**4. Analysis**

In presenting the empirical results, the article starts with VAR calculations. Thereafter, Markov regime-switching results are presented in order to explore if one can infer interdependence of volatilities regimes. In order to verify which VAR is suitable, the first and second order tests (i.e. residual serial correlation) testing validity are used. Thereafter, a lag-length criterion is used. All those tests confirmed the appropriateness of VAR (1) model. Further, in order to interpret the results Cholesky decomposition is used. Generally, when using Cholesky decomposition the order of VAR parameters order matters. The BRICS countries are inputted in alphabetical order because that order is consisted with normal writing order. Although, VAR results might be different when one inputs them in a different format, one views normal order as an appropriate one. It can be inferred from [31] alphabetical order modelling leads to better estimates. In **Tables 2** and **3** all variables highlighted in grey are statistically significant for VAR values as they are at least 2 irrespective of being negative or positive. The F-statistic is basically Anova values and one reads the in the following manner. Assume the following inequality *F*ð Þ¼ 2, 12 22*:*59, *p*< 0*:*05Þ, the 2 is the degrees of freedom numerator, 12 is total observations of freedom denominator, 22.59 is the calculated Anova value and 0.05 is alpha (i.e. significance level). This article assumes that both the degrees of freedom numerator and total observations of freedom denominator are infinities in order to illustrate the best case scenario. In the latter situation, the critical value is 1.22. Thus, F-statistic values highlighted in grey fall within the non-rejection (i.e. acceptable) regions while values which are not highlighted fall within rejection regions. That is, latter values exemplify autocorrelation for those VAR(1) model.

The results panel 5 of **Table 2** illustrates that one-lag in Brazilian indexed volatility of bonds cause one-lag in Brazilian indexed volatility of bonds by 0.18 units. The letter statement is sensible given that what happens in one market should have similar effect in the short run-regimes show that regimes time is just over 2 weeks. Similarly, a one-lag in Brazilian indexed volatility of bond cause onelag in South African indexed volatility of bonds-this probably that of similarities between the two countries, i.e. ruling political parties stay in power much longer; historically, Brazil and South Africa have good trade relations and further, the BRICS formation is strengthening that relationship even more. The one-lag in Indian volatility of bonds cause one-lag in Indian volatility of bonds. The phenomenon is similar with the one of Brazil lags; however, Indian one is negative while Brazil one is positive. One possible explanation for India negative lag is that in India the government is highly involved in driving economic growth than in Brazil.


All other indexed volatilities of bonds in other BRICS countries are statistically insignificant. However, those latter results should be read with caution as using Cholesky decomposition for curves for those countries to start at zero. Panel 6 of

F-statistic 0.2134 2.6753 3.8118 5.8949 0.6335

*Note: in each cell, the first number is the coefficient and the number in brackets is the t-test. All variables highlighted in grey are statistically significant for VAR values as they are at least 2 irrespective of being negative or positive. The*

The statistically significant results are for Brazil and Brazil-this is for the same reasons as in panel 5, Brazil and China-Brazil is the producer of commodities while China is a consumer. This implies that the one-lag in producer of commodities indexed volatilities causes one-lag in consumer indexed volatilities but not visa verse. More, the coefficient is negative because the effects spillover to the consumer from the producer. The results for China lags can be explained by same reasons as the Brazil lags. Similarly, the one-lag in Indian index volatility cause a one-lag in South African indexed commodities volatility-the same as the Brazil and China one lags. The Russian lags are the same as China lags. Note that China lag with itself is positive while Russia lag with itself is negative. The positive lag for China lag with itself is probably due the economic influence that China has on the major world issues. The influence of Russian on major economic issues is limited. Thus, it might imply that South Africa needs to establish itself globally before the South African

**Brazil China India Russia South Africa**

12.2983 3.6080 3.7334 3.0728 3.4525

12.2520 3.5618 3.6871 3.0266 3.4062

**Brazil China India Russia South Africa**

0.1344 (2.5099) 0.0325

0.0162 (0.3345) 0.1256

0.1783 (1.7871) 0.0010

0.0276 (0.4412) 0.0031

(0.5584)

(2.3889)

0.0466 (1.2075) 0.1679 (4.0062) 0.0332 (1.6033)

(0.0093)

(0.1009)

0.0011 (0.0391)

0.0097 (0.3717)

0.0233 (0.0449)

0.0720 (1.2489)

2.6706 3.0149 2.5382 2.3731 3.7809

2.6244 2.9687 2.4919 2.3269 3.7347

F-statistic 1.9912 2.5000 2.7793 2.7791 2.7064

0.1362 (2.9988)

(0.9456)

0.0286 (0.7487)

0.0504 (1.6582)

(0.9927)

Panel 7 shows that spillovers which are statistically significant are for Brazil lags with itself-this pattern has been explained before, Brazil lag with Russian lag-in

**Table 2** illustrates results for commodities indexed volatilities.

**Panel 7: equities**

*The Independence of Indexed Volatilities DOI: http://dx.doi.org/10.5772/intechopen.90240*

Akaike AIC

Schwarz SC

South Africa

Akaike AIC

Schwarz SC

**Table 2.**

**143**

**Panel 8: real estate**

Brazil 0.0197

India 0.0259

Russia 0.0229

(0.3642)

(0.5738)

(0.6359)

0.0107 (0.1145) 0.0780

*interpretation of results is based on Cholesky decomposition.*

*VAR (1): out-sample period (2007–2017).*

China 0.0236 (0.4708) 0.0399

government can play a major on South African economic issues.


*The Independence of Indexed Volatilities DOI: http://dx.doi.org/10.5772/intechopen.90240*

*Note: in each cell, the first number is the coefficient and the number in brackets is the t-test. All variables highlighted in grey are statistically significant for VAR values as they are at least 2 irrespective of being negative or positive. The interpretation of results is based on Cholesky decomposition.*

#### **Table 2.**

*VAR (1): out-sample period (2007–2017).*

All other indexed volatilities of bonds in other BRICS countries are statistically insignificant. However, those latter results should be read with caution as using Cholesky decomposition for curves for those countries to start at zero. Panel 6 of **Table 2** illustrates results for commodities indexed volatilities.

The statistically significant results are for Brazil and Brazil-this is for the same reasons as in panel 5, Brazil and China-Brazil is the producer of commodities while China is a consumer. This implies that the one-lag in producer of commodities indexed volatilities causes one-lag in consumer indexed volatilities but not visa verse. More, the coefficient is negative because the effects spillover to the consumer from the producer. The results for China lags can be explained by same reasons as the Brazil lags. Similarly, the one-lag in Indian index volatility cause a one-lag in South African indexed commodities volatility-the same as the Brazil and China one lags. The Russian lags are the same as China lags. Note that China lag with itself is positive while Russia lag with itself is negative. The positive lag for China lag with itself is probably due the economic influence that China has on the major world issues. The influence of Russian on major economic issues is limited. Thus, it might imply that South Africa needs to establish itself globally before the South African government can play a major on South African economic issues.

Panel 7 shows that spillovers which are statistically significant are for Brazil lags with itself-this pattern has been explained before, Brazil lag with Russian lag-in


both countries, commodities firms are the main constituents of equities indices. And the causal relationship is slightly negative. Thus, 1 unit lag in Brazilian indexed volatilities emanating from equities cause 0.0008 lag in Russian indexed volatility of the same index. The latter strategy is synonymous with hedging and speculation in equity markets. More, straddles work in a similar manner. Panel 8 shows the results of lags in real estate indices. The statistically significant lags are for Russia with itself-that pattern has been explained before, China and Brazil-Brazil is probably the most powerful economy in South American while China is the second biggest economy after the United States. China has been on major infrastructure projects including real estate and many academics and practitioners have

12.7188 3.8867 4.3692 3.6203 4.1355

**Brazil China India Russia South Africa**

0.1126 (2.1609)

0.0174 (0.4013)

0.0362 (0.6179)

(1.7336)

0.1037 (1.4455) 0.0393 (0.7707) 0.0794

0.0207 (0.4699)

(1.8378)

0.0282 (0.7678)

0.0266 (0.5363)

0.0415 (0.6271)

(0.9954)

0.0426 (0.6990)

0.0512 (0.6213)

3.2510 3.4551 3.0200 3.7027 4.0345

3.1787 3.3828 2.9477 3.6305 3.9622

0.0293 (0.3308) 0.1061 (0.9652) 0.1355

F-statistic 1.0215 0.3552 0.0529 1.5103 0.8958

*Note: in each cell, the first number is the coefficient and the number in brackets is the t-test. All variables highlighted in grey are statistically significant for VAR values as they are at least 2 irrespective of being negative or positive. The*

questioned whether the bubble is in the horizon in China. The negative coefficient is probably due to 'overbuilding' in China. Indian lagged volatility cause a positive lag in China. The latter finding is probably due to ruling parties' influences in managing their economies. Interestingly, one-lag in Russian volatility causes one-lag in India. Normally, collapse of currencies and commodities markets precede other capital markets products. Overall, one can see that volatility spillovers in the BRICS countries based on four indices during 2007–2017 period, exemplify opportunities to diversification opportunities-when indexed volatilities move in different directions and risk management opportunities-when indexed volatilities move the same

The influence of Brazil lag to South Africa lag during period of 2012–2017 is the same as during the 2007–2017 period as illustrated in panel 9. The period of 2012– 2017 was largely a bull market while 2007–2017 had some bearish years, i.e. 2008/ 2009 period. This implies that indexed volatilities of bonds during out-sample

direction.

