4. EMPIRICAL RESULTS
4.3 D OES SEARCH VOLUME HELP TO IMPROVE VOLATILITY FORECASTS ?
4.3.1 In-sample forecast evaluation
-SVt-1 are all positive indicate that search volume positively influences volatility, which is in line with Foucault, Sraer and Thesmar (2011).
On the other hand, for almost all of those countries which search volume do not Granger cause volatility, search volume neither does not add information for modeling volatility, like Hong Kong. To South Africa and Croatia, we could say search volume has additional information about future volatilities since lagged search volume enter insignificantly in only one model for each country, while Granger causality tests shows can’t.
The phenomenon, that search volume has statistically significant information about future volatility, becomes more unobvious as the developed level of markets is worse. In frontier markets, the p-values are larger than those in developed markets and search volume contains significance about future volatility only in AR(1) model.
4.3 Does search volume help to improve volatility forecasts?
4.3.1 In-sample forecast evaluation
Table 11, Table 12 and Table 13 contain the in-sample forecasts evaluation of one-step ahead forecasts of realized volatility. The models are the univariate models (Uni.) and the respective augmented models (Aug.) including lagged search volume.
Table 11, Table 12 and Table 13 display the comparison results of AR(1) vs.
AR(1)+SV, HAR vs. HAR+SV and EGARCH vs. EGARCH+SV respectively.
Forecasting ability are measured by the mean squared error (MSE, × 105), the quasi-likelihood loss function (QL, ×102) and the R2 (%) of the regression. P-value is result of test which testing if the differences between loss functions of the univariate models and ones of the respective augmented models are statically significant. The model is better when MSE decreases, QL decreases and R2 increases.
We discuss the results of the USA indices first. From Panel A of each table, only
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Table 11
In- sample forecast evaluation of AR(1) and AR(1)+SV models
This table compares the in-sample forecasts of AR(1) and AR(1)+SV model. Uni. means the univariate model, AR(1) here. Aug. means the augmented model with lagged search volume, AR(1)+SV here. Performance measures are the mean squared error (MSE, × 105), the quasi-likelihood loss function (QL, ×102) and the R2 (%) of the regression. P-value is result of test which testing if the differences between loss functions of the univariate models and ones of the respective augmented models are statically significant. The model is better as MSE decreases, QL decreases and R2 increases. For the name of countries in italic type mean that the data is at weekly frequency, ex: Austria. Panel A, B and C provide the list of developed, emerging and frontier markets respectively.
Panel A: Developed Markets
MSE (×105) QL (×102) R2 (%) Country Uni. Aug. p-value Uni. Aug. p-value Uni. Aug.
Australia 2.05 2.00 (0.008) 11.80 11.59 (0.030) 32.32 34.93
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Table 11- continued Panel B: Emerging Markets
MSE (×105) QL (×102) R2 (%) Country Uni. Aug. p-value Uni. Aug. p-value Uni. Aug.
China 12.90 12.93 (0.999) 5.45 5.25 (0.129) 41.93 41.80 India 4.60 4.36 (0.024) 10.71 10.46 (0.081) 35.47 38.75 Malaysia 0.82 0.82 (0.498) 12.61 12.63 (0.891) 19.48 19.89 Mexico 3.52 3.52 (0.833) 12.02 11.98 (0.383) 30.11 30.15 Peru 23.96 23.81 (0.240) 14.06 14.10 (0.915) 27.09 28.01 South Africa 5.08 5.11 (0.430) 3.82 3.84 (0.933) 67.08 66.97 Thailand 2.56 2.57 (0.950) 10.20 10.21 (0.670) 33.85 33.82 Turkey 4.02 3.86 (0.001) 8.57 8.35 (0.011) 20.90 24.11
Panel C: Frontier Markets
MSE (×105) QL (×102) R2 (%) Country Uni. Aug. p-value Uni. Aug. p-value Uni. Aug.
Croatia 18.09 18.33 (0.499) 11.06 11.03 (0.758) 42.91 42.59 Pakistan 1.50 1.48 (0.380) 20.66 20.39 (0.285) 18.91 19.20 Romania 3.92 3.75 (0.109) 10.97 10.77 (0.323) 36.89 40.65
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Table 12
In- sample forecast evaluation of HAR and HAR+SV models
This table compares the in-sample forecasts of HAR and HAR+SV model. Uni. means the univariate model, HAR here. Aug. means the augmented model with lagged search volume, HAR+SV here. Performance measures are the mean squared error (MSE, × 105), the quasi-likelihood loss function (QL, ×102) and the R2 (%) of the regression. P-value is result of test which testing if the differences between loss functions of the univariate models and ones of the respective augmented models are statically significant. The model is better as MSE decreases, QL decreases and R2 increases. For the name of countries in italic type mean that the data is at weekly frequency, ex: Austria. Panel A, B and C provide the list of developed, emerging and frontier markets respectively.
