Analysing Rational Bubbles in African Stock Markets: Evidence from Econophysics Frequency Domain Estimates and DCC MGARCH Model
Abstract
:1. Introduction
Literature Review
2. Methodology
2.1. Data
2.2. The Model
Econophysics Frequency Domain Estimation Techniques
3. Results
4. Discussion
Robustness Check
5. Conclusions
Author Contributions
Funding
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
1 | Botswana, Egypt, Ghana, Kenya, Mauritius, Morocco, Nigeria and South Africa (BRVM (Bourse Régionale des Valeurs Mobilières) and Dar es Salaam Stock Exchange were dropped because of too many missing values for some years)). S&P started recording daily data for most African stock markets in the mid-1995. |
2 | A jump simply implies a trading stop or news. |
3 | Experts have raised concern about the ability of monetary policy tools effectiveness in tackling bubbles because they are blunt instruments designed to influence the aggregate level of economic activities and not usually sectorial activities. |
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Parameters/Series | South Africa | Nigeria | Egypt | Botswana | Morocco | Ghana | Kenya | Mauritius |
---|---|---|---|---|---|---|---|---|
Mean | 49.139 | 43.314 | 48.241 | 49.931 | 47.99 | 48.18 | 48.41 | 44.016 |
Standard Deviation | 28.456 | 29.521 | 27.411 | 31.481 | 30.354 | 30.411 | 31.210 | 27.382 |
Minimum | 10.345 | 10.511 | 10.811 | 11.1901 | 9.284 | 9.678 | 10.211 | 11.011 |
Maximum | 157.83 | 158.711 | 158.012 | 156.97 | 156.93 | 190.211 | 158.114 | 158.62 |
Skewness | 1.190 | 1.2141 | 1.3421 | 1.341 | 1.0121 | 1.592 | 1.299 | 1.923 |
Kurtosis | 0.158 | 0.168 | 0.166 | 0.174 | 0.1750 | 0.1701 | 0.1711 | 0.1734 |
Jarque-Bera | 1648.3960 *** | 1649.416 *** | 1647.341 *** | 1644.304 *** | 1640.311 *** | 1647.312 *** | 1639.311 *** | 1661.011 *** |
Ljung–Box Q-statistics | 24.093 *** (12) | 32.088 *** (15) | 25.107 *** (12) | 18.765 *** (15) | 22.982 ** (12) | 19.644 *** (12) | 26.055 *** (18) | 23.053 *** (15) |
Engle (1982) ARCH test | 55.022 *** (12) | 62.044 *** (12) | 25.107 *** (18) | 38.115 *** (12) | 47.112 ** (12) | 8.906 *** (16) | 46.026 *** (12) | 31.073 *** (12) |
Series | Levels | First Differences | ||||
---|---|---|---|---|---|---|
ADF | PP | KPSS | ADF | PP | KPSS | |
South Africa | −2.503 | −2.115 | 0.622 *** | −10.443 *** | −10.107 *** | 0.083 |
Nigeria | −2.771 | −2.453 | 0.559 *** | −10.094 *** | −10.155 *** | 0.076 |
Egypt | −2.288 | −2.267 | 0.889 *** | −11.037 *** | −11.094 *** | 0.049 |
Botswana | −2.104 | −2.780 | 0.903 *** | −13.098 *** | −14.055 *** | 0.055 |
Morocco | −2.255 | −2.098 | 0.917 *** | −11.098 *** | −13.077 *** | 0.069 |
Ghana | −2.088 | −2.304 | 0.443 *** | −10.098 *** | −10.177 *** | 0.167 |
