Search Volumes 11
2.4 Forecast Evaluation
2.4.1 In-Sample Fit
For the return models, evidence for model significance is mixed. The results are summarized in the upper panel of Table 2.4. For all cryptocoins but Bitcoin, EOS-Token, and Litecoin, the null hypothesis that the parameter estimates are jointly zero cannot be rejected. Hence, the specified models are not able to explain the variation in the return series of these cryptocurrencies significantly better than a simple time series average. Considering that we have conducted 60 tests, we would consider the statistical significance of the five models for Bitcoin, EOS-Token, and Litecoin to be pure coincidence.
For the volatility models, the picture is exactly the opposite as documented by the lower panel of Table 2.4. We can reject the null hypothesis that the respective model specification has no explanatory power on a 1% significance level for all cryptocurrencies for all models.
Concerning Granger causality, Table 2.5 provides an overview of the results. For the return models, the results of the test for no Granger causality are in line with the model specification tests. The predictive ability of Google SVIs is in general not given. The only two cryptocurrencies where the SVIs help to predict returns are EOSToken and Ripple.
However, significance is still rather weak and might also be attributed to chance given the number of tests conducted.
The finding of no Granger causality for the vast majority of the coins comes at no surprise.
In an efficient market, we would expect that asset price movements are not predictable in the short run. For the majority of cryptocoins, it seems, the market is aware of the demand driven nature of the coins. Available information is already largely incorporated in prices.
Concerning the volatility models, the picture is also mixed. For Gnosis and EOS-Token, we cannot reject the hypothesis of no Granger-causality of Google search volume on volatility on any conventional significance level. However, for all other coins at least for one of the models including Google’s SVI we find that search volume Granger causes volatility.
From the comparison of the model specification test in Table 2.4 and the Granger-causality test in Table 2.5 we conclude that volatility is rather persistent and can be explained well exploiting its autoregressive dynamics. We also find that for the majority of the cryptocurrencies considered, Google SVIs have non-negligible predictive power for development of future volatility.
Whether public or coin specific interest is more important in predicting volatility can also be inferred from the two tables. For Bitcoin, we can reject the null hypothesis of no
Table 2.4: Model Significance
The table summarizes the results of Wald tests for the joint significance of all variables for the various model specifications and cryptocurrencies. * (**,***) denotes statistical significance on a 10% (5% and 1%, respectively) significance level.
Returns
Model 1 Model 2 Model 3 Model 4 Model 5 BitcoinCash
Bitcoin * – –
Dashcoin
EOSToken ** *
EthereumClassic Ethereum
Gnosis
Litecoin * **
AugurCoin Monero Ripple zCash
Volatility
Model 1 Model 2 Model 3 Model 4 Model 5
BitcoinCash *** *** *** *** ***
Bitcoin *** *** – *** –
Dashcoin *** *** *** *** ***
EOSToken *** *** *** *** ***
EthereumClassic *** *** *** *** ***
Ethereum *** *** *** *** ***
Gnosis *** *** *** *** ***
Litecoin *** *** *** *** ***
AugurCoin *** *** *** *** ***
Monero *** *** *** *** ***
Ripple *** *** *** *** ***
zCash *** *** *** *** ***
Table 2.5: Granger-Causality
The table summarizes the results from the results of the Granger-causality test for the various model specifications. The null hypothesis for each model is that the Google SVI variables do not Granger cause returns or volatility, respectively. * (**,***) denotes statistical significance on a 10% (5% and 1%, respectively) significance level.
Returns
Model 1 Model 2 Model 3 Model 4 Model 5 BitcoinCash
Bitcoin – –
Dashcoin
EOSToken * ** *
EthereumClassic
Ethereum *
Gnosis Litecoin AugurCoin Monero
Ripple * ** ** *
zCash
Volatility
Model 1 Model 2 Model 3 Model 4 Model 5
BitcoinCash * *
Bitcoin *** – *** –
Dashcoin *** ** *
EOSToken
EthereumClassic ** ** *** ** ***
Ethereum *** ** ** *** ***
Gnosis
Litecoin *** *** *** *** ***
AugurCoin * ** **
Monero *** *
Ripple *** ** ** *** ***
zCash *
Granger causality on a 1% significance level. Hence, the volatility of Bitcoin is clearly driven by the coin specific interest in Bitcoin. The volatility of BitcoinCash, Dashcoin, and Monero feed off the general attention in cryptocurrencies (Model 2). The volatility of zCash is driven partially by the attention to the cryptocurrency flagship Bitcoin (Model 3).
For all other coins, a mix of coin-specific and general interest in cryptocurrencies precedes volatility (Model 4 and 5).
For Bitcoin, Ethereum Classic, Ethereum, Litecoin, AugurCoin, and Ripple, the searches for these cryptocurrencies Granger cause their own volatility. For the remaining coins, only the SVIs which capture general interest, Granger cause their volatility. As the literature associates Google queries with the trading of individual investors (see for example Dimpfl and Jank 2016) who add to overall volatility (e.g. Foucault, Sraer and Thesmar 2011), we may conclude that trading of Bitcoin, Ethereum Classic, Ethereum, Litecoin, AugurCoin and Ripple is attractive due to reasons rooted in the nature of these coins themselves as opposed to a general interest in cryptocurrencies documented for the other cryptocurrencies.
Interestingly, those coins are also the most liquid ones (with the exception of AugurCoin).
Turning to the fit of the Mincer-Zarnowitz regression and the RM SE for the fitted values of returns, we find that the in-sample fit is very low throughout the panel. Table 2.6 presents the detailed results. For the highly volatile return series of cryptocoins this is an expected result. When forecasting returns within the framework of traditional factor models, the R2M Z is usually low (see for example Cochrane 2008). Even though we find that Model 5 produces a significantly lower RM SE as well as a higher R2M Z (compared to the benchmark Model 0), we conclude that the gains in forecasting are economically insignificant. Only for zCash the reduction in RM SE is sizeable; when SVIs are included in the model, the RM SE is almost divided in half.
For Ethereum, the RM SE is reduced by roughly 20% when including all three SVIs for the coin-name, the search-term cryptocurrency and the search-term Bitcoin which is a non-negligible reduction from an economic point of view. For all other coins the reduction of the RM SE is often limited to a few basis points, for example in the case of Bitcoin.
While the RM SE is always reduced when using Models 1 to 5 instead of Model 0, the forecast error is still huge. It ranges from 0.0426 to 0.15. By Chebyshev’s inequality, in the case of Bitcoin which has the lowest RM SE of 4.26%, this means that in up to 50% of all forecasts, the absolute value of the forecast error is larger than 6%.
For the volatility models, the evaluation measures are presented in Table 2.7. First, for Gnosis the RM SE cannot be reduced at all when any of the SVI variables are added to model 0. For EOS-Token and zCash, the RM SE is reduced, albeit the reduction not being statistically significant. The addition of SVIs for the coin-names improves the RM SE significantly for Bitcoin, Dashcoin, Ethereum Classic, Ethereum, Litecoin, