**3. Data and methodology**

#### **3.1 Data**

We use a daily dataset including credit default swaps (CDSs), exchange rates of South Africa (RD), gold prices, and platinum prices for the period of 05.01.2010–2017.06.2022. We transform the dataset into logarithmic return series before we start the empirical analysis stage. Hence, the descriptive statistic of our dataset is given in **Table 1**.

According to the kurtosis value in **Table 1**, which is the fourth moment, CDS has high variability, i.e., 54.68, compared to the kurtosis values of gold, platinum, and RD variables. This interpretation is valid for the entire data set since the other kurtosis values are all greater than three, i.e., 8.90; 9.42; 4.67, respectively.

Considering the skewness parameters in **Table 1**, which measure the asymmetry, the values of CDS and RD variables are greater than zero and are also positive. However, the asymmetry parameters of gold and platinum, i.e., the skewness values, reveal that the negative effects in these markets are more dominant than the positive effects. Notably, the skewness value of CDS, i.e., 2.28, appears as the financial risk indicator of South Africa, and the size of the asymmetric effect in the exchange rates seems to be an important indicator, as a country-specific condition. Therefore, the interconnectedness of these variables provides valuable information as an important financial risk indicator considering the South African economy. From this point of view, the results allow the analysis of the possible country risk according to the price movements in the international markets, while the feedback effects between the indicators of this can be seen. In this respect, the transition effect of the said negative effects from international markets to the country's financial risk indicator is calculated via CDS. The channel of transmission of this effect on the country's economy is through the exchange rates.


#### **Table 1.**

*Descriptive statistics of dataset for South Africa – (2010–2022).*

*Asymmetric TVP-VAR Connectedness Approach: The Case of South Africa DOI: http://dx.doi.org/10.5772/intechopen.107248*


#### **Table 2.**

*Unit-root test results of South African daily return series (2010–2022).*


*\*\*\*Significant at 5% chi-square distribution.*

*\*\*Significant at 1% chi-square distribution.*

#### **Table 3.**

*ARCH effects on return series.*

It is seen that the kurtosis values of all the variables are greater than three, that there is a significant risk in these markets and that the possible risk may have a high impact on the country's economy through the financial risk indicator channel. The presence of asymmetric effects and kurtosis values higher than three indicate that there may be a time-varying parameter relationship between these variables. Based on this assumption, we proceed to the next step to apply TVP-VAR Model.

All the return series are stationary, based on the unit-root test results given in **Table 2**. Along with the Augmented Dickey-Fuller-ADF test [20], the Kwiatkowski-Phillips-Schmidt-Shin-KPSS test was also applied [21]. Thus, the test result, which may be due to the insensitivity to the possible degree of integration being less than one, was verified with the KPSS test. Therefore, the data are considered stationary as I (0), since the test results support the results of the ADF test with a constant.

The ARCH test and Ljung Box Test, applied up to 20 lags to determine the presence of fat tails in the return series. Hence, as shown in **Table 3**, the ARCH effect is statistically significant and shows the presence of time-varying volatility<sup>2</sup> and Ljung

<sup>2</sup> The ARCH test is a major instrument for determining the "conditional variance" based on the time dynamics of the second moments of the data. Hence, we could interpret a statistically significant ARCH test result as a representative of the time-varying volatility condition for the data. In addition, we could say that we have a volatility clustering with the existence of a fat-tailed distribution as a sign of mean reversion tendency in the return series. On the other hand, it should be noted that the existence of a significant excess kurtosis (i.e., excess kurtosis >0) is not representative of time-varying volatility. Still, the inverse of this hypothesis is true.

#### **Figure 1.**

*Daily return series of gold, platinum, CDS, and RD (2010–2022).*

Box test is used for analysing whether the specification is relevant to get "autocorrelation" and to capture the "time-varying volatility" in the return series.

After having the unit root test and ARCH test results, a daily percentage change of the dataset is prepared to determine absolute negative and positive return series. The dispersions of the daily change in return series are illustrated in **Figure 1**. In this respect, all the return series appear significantly skewed, and the JB test statistics support that these series are not normally distributed [22]. These initial descriptive findings of our return series support our method to apply TVP-VAR modelling with "time-varying variance-covariances".