Kenya | −2.509 | −2.408 | 0.089 *** | −12.098 *** | −12.039 *** | 0.087 |
Mauritius | −2.155 | −2.006 | 0.459 *** | −13.078 *** | −13.655 *** | 0.085 |
Series | Residual Sum of Squares (RSS) | ||||
---|---|---|---|---|---|
South Africa | 0.148 | 1 | 173.803 *** | 3 | −1.866 |
Nigeria | 0.655 | 1 | 205.554 *** | 2 | −1.409 |
Egypt | 0.877 | 1 | 155.033 *** | 3 | −1.402 |
Botswana | 0.165 | 1 | 161.275 *** | 3 | −1.711 |
Morocco | 0.544 | 1 | 180.332 *** | 2 | −1.455 |
Ghana | 0.787 | 1 | 206.098 *** | 3 | −1.806 |
Kenya | 0.771 | 1 | 165.099 *** | 3 | −1.564 |
Mauritius | 0.634 | 1 | 183.087 *** | 3 | −1.733 |
Series | Beginning Dates | Ending Dates |
---|---|---|
Egypt | 13 March 1999 | 24 October 2004 |
2 February 2009 | 18 December 2010 | |
4 November 2016 | 28 May 2018 | |
Morocco | 13 January1999 | 15 May 2000 |
1 August 1996 | 18 December 1996 | |
2 February 2000 | 9 December 2001 | |
Botswana | 9 February 2000 | 6 August 2005 |
1 February 2010 | 30 November 2015 | |
Ghana | 3 April 2005 | 3 May 2008 |
1 June 2010 | 3 November 2014 | |
Nigeria | 8 August 1999 | 21 December 2002 |
1 December 2004 | 8 August 2007 | |
5 May 2012 | 8 August 2014 | |
South Africa | 3 April 1998 | 10 October 1998 |
4 June 2001 | 12 October 2001 | |
10 March 2003 | 13 August 2003 | |
11 September 2008 | 12 October 2008 | |
4 February 2016 | 10 October 2016 | |
Kenya | 4 September 1996 | 12 December 1996 |
1 July 2000 | 11 December 2001 | |
5 May 2003 | 12 October 2008 | |
6 June 2014 | 12 August 2018 | |
Mauritius | 5 February 2000 | 16 October 2005 |
6 October 2007 | 30 September 2010 | |
7 March 2012 | 10 October 2015 |
Panel A: Linear Model | ||
Series | Rank Test Statistic | Linear Score Test Statistic |
South Africa | 1.10561 *** | 4.0087603 *** |
Nigeria | 0.97633 *** | 0.7865509 * |
Egypt | 0.91089 *** | 1.954407 *** |
Botswana | 0.81712 *** | 4.006591 *** |
Morocco | 0.82771 *** | 0.754493 *** |
Ghana | 0.52433 *** | 2.876601 *** |
Kenya | 0.71891 *** | 0.743388 *** |
Mauritius | 0.71166 *** | 1.89056 *** |
Critical value (%) | ||
10 | 0.0514 | 3.05 |
5 | 0.0951 | 4.62 |
1 | 0.0433 | 6.76 |
Panel B: Nonlinear Model | ||
Series | Rank Test Statistics | Nonlinear Score Test Statistic |
South Africa | 0.82935 *** | 4.006629 *** |
Nigeria | 0.89169 ** | 0.677702 *** |
Egypt | 0.90322 ** | 1.872034 *** |
Botswana | 0.94625 ** | 0.987232 *** |
Morocco | 0.82999 *** | 1.908821 *** |
Ghana | 0.744662 *** | 0.788292 *** |
Kenya | 0.964461 *** | 1.872209 *** |
Mauritius | 0.983385 * | 1.859663 *** |
Critical value (%) | ||
10 | 0.0356 | 3.99 |
5 | 0.0198 | 4.73 |
1 | 0.0177 | 7.06 |
Panel A: Dynamic Conditional Correlation MGARCH Model | ||||||||
Series | South Africa | Nigeria | Egypt | Botswana | Morocco | Ghana | Kenya | Mauritius |
Cons | 1.292 a [0.007] | 1.261 a [0.006] | 1.241 a [0.022] | 1.206 [0.006] | 1.401 a [0.014] | 1.014 a [0.020] | 1.414 a [0.012] | 1.843 a [0.016] |
L1arch | 0.941 a [0.038] | 0.913 a [0.038] | 0.849 a [0.030] | 0.914 a [0.029] | 0.941 [0.051] | 0.721 a [0.039] | 0.821 a [0.044] | 0.928 a [0.042] |
L2garch | 0.250 a [0.023] | 0.2419 [0.024] | 0.214 a [0.014] | 0.239 a [0.023] | 0.204 a [0.024] | 0.341 a [0.017] | 0.290 a [0.019] | 0.214 a [0.027] |
Cons arch | 0.008 a [0.001] | 0.009 a [0.001] | 0.016 a [0.002] | 0.007 a [0.001] | 0.061 a [0.005] | 0.042 [0.005] | 0.009 a [0.001] | 0.044 a [0.004] |
N | ||||||||
Log likelihood | 3994.7 | |||||||
Lamda1 (0.006) | 0.289 a | |||||||
Lamda2 (0.006) | 0.711 a | |||||||
Panel B: The Estimated Conditional Quasi-Correlation in DCC MGARCH Model | ||||||||
Correlations | South Africa | Nigeria | Egypt | Botswana | Morocco | Ghana | Kenya | Mauritius |
South Africa | - | |||||||
Nigeria | 0.764 a [0.031] | - | ||||||
Egypt | 0.643 a [0.036] | 0.614 a [0.049] | - | |||||
Botswana | 0.624 a [0.040] | 0.572 a [0.051] | 0.643 a [0.052] | - | ||||
Morocco | 0.562 a [0.041] | 0.561 a [0.061] | 0.610 a [0.048] | 0.622 a [0.041] | - | |||
Ghana | 0.598 a [0.043] | 0.621 a [0.070] | 0.572 a [0.081] | 0.601 a [0.048] | 0.524 a [0.058] | - | ||
Kenya | 0.608 a [0.041] | 0.591 a [0.046] | 0.589 a [0.052] | 0.548 a [0.064] | 0.701 a [0.062] | 0.543 a [0.0049] | - | |
Mauritius | 0.566 [0.042] | 0.553 [0.054] | 0.543 [0.053] | 0.540 [0.0501] | 0.538 [0.0498] | 0.531 [0.0477] | 0.511 [0.049] | - |
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Lawal, A.I.; Oseni, E.; Ahmed, A.; Riyadh, H.A.; Tabash, M.I.; Abaver, D.T. Analysing Rational Bubbles in African Stock Markets: Evidence from Econophysics Frequency Domain Estimates and DCC MGARCH Model. Economies 2024, 12, 217. https://doi.org/10.3390/economies12080217
Lawal AI, Oseni E, Ahmed A, Riyadh HA, Tabash MI, Abaver DT. Analysing Rational Bubbles in African Stock Markets: Evidence from Econophysics Frequency Domain Estimates and DCC MGARCH Model. Economies. 2024; 12(8):217. https://doi.org/10.3390/economies12080217
Chicago/Turabian StyleLawal, Adedoyin Isola, Ezeikel Oseni, Adel Ahmed, Hosam Alden Riyadh, Mosab I. Tabash, and Dominic T. Abaver. 2024. "Analysing Rational Bubbles in African Stock Markets: Evidence from Econophysics Frequency Domain Estimates and DCC MGARCH Model" Economies 12, no. 8: 217. https://doi.org/10.3390/economies12080217
APA StyleLawal, A. I., Oseni, E., Ahmed, A., Riyadh, H. A., Tabash, M. I., & Abaver, D. T. (2024). Analysing Rational Bubbles in African Stock Markets: Evidence from Econophysics Frequency Domain Estimates and DCC MGARCH Model. Economies, 12(8), 217. https://doi.org/10.3390/economies12080217