**145**

**Panel 11: equites**

**Panel 12: real estate**

India 0.0482

Russia 0.0309

Brazil 0.0041 (0.0635) 0.0284 (0.4825) 0.0729

(0.5308)

0.0046 (0.0943)

0.0771 (1.1644)

China 0.1213 (1.8983) 0.0306

*The Independence of Indexed Volatilities DOI: http://dx.doi.org/10.5772/intechopen.90240*

(0.8873)

(0.4209)

0.0128 (0.1304)

*interpretation of results is based on Cholesky decomposition.*

*VAR(1;1): In-sample period (2012–2017).*

Schwarz SC

South Africa

Akaike AIC

Schwarz SC

**Table 3.**

*The Independence of Indexed Volatilities DOI: http://dx.doi.org/10.5772/intechopen.90240*


*Note: in each cell, the first number is the coefficient and the number in brackets is the t-test. All variables highlighted in grey are statistically significant for VAR values as they are at least 2 irrespective of being negative or positive. The interpretation of results is based on Cholesky decomposition.*

#### **Table 3.**

*VAR(1;1): In-sample period (2012–2017).*

both countries, commodities firms are the main constituents of equities indices. And the causal relationship is slightly negative. Thus, 1 unit lag in Brazilian indexed volatilities emanating from equities cause 0.0008 lag in Russian indexed volatility of the same index. The latter strategy is synonymous with hedging and speculation in equity markets. More, straddles work in a similar manner. Panel 8 shows the results of lags in real estate indices. The statistically significant lags are for Russia with itself-that pattern has been explained before, China and Brazil-Brazil is probably the most powerful economy in South American while China is the second biggest economy after the United States. China has been on major infrastructure projects including real estate and many academics and practitioners have questioned whether the bubble is in the horizon in China. The negative coefficient is probably due to 'overbuilding' in China. Indian lagged volatility cause a positive lag in China. The latter finding is probably due to ruling parties' influences in managing their economies. Interestingly, one-lag in Russian volatility causes one-lag in India. Normally, collapse of currencies and commodities markets precede other capital markets products. Overall, one can see that volatility spillovers in the BRICS countries based on four indices during 2007–2017 period, exemplify opportunities to diversification opportunities-when indexed volatilities move in different directions and risk management opportunities-when indexed volatilities move the same direction.

The influence of Brazil lag to South Africa lag during period of 2012–2017 is the same as during the 2007–2017 period as illustrated in panel 9. The period of 2012– 2017 was largely a bull market while 2007–2017 had some bearish years, i.e. 2008/ 2009 period. This implies that indexed volatilities of bonds during out-sample


#### **Figure 2.**

*Filtered regime probabilities-out sample: 2007–2017.*

reflect similar patterns as in-sample period. The sample phenomenon can be advocated on the influence the one-lag of Indian volatility on the lag of India. The interesting result in panel 9 is the one-lag of South Africa with itself-during the in sample period the lag is influential. During 2012–2017, the South African long-and short-term yields were on an upward trajectory. This is probably why one-lag for South Africa in during the in-sample period had a casual effect. For commodities indices-panel 10, the rests are the same as in **Table 2** except the one-lag of Brazilian volatility on one-lag of Russia. During 2012–2017, commodities prices were stable. In panel 11, one-lag of China has influence on one-lag of Russia and one-lag of South Africa had one-lag on China-all the lags are negative. This is probably to declining consumption on commodity products by China. The rest of results are in panel 11 are the same as in panel 7. For panel 12, only one-lag of has a negative influence onelag of Brazil. In short-run volatilities tend to be spiky than in the long run. That is, the volatility spillovers might be temporary.

For every index type in **Figure 2** in every row, the first country is Brazil followed by China and then India; thereafter Russia. The last country is always South Africa. For equities indices, all the five countries have main shocks in 2007– 2008 period as illustrated by residuals. This is the period of the last subprime crisis. However, the actual date reveals a similar picture. The upward regimes in all countries were during 2007–2009 period. It can be inferred from [6, 27] that when indices move in the same direction, the volatilities should follow a similar pattern. But, those graphs do not tell one from and to which are the volatilities. The equities volatilities in Brazil and South Africa seem to hover around the same level during the entire out sample. In [30], it was illustrated the subprime effects of 2007–2009 in South Africa were minimal. From what was reported in media, Brazil never suffered much from the subprime effects of 2007–2009. Real estate indices show the similar patterns as equities indices except for China and India. Sometimes during subprime crises, equities movements preceded real estate movements. The real estate indices of China and India show similar and strong patterns. One of the reasons for that is the BRIC relation between those two countries precedes the establishment of the BRIC countries. More, they have large populations and their respective governments are at the heart of driving those economies.

are rich in mineral resources. On the other hand, China and India consume most of commodities products. Surprisingly, Russia had the most stable commodity index during 2007–2017 period. Unlike Brazil and South Africa, Russia is mainly rich in oil while the other two countries are rich in minerals. The bonds indices show similar patterns to real estate indices. Numerous studies illustrate that listed real estate exhibit traits of other capital markets, especially bonds. The patterns of bonds indices are dissimilar except for China and Russia. It can be inferred that bonds volatilities of those two countries follow in the same direction. The graphs show diagnostic patterns and in order to have more depth, this article illustrates Markov transitions as shown in **Table 4**. In most studies, transition probabilities and

**Brazil China India Russia South Africa** CTP 1 2 1 2 1 2 1 2 1 2 1 0.5703 0.4297 0.5009 0.4991 0.4943 0.5057 0.5058 0.4942 0.5661 0.4339 2 0.4993 0.5107 0.5126 0.4874 0.5034 0.4967 0.5216 0.4784 0.6033 0.3967 CED 1 2 1 2 1 2 1 2 1 2

2.3274 2.0436 2.0034 1.9507 1.9775 1.9864 2.0233 1.9171 2.3047 1.6577

1.9932 2.0439 1.0000 40.9669 57.7020 1.1116 1.8827 47.5343 1.5248 134.6585

2.0857 1.9903 11.0248 485.6439 1.8999 2.2007 1.9859 2.0007 1.0000 70.8325

1.9841 556.1991 1.4009 2.1748 123.8068 1.2908 1.9285 2.6323 2.0270 2.0605

CTP 1 2 1 2 1 2 1 2 1 2 1 0.4983 0.5017 0.0000 1.0000 0.9827 0.0173 0.4689 0.5311 0.3442 0.6558 2 0.4893 0.5107 0.0244 0.9756 0.8896 0.1004 0.0210 0.9789 0.0074 0.9926 CED 1 2 1 2 1 2 1 2 1 2

CTP 1 2 1 2 1 2 1 2 1 2 1 0.5206 0.4795 0.9093 0.0907 0.4737 0.5263 0.4965 0.5035 0.0000 1.0000 2 0.5024 0.4976 0.0021 0.9979 0.4544 0.5456 0.4998 0.5002 0.0141 0.9859 CED 1 2 1 2 1 2 1 2 1 2

CTP 1 2 1 2 1 2 1 2 1 2 1 0.4959 0.5040 0.2862 0.7138 0.9919 0.0081 0.4817 0.5185 0.5067 0.4933 2 0.0018 0.9985 0.4598 0.5402 0.7747 0.2253 0.3799 0.6201 0.4853 0.5147 CED 1 2 1 2 1 2 1 2 1 2

*Note: CTP and CED stand for constant transition probabilities and expected duration, respectively.*

Panel 13 (14) illustrates Markov transitions for equities (real estate) while panel 15 (16) shows Markov transitions for commodities (bonds). For equities indices, for the four countries; Brazil, China, India and Russia, there is considerable transition dependence between the two regimes as the original regimes start from as low 0.50

and increase to as high as 0.57. The non-original regimes are as low as 0.50.

expected durations, are used to illustrate Markov transitions.

**Panel 13: equities**

*The Independence of Indexed Volatilities DOI: http://dx.doi.org/10.5772/intechopen.90240*

**Panel 14: real estate**

**Panel 15: commodities**

**Panel 16: bonds**

*Markov transition-out sample: 2007–2017.*

**Table 4.**

**147**

For the commodities indices, Brazil and South Africa have the most and similar volatile indices patterns. One of the reasons of that is that Brazil and South Africa
