Forecasting performance

The forecasting performance metrics are reported in tables 4.27 and 4.28 below.

Table 4.27: GARCH forecasting performance

GARCH GJR-GARCH EGARCH

RMSE MAE RMSE MAE RMSE MAE

Can 0.007730 0.005644* 0.007730 0.005670 0.007725* 0.005660 Aus 0.008916* 0.006738* 0.008920 0.006750 0.008920 0.006750 SA 0.009836* 0.007294* 0.009840 0.007310 0.009870 0.007370

Source: Thomson Reuters Datastream and Eviews

Table 4.28: GARCH forecasting performance (including trading volume)

GARCH GJR-GARCH EGARCH

RMSE MAE RMSE MAE RMSE MAE

Can 0.007730 0.005640 0.007730 0.005640 0.007725* 0.005649*

Aus 0.008940 0.006730 0.008916* 0.006740 0.008920 0.006733*

SA 0.009840 0.007293* 0.009835* 0.007310 0.009840 0.007310 Source: Thomson Reuters Datastream and Eviews

The forecast performance metrics show that the symmetric GARCH model is the most reliable when trading volume is not included as a variance re-gressor. Moreover, when trading volume is included as a variance regressor, the asymmetric models (GJR-GARCH and EGARCH models) outperform the symmetric GARCH model in most cases. Finally, when the RMSE and MAE of the models which include trading volume are compared to the standard GARCH models, the models which include trading volume are more reliable.

This suggests that new information (trading volume) does improve forward-looking estimates of volatility. There is not a significant difference in terms of the effect of new information in volatility modelling when developed and emerging markets are considered. This implies that when forecasting volatil-ity using univariate GARCH models, investors should include trading volume (new information) as a variance regressor, this improves the forecasting perfor-mance of GARCH models regardless of whether it is a developed or emerging market.

Chapter 5 Conclusion

In this dissertation, the effect and significance of new information on different markets (developed versus emerging) was determined and interpreted. Firstly, it was examined how the different markets react if shocks occur; secondly, it was determined how big the difference was between the emerging and developed markets; and lastly, it was considered how long it would take the different markets to absorb the shocks. Therefore, if a shock was introduced as new information, how did the market react? The markets would eventually reach a new equilibrium, but how long would it take to reach the new equilibrium in the different markets? However, this does not give an indication of the informational efficiency of volatility.

The effect of new information on volatility was also tested in a GARCH framework. A similar approach to Chen et al. (2001) was used in this dis-sertation. GARCH models which included trading volume as an explanatory variable, which is a proxy of information flow, were used to forecast volatility.

This gave an indication of whether trading volume (flow of information) is significant when forecasting volatility.

A similar approach to Sreedharan (2004) and Oberholzer and Venter (2015a), which looked at different market prices (high, low, open and close) of differ-ent equity exchanges, was used in a VAR framework to illustrate how markets would react to shocks in market prices. This then illustrated how efficiently the market captures new information. However, new information was not included in the studies by Oberholzer and Venter (2015a) and Sreedharan (2004). In this study, a vector autoregressive model (VAR), a VECM and impulse re-sponses were used to examine how markets react to shocks in different market prices, and whether the prices move rapidly to equilibrium or take a longer time to reach a new equilibrium. Trading volume was used as a proxy for new information; which is consistent with the work by Chen et al. (2001).

A similar approach to Chen et al. (2001) was also applied in this dis-sertation to determine the significance of new information when modelling and forecasting volatility. Chen et al. (2001) also made use of GARCH and EGARCH models to determine what effect trading volume will have on volatil-ity. The EGARCH(1,1) model was used to determine asset return volatilvolatil-ity.

The results showed that the representation of the returns in the data of the share indices is reflected properly. In addition, trading volume also gave some information about the share indices of the returns processes and that after including simultaneous and lagged volume effects (which were used as proxies for the flow of information), the persistence in volatility was still present.

However, in this dissertation, the work by Chen et al. (2001) was extended by making use of GARCH, EGARCH and GJR-GARCH models. These models were applied to determine whether the forecasting ability of the model would improve when trading volume was included. The volatility modelling section in this dissertation was based on similar studies by Chen et al. (2001), and Kalu and Chinwe (2014). The AIC and SIC of the GARCH, GJR-GARCH and EGARCH models were compared to determine the best fitting univari-ate GARCH family model in this dissertation. The information criterion was also used to compare models which included trading volume to the standard GARCH model specification. Finally, forecast performance metrics of the dif-ferent models were used to determine the most reliable forecasting model.

Four of the CARBS (Canada, Australia, Russia, Brazil and South Africa) countries were used in this dissertation, namely: Canada, Australia, Russia and South Africa. The reason for using this group of countries was because it represented both developed and emerging markets. The CARBS countries are known as the main exporting countries of commodities, which lead the global commodity market. Only four of the five CARBS countries were used to determine what effect new information and shocks would have on the different markets (emerging and developed) and whether the impact of new information was significant when explaining the variation in different market prices. This was formally tested in Chapter Four in the study by using a VECM.

In Chapter Four, the preliminary data analysis for equity indices as well as trading volume was discussed. The different models that were used in this dissertation were also discussed, and the empirical results were interpreted. A VAR model was estimated first which examined the interrelationship between market prices. Secondly, a VECM was used to determine what the long- and short-run dynamics were of the model. Before a VECM could be used, the number of cointegrating equations needed to be determined first; this was be done by making use of the Johansen cointegration method. Volatility models,

such as GARCH, GJR-GARCH and EGARCH were also used to determine the significance of new information.

