0236) | −0.0069 * (0.0027) | −0.0069 (0.0422) | −0.0039 (0.0049) | −0.0668 * (0.0279) | −0.007 * (0.0032) |
vol(-1) | 0.4183 * (0.1780) | 0.5676 *** (0.0205) | 0.2362 (0.2018) | 0.5785 *** (0.0232) | 1.4935 ** (0.5189) | 0.6000 *** (0.0598) | −0.1141 (0.3237) | 0.5889 *** (0.0373) |
vol(-2) | 0.0722 (0.1877) | 0.1409 *** (0.0216) | 0.3307 (0.2048) | 0.1466 *** (0.0236) | −1.6279 ** (0.5322) | 0.0512 (0.0613) | 0.4568 (0.3652) | 0.1277 ** (0.0421) |
vol(-3) | −0.1484 (0.1846) | 0.0479 * (0.0212) | −0.2420 (0.2003) | 0.0439 (0.0231) | 0.1456 (0.5121) | 0.0779 (0.0590) | 0.5060 (0.3854) | 0.1595 *** (0.0444) |
vol(-4) | −0.1196 (0.1792) | 0.0733 *** (0.0206) | −0.1397 (0.1969) | 0.0570 * (0.0227) | 0.3506 (0.4612) | 0.1513 ** (0.0531) | −0.5460 (0.4230) | 0.0383 (0.0487) |
vol(-5) | −0.0393 (0.1801) | 0.0509 * (0.0207) | 0.0402 (0.1958) | 0.0720 ** (0.0226) | −0.3109 (0.4921) | −0.0764 (0.0567) | −0.5117 (0.4010) | 0.0426 (0.0462) |
vol(-6) | −0.0546 (0.1548) | 0.0814 *** (0.0178) | −0.1211 (0.1685) | 0.0669 *** (0.0194) | 0.2811 (0.4285) | 0.1669 *** (0.0494) | 0.0437 (0.3277) | −0.0195 (0.0377) |
Constant | 0.0321 (0.0288) | −0.0033 (0.0033) | 0.0219 (0.0328) | 0.0005 (0.0038) | −0.0165 (0.0947) | −0.0239 * (0.0109) | 0.1847 (0.1063) | 0.0065 (0.0122) |
Explanatory Variable | (1) | (2) | (3) | (4) | ||||
---|---|---|---|---|---|---|---|---|
Equation ret | Equation vol | Equation ret | Equation vol | Equation ret | Equation vol | Equation ret | Equation vol | |
ret(-1) | 0.0497 * (0.0223) | 0.0501 *** (0.0026) | 0.0540 (0.0278) | 0.0560 *** (0.0032) | 0.0107 (0.0389) | 0.0362 *** (0.0045) | −0.0628 * (0.0261) | 0.0143 *** (0.0030) |
ret(-2) | −0.0730 ** (0.0225) | 0.0025 (0.0026) | −0.0913 ** (0.0279) | 0.0029 (0.0032) | −0.0809 (0.0417) | −0.0026 (0.0048) | −0.0047 (0.0293) | 0.0020 (0.0034) |
ret(-3) | 0.0424 * (0.0211) | 0.0066 ** (0.0024) | 0.0324 (0.0254) | 0.0083 ** (0.0029) | 0.0645 (0.0394) | 0.0013 (0.0045) | −0.0448 (0.0308) | 0.0006 (0.0035) |
ret(-4) | −0.0092 (0.0206) | 0.002 (0.0024) | −0.0213 (0.0250) | 0.0027 (0.0029) | −0.0158 (0.0385) | −0.0031 (0.0044) | 0.1648 *** (0.0312) | −0.0053 (0.0036) |
ret(-5) | −0.0191 (0.0205) | −0.0012 (0.0024) | −0.0257 (0.0254) | −0.0005 (0.0029) | −0.0226 (0.0361) | −0.0046 (0.0042) | 0.0224 (0.0306) | −0.0055 (0.0035) |
ret(-6) | −0.0579 ** (0.0195) | −0.0060 ** (0.0022) | −0.0752 *** (0.0225) | -0.0070 ** (0.0026) | −0.0194 (0.0398) | −0.0034 (0.0046) | −0.0635 * (0.0308) | −0.0105 ** (0.0035) |
vol(-1) | 0.4115 * (0.1649) | 0.5956 *** (0.0190) | 0.3268 (0.1852) | 0.5920 *** (0.0213) | 1.3405 ** (0.4545) | 0.6616 *** (0.0524) | 0.1230 (0.3851) | 0.5975 *** (0.0444) |
vol(-2) | 0.0647 (0.1795) | 0.1285 *** (0.0207) | 0.2910 (0.1956) | 0.1273 *** (0.0225) | −1.2933 ** (0.4763) | 0.1144 * (0.0549) | 0.3342 (0.4413) | 0.0994 (0.0508) |
vol(-3) | −0.2174 (0.1776) | 0.0541 ** (0.0205) | −0.2845 (0.1912) | 0.0477 * (0.0220) | 0.2600 (0.4921) | 0.0875 (0.0567) | 0.6945 (0.4889) | 0.1774 ** (0.0563) |
vol(-4) | −0.0445 (0.1740) | 0.0731 *** (0.0201) | −0.1192 (0.1900) | 0.0626 ** (0.0219) | 0.5712 (0.4480) | 0.1502 ** (0.0516) | −0.8105 (0.5586) | −0.0274 (0.0643) |
vol(-5) | 0.0043 (0.1743) | 0.0486 * (0.0201) | 0.0401 (0.1887) | 0.0667 ** (0.0217) | −0.2831 (0.4557) | −0.0505 (0.0525) | −1.0655 * (0.5171) | 0.0556 (0.0596) |
vol(-6) | −0.1127 (0.1485) | 0.0666 *** (0.0171) | −0.0800 (0.1612) | 0.0706 *** (0.0186) | −0.4978 (0.4066) | 0.0260 (0.0468) | 0.6897 (0.4241) | 0.0420 (0.0488) |
Constant | 0.0343 (0.0275) | 0.0006 (0.0032) | 0.0656 * (0.0309) | 0.0023 (0.0036) | −0.1636 (0.0986) | −0.0288 * (0.0114) | −0.0169 (0.1444) | −0.0239 (0.0166) |
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Wang, P.; Ho, T.; Li, Y. The Price-Volume Relationship of the Shanghai Stock Index: Structural Change and the Threshold Effect of Volatility. Sustainability 2020, 12, 3322. https://doi.org/10.3390/su12083322
Wang P, Ho T, Li Y. The Price-Volume Relationship of the Shanghai Stock Index: Structural Change and the Threshold Effect of Volatility. Sustainability. 2020; 12(8):3322. https://doi.org/10.3390/su12083322
Chicago/Turabian StyleWang, Panpan, Tsungwu Ho, and Yishi Li. 2020. "The Price-Volume Relationship of the Shanghai Stock Index: Structural Change and the Threshold Effect of Volatility" Sustainability 12, no. 8: 3322. https://doi.org/10.3390/su12083322
APA StyleWang, P., Ho, T., & Li, Y. (2020). The Price-Volume Relationship of the Shanghai Stock Index: Structural Change and the Threshold Effect of Volatility. Sustainability, 12(8), 3322. https://doi.org/10.3390/su12083322