**3.1 Data**

The weekly data is for the five BRICS countries (general equities, real estate, commodities and bonds) for the period 1 January 2007–31 December 2017 obtained from Bloomberg. The out-sample is from 2007 to 2017 and in-sample from 2012 to 2017. The in-sample is for parameters estimation and out-sample for evaluating forecasting performance. The use of weekly data ameliorates concerns over nonsynchronicities and bid-ask effects in daily data [13]. The phenomenon of using returns to illustrate the descriptive nature of volatility spillovers is synonymous with [6, 27]. The returns are logarithm returns and they are consistent with VAR model. All returns are calculated based on the indices of those countries. The indices are as follows; (i) general equities, Brazil IBRX 50 for Brazil, Moex Russian index for Russia, Nifty 50 for India, SSE50 for China and JSE top 40 index for South Africa, (ii) listed real estate, IMOB for Brazil, for Russia the index is created based on PIKK Group, PJSC LSR Group, World Trade Centre 'ordinary shares' and World Trade Centre 'preferred shares' because Russia does not have a listed real estate index-the market capitalisations of those firms where aggregated over time, Nifty Realty for India, SHROP for China and all Property index (J803) for South Africa, (iii) commodities, BM&F BOVESPA for Brazil, MICEX Oil and Gas Index-from the Moscow exchange for Russia, Nifty Commodities for India, CCI for China and JCGMSAG (gold mining index) for South Africa and (iv) bonds, for Brazil-Brazil 8 7/8 04/15/24 bond, Russia-RFLB 08/29/18 bond, India-Nifty 10 yr. benchmark, China-GT USDCN 15yr bond and South Africa-SAGB 10 ½ 12/26 bond. Skintzi and Refenes [28] used indices to investigate regional and country shocks. This article is the first one that uses indices to illustrate shocks in the BRICS countries. According to [28], one of the advantages of modelling volatility shocks using indices is that

**Figure 1.** *BRICS log returns.*

shocks are captured both as endogenous and exogenous variables. Just like [6, 27], this article presents diagnostic analysis based on graphs as part of volatilities transmission investigation.

For every index per a row, the first country is Brazil, followed by Russia, then India; thereafter, China and finally South Africa. A close inspection of **Figure 1** illustrate that the log returns of BRICS countries as shown by different graphs, BRICS returns were characterised by spikes during 2007–2017 period. The latter statement might be interpreted as the presence of changing volatility patterns and probably spillovers. Similar arguments were put forward by [6, 27] on return patterns. The years are on the x-axis and the log-returns on the y-axis. During 2008/ 2009, there was a global financial crisis that mainly affected western countrieswestern Europe and U.S. were the hardest hit by that subprime crisis. According to the Bank of International Settlements (BIS) Brazil only reacted to the global subprime crisis after Lehman Brothers collapsed. Due to that reaction, there was panic in Brazil lead to property market falling but IBOVESPA rose by 20%-in local currency; local capital issuance stood around \$165 billion around 5.6% of Brazilian GDP. And bank credit increased to 36% from 32% during that period. Although, there still spikes after 2009, but they hoovered around same levels until 2017. For Russia, one sees similar pattern to Brazil. For both countries-Brazil and Russia, during subprime crisis, real estate reacts more than other indices. Does that imply that during subprime crisis volatilities are much higher in real estate?

Volatility modelling will provide answer(s) to that. Similar patterns are observable about Indian and Chinese indices. However, India and China have very strong capital markets and those countries are self-reliant on financing countries infrastructure. It seems that India and China tend to be insulated from external capital shocks [29]. South Africa is a unique member of the BRICS which joined through invitation. During year 2008, South African indices reacted to global capital markets movement; however, there was no subprime crisis effects felt in South Africa [30]. A study by PWC South Africa in 2016 illustrate that there was (i) a decline in new equity capital raised in South Africa, (ii) active and growing bond market in South Africa and (iii) number of corporate transactions decreased in South Africa. The decline in commodities index during 2014–2016 can be attributed to decline in commodities price and demand in commodities by South Africa trading partners. All those graphs illustrated diagnostic analysis on volatility spills. Now, the article takes the analysis further and it explores formative assessment of global transmission in the BRICS countries. The next section presents descriptive statistics of indices of the BRICS countries.