A VAR model without trading volume was constructed first, and the op-timal lag length was determined. In this study, the Hannan-Quinn method was used to choose the optimal lag length, which will be used in the VAR model. The optimal lag length for Canada and South Africa was two lags while for Australia and Russia the optimal lag length was one lag. Next, a stability test was done to determine whether the VAR model was stable when the above-mentioned lags were included. This was done by looking at the AR roots of the VAR for each country. The results obtained from the stability tests showed that all the roots of all the countries lied within the unit circle.

This suggested that each VAR model was stable, when estimated using the optimal lag length.

The number of cointegrating equations was determined by using the Jo-hansen cointegration method. The trace test and maximum eigenvalue statis-tics indicated the maximum number of cointegrating equations that had to be included in the VECM; therefore, three cointegrating equations were included for each country. The results obtained were in line with the results obtained by Sreedharan (2004) and Oberholzer and Venter (2015a). The coefficient of the opening price was positive and close to one in each case, which is consis-tent with futures spot parity. The time period between the closing price and opening price (one trading day) was short; therefore, the coefficients were close to one.

Cointegrating equation one for SA was considered and was clear that the highest, lowest and opening prices were all significant but of the incorrect sign, therefore, they were non-responsive and will take a long time to move back to equilibrium. However, when cointegrating equation three for SA was consid-ered, it was evident that both the highest and lowest prices were significant and of the correct sign (negative). This indicated that it will move back to equilibrium. Furthermore, the highest price was closer to zero, which meant that it will move to equilibrium at a slower pace than the lowest price. The lowest price was closer to -1 and would move back to equilibrium rapidly when there was a deviation from the long run equilibrium.

When the impulse response functions for each country were considered it could be seen that in most cases, the variables responded by first increasing then decreasing slowly to reach a new equilibrium. However, in some cases, a shock did not lead to a significant impact. One such case was the response of the logged intra-day lowest price of Australia to a shock in the intra-day opening price of Australia. It was clear that the shock in the intra-day opening

price of Australia did not have a significant impact on the intra-day low price.

However, when the response of the logged high price of SA was considered, it was evident that a one standard deviation shock to the closing price caused the logged high price to rapidly increase and reach a peak and then slowly decrease to reach a new equilibrium.

When trading volume was included as an exogenous variable in the model, similar results were obtained for the optimal lag length, cointegration tests and error correction coefficients. When the adjusted R² values were considered, it was evident that the explanatory power of the model did improve slightly.

In the next section of Chapter Four, a similar approach to Chen et al.

(2001) and Kalu and Chinwe (2014) was used. Different univariate GARCH models were applied to the CARS countries to determine the best fitting model based on different information criteria. In addition, the forecasting perfor-mance of the models was compared to models which include trading volume.

The ARCH LM test indicated that ARCH effects were present for all the variables considered, except Russia. Therefore, Russia was excluded from the analysis that followed. According to Alexander (2008), if the θ parameter in the GARCH(1,1) model is relatively large (i.e greater than 0.1), then it implies that the market is sensitive to market shocks. This was the case for Canada.

Furthermore, the coefficient of the lagged volatility ϕ is a measure of volatility persistence (Alexander, 2008). This suggested that shocks to the Australian market would take a long time to die out.

According to Asteriou and Hall (2015), if the coefficient of the dummy variable (λ) is positive, it implies that bad news will lead to a greater rise in volatility when compared to good news; this is also known as the leverage effect.

The ϑ coefficient was positive and statistically significant at a one per cent level for all the countries when a GJR-GARCH model was considered. According to Brooks (2014), if ϑ in the EGARCH model is negative, and statistically significant, it, therefore, indicated signs of the leverage effect. This was the case for the three markets considered (at a one per cent level of significance).

According to Brooks (2014), information criteria can be used to determine the best fitting model. The best fitting model is the one which minimises the information criteria. In this case, the AIC and SIC indicated that the EGARCH model was the best fit.

When trading volume was included as a variance regressor, the estimated parameters showed that there was a statistically significant (at a one per cent level) positive relationship between the conditional volatility and trading

vol-ume. This was consistent with the findings by Kalu and Chenwe (2014) and Chen et al. (2001). Furthermore, when the information criteria of the mod-els which included trading volume were considered, the EGARCH model was the best fit. Finally, when the AIC and SIC of all the models (including and excluding trading volume) were compared, the AIC and SIC showed that the EGARCH model which included trading volume was the best fit.

The forecast performance metrics showed that the symmetric GARCH model was the most reliable when trading volume was not included as a vari-ance regressor. Moreover, when trading volume was included as a varivari-ance regressor, the asymmetric models (GJR-GARCH and EGARCH models) out-performed the symmetric GARCH model in most cases. Finally, when the RMSE and MAE of the models which included trading volume were compared to the standard GARCH models, the models which included trading volume were more reliable. This indicated that new information (trading volume) does improve forward-looking estimates of volatility.

A shortcoming of this study was that only four countries were used to com-pare developed and emerging markets. However, the focus was on commodity exporting countries. Therefore, an area for future research might involve a similar analysis based on greater variety equity indices. Furthermore, the spillover of shocks in the commodity markets to equity markets should also be considered.

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