Panel A: Developed Markets
MSE (×105) QL (×102) R2 (%) Country Uni. Aug. p-value Uni. Aug. p-value Uni. Aug.
Australia 1.56 1.52 (0.002) 8.85 8.76 (0.054) 47.64 48.94
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Table 12- continued Panel B: Emerging Markets
MSE (×105) QL (×102) R2 (%) Country Uni. Aug. p-value Uni. Aug. p-value Uni. Aug.
China 11.89 11.70 (0.462) 4.83 4.71 (0.176) 46.88 47.76 India 3.70 3.63 (0.066) 8.36 8.32 (0.328) 45.40 46.31 Malaysia 0.83 0.83 (0.583) 12.26 12.20 (0.554) 21.25 21.76
Mexico 2.93 2.91 (0.190) 10.12 10.06 (0.228) 41.85 42.19 Peru 22.21 22.22 (0.607) 12.65 12.65 (0.704) 31.96 31.92 South Africa 5.05 4.89 (0.197) 3.65 3.56 (0.231) 68.21 69.19
Thailand 2.37 2.37 (0.096) 9.09 9.09 (0.620) 38.51 38.57 Turkey 3.79 3.69 (0.004) 7.99 7.87 (0.044) 25.73 27.66
Panel C: Frontier Markets
MSE (×105) QL (×102) R2 (%) Country Uni. Aug. p-value Uni. Aug. p-value Uni. Aug.
Croatia 15.59 15.48 (0.267) 9.71 9.68 (0.690) 51.11 51.48 Pakistan 1.47 1.46 (0.533) 21.17 20.93 (0.265) 20.46 20.70 Romania 4.20 3.71 (0.086) 11.08 10.44 (0.096) 34.62 41.74
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Table 13
In- sample forecast evaluation of EGARCH and EGARCH+SV models This table compares the in-sample forecasts of EGARCH and EGARCH+SV model. Uni.
means the univariate model, EGARCH here. Aug. means the augmented model with lagged search volume, EGARCH+SV here. Performance measures are the mean squared error (MSE,
×105), the quasi-likelihood loss function (QL, ×102) and the R2 (%) of the regression. P-value is result of test which testing if the differences between loss functions of the univariate models and ones of the respective augmented models are statically significant. The model is better as MSE decreases, QL decreases and R2 increases. For the name of countries in italic type mean that the data is at weekly frequency, ex: Austria. Panel A, B and C provide the list of developed, emerging and frontier markets respectively.
Panel A: Developed Markets
MSE (×105) QL (×102) R2 (%) Country Uni. Aug. p-value Uni. Aug. p-value Uni. Aug.
Australia 2.86 2.82 (0.214) 14.63 14.31 (0.000) 49.95 51.41
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Table 13- continued Panel B: Emerging Markets
MSE (×105) QL (×102) R2 (%) Country Uni. Aug. p-value Uni. Aug. p-value Uni. Aug.
China 20.35 19.33 (0.006) 7.74 7.51 (0.005) 38.58 41.85 Country Uni. Aug. p-value Uni. Aug. p-value Uni. Aug.
Croatia 91.72 77.53 (0.032) 17.17 17.10 (0.833) 53.06 53.48 Pakistan 2.22 2.33 (0.248) 20.57 21.36 (0.048) 13.42 8.06 Romania 4.14 4.08 (0.326) 13.24 13.02 (0.009) 38.98 40.09
DJIA’s search volume can significantly improve the volatility forecasting in all three models with 95% confidence level. Search volume of S&P 500 can help to predict volatility both in HAR and EGARCH models. For NASDAQ, search volume is not helpful in forecasting future volatility except the HAR model. These results are consistent with the results of previous works, regression models and Granger causality tests. Just like what we do in previous section, we consider DJIA as the representative index of USA as we compare results among countries.
Throughout the results of comparison of in-sample volatility forecasts, we find in general, search volume can improve volatility forecasting since the loss functions, MSE and QL, reduce and R2 increases in most countries. This conclusion is consistent with but not as statically significant as the results of regression models and Granger causality tests. Only half of countries in developed markets and two out of 8 countries
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in emerging countries show that search volume can significantly help to predict future volatilities. The valuation results of all three frontier countries are almost insignificant.
That indicates that as the developed level of markets is worse, the phenomenon that search volume can help to forecast future volatility occur less.