#### **3.2 Data description and preliminary statistics**

**Table 1** provides the descriptive statistics of the returns of general equities, real estate, commodities and bonds.

3.68%. All five countries exceed the kurtosis of 3 and with the exception of Brazil

*Note: SD stands for standard deviation and JB for Jarque-Bera test for the return normality.*

**Descriptions Mean Minimum Maximum SD Kurtosis Skewness JB**

Brazil 0.0007 0.3547 0.2385 0.051 7.0571 0.6941 1235.05 Russia 0.0009 0.4031 0.2841 0.052 9.1638 0.0484 1987.64 India 0.001 0.1906 0.1956 0.037 3.2816 0.2699 264.06 China 0.001 0.1704 0.168 0.04 2.1323 0.0068 106.28 South Africa 6E 04 0.2606 0.1984 0.043 5.1509 0.0227 633.49

Brazil 0.002 0.5044 0.3097 0.066 8.8189 1.0306 1780.53 Russia 0.001 0.7145 0.5282 0.077 22.483 1.3087 11613.2 India 0.003 0.3752 0.3719 0.072 4.0292 0.2754 384.67 China 0.002 0.2161 0.2894 0.054 2.6673 0.3788 179.68 South Africa 0.001 0.1961 0.1781 0.037 4.2404 0.4225 428.42

Brazil 0.0002 0.529 0.5435 0.177 2.0477 0.0046 100.11 Russia 8E 04 1.6035 1.6337 0.199 22.8521 0.2209 12.385 India 0.0009 0.2369 0.2432 0.042 3.8767 0.0754 359.35 China 0.0005 0.1096 0.0768 0.02 4.0293 0.7607 442.87 South Africa 0.002 0.2866 0.286 0.065 2.0176 0.3055 106.1

Brazil 0.0001 0.0845 0.1474 0.016 21.5203 1.6562 7763.32 Russia 2E 04 0.2019 0.1777 0.029 20.4736 0.7622 9466 India 3E 04 0.5151 0.5113 0.065 26.9833 1.1651 17455.1 China 3E 04 0.1126 0.0661 0.015 7.2105 0.5118 1266.32 South Africa 1E 04 0.2019 0.1777 0.029 20.4549 0.7619 9431.2

For commodities indicated in panel 3, Russia reports the highest maximum of 163.37% in returns, while India reports the lowest at 7.68%. Russia commodity stocks are more volatile with a standard deviation of 19.87% and the Chinese stocks are the least volatile at the standard deviation of 2.02% All countries exceed the kurtosis of 3 and the data is negatively skewed with the exception of Brazil and South Africa. In the bonds market indicated in panel 4, India has the highest return at 51.13% while China has the lowest maximum return at 6.61%. India is also the most volatile with a standard deviation of 6.50% and China. The data is also leptokurtic and is negatively skewed with the exception of Brazil. JB values in all panels (i.e. 1–4) illustrate that the four indices are abnormal and that can be interpreted as the presence of shocks. In [6], the same view on JB values was stated. The skewness values show that some countries have negative skews while others have positive skews for different capital markets. That mixture of different skewness assist in hedging volatility while positive skewness assist in generating high

and Russia, the data is positively skewed.

**Panel 1: general equity**

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

**Panel 2: real estate**

**Panel 3: commodities**

**Panel 4: bonds**

**Table 1.**

**139**

*Descriptive statistics.*

Panel 1 indicates the equity information across all countries. Russia leads with the highest return at 28.41% while China has the lowest maximum return of 16.80%. Over the full period, Russian equities are also the most volatile with a standard deviation of 5.20% and the lowest volatile equities being that of China at 3.72%. The distribution of returns over time is negatively skewed with the exception of India and China. In addition, for all countries, the excess kurtosis exceeds 3, indicating that the return series is leptokurtic which is inconsistent with a normal distribution. The real estate data in panel 2 for the five countries indicate Russia with the highest return of 52.82% while the South Africa closed off with a lowest maximum return of 17.81% return. Russia is the most volatile with a weekly standard deviation of 7.65% while South Africa reports the lowest standard deviation of
