Chapter 5: Results and Discussion
5.3 Preliminary Tests
This section presents the results of preliminary tests in terms of stationarity, normality, volatility clustering, autocorrelation, ARCH effect to determine whether GARCH models are applicable to both data set (Yadav 2020).
53 5.3.1 Stationarity Test
According to the ADF unit root stationarity test results in table 3, it is evident that the weekly prices for the GB and the CB are not stationary as the p-value is greater than 10%. In this case, it is said that the data has a unit root. On the other hand, using equation (8), the returns of GB and CB are stationary as the p-value is less than 1% significance level. The return data is now described as a one that does not have a unit root and is stationary at order 1. In fact, this is consistent with numerous studies where their raw data was not stationary and then became stationary at first order (see e.g. Park, Park & Ryu (2020); Reboredo (2018); Hassan et al. (2017); Lahrech & Sylwester (2013); Pham 2016; Sclip et al. (2016); Liow et al. 2009, and many others). In figure 7, we can also see that the returns of GB (Panel A) and CB (Panel B) have a mean that is reverting back. Brooks (2014) states that stationarity is a key feature of a time series data set that must be examined. This is due to multiple reasons. Firstly, stationarity can significantly affect the data’s behavior and properties in terms of shocks’
persistence. Secondly, relying on non-stationary data can lead to bogus regressions. Finally, if a regression analysis is carried out using non-stationary data, then the results will be inaccurate and result in limitations.
54
Table 3
Unit Root test of weekly prices and returns for GB and CB
Bloomberg Barclays MSCI Global Green Bond Index (GB)
Bloomberg Barclays Global Aggregate Total Return Index (CB)
Augmented Dickey-Fuller (ADF) test
Prices
ADF statistics 0.393231 0.603894
p-value 0.9827 0.9899
Returns
ADF statistics -14.7892 -15.2338
p-value <0.00001*** <0.00007***
Note: The *** beside p-values figures indicate that they are statistically signification at 1%.
5.3.2 Volatility Clustering Test
Figure 7, presents the time series plot for the GB and CB returns and squared returns. All graphs for both indices clearly show volatility clustering. For example, we can see that the low volatility in 2019 was followed by low volatility and the high volatility that started in the beginning of 2020 continued to be high up to April 2020. Moreover, Panel A and B are following a white noise process which means that both variables are independent, distributed with a mean equal to zero, have an identical variance, and there is no correlation with other variables in the series itself. Moreover, this conclusion is supported by the numerical test of ARCH-LM test in table 4.
It is worth mentioning that, in March 2020, both bonds indices experienced the highest level of volatility since the past six years.
The findings of this paper is also consistent with many studies (see e.g. Park, Park & Ryu (2020); Papaioannou et al. (2017); Pham (2016), Sclip et al. (2016); Lahrech & Sylwester
55
(2013) and many others). In fact, Cont (2007) stated that the returns of financial time series data often demonstrate volatility clustering feature.
Figure 7. Time series plot of GB and CB regular and squared weekly returns
Panel A: GB Weekly Returns Panel B: CB Weekly Returns
Panel C: GB Squared Weekly Returns Panel D: CB Squared Weekly Returns
Note: The sample period 17/10/2014 to 18/09/2020. Panel A and B present the weekly returns of GB and CB while Panel C and D present the weekly squared returns.
56 Table 4
ARCH Effect for weekly returns
Bloomberg Barclays MSCI Global Green Bond Index (GB)
Bloomberg Barclays Global Aggregate Total Return Index (CB) Test for autocorrelation
LM for returns (14) 145.353 137.253
p-value <0.00006*** <0.00002***
Note: The lag order 14 was used as per Gretl’s suggestion. The ***, **, and * beside p- values figures under the Lagrangean Multiplier test indicates that they are statistically significant at 1%, 5%, and 10%.
5.3.3 Autocorrelation Test
The Ljung-Box test for autocorrelation results of the returns and squared returns are shown in Table 5. The p-value of the Ljung-Box test for the squared returns is less than 1%
significance level which allows us to reject the null hypothesis of no autocorrelation in the green and conventional bonds’ indices. In other words, the results provide evidence that both, the green and its non-green counterpart, experience autocorrelation at a 1% significance level. While the p-values for returns and squared returns for both bonds are statistically significant, the squared returns experienced a higher level of significance. This indicates that the returns tend to continue in increasing in terms of autocorrelation overtime showing persistency. The high level of significance of the returns and squared returns, also numerically supports the fact that both indices experience volatility clustering as discussed in the previous section. This conclusion was also found in many studies, however, there was a variation in the number of lags selected (see e.g. Park, Park & Ryu (2020); Reboredo (2018); Hassan et al. (2017); Lahrech & Sylwester (2013); Pham 2016; Sclip et al. (2016);
and many others).
57 Table 5
Autocorrelation for weekly returns and squared returns
Bloomberg Barclays MSCI Global Green
Bond Index (GB)
Bloomberg Barclays Global Aggregate Total Return Index (CB) Test for autocorrelation
Ljung-Box for returns (14) 23.6132 27.3468
p-value 0.051* 0.0173**
Ljung-Box for squared
returns (14) 176.365 167.853
p-value <0.00003*** <0.00001***
Note: The lag order 14 was used as per Gretl’s suggestion. The ***, **, and * beside p- values figures under the Ljung-Box test indicates that they are statistically significant at 1%, 5%, and 10%.
In conclusion, since the weekly returns of the Bloomberg Barclays MSCI Global Green Bond Index (GB) and Bloomberg Barclays Global Aggregate Total Return Index (CB) experience stationarity at the first order, volatility clustering, ARCH effect, and autocorrelation we can conclude that a GARCH model can be applied to model the data for both variables (Park, Park, & Ryu 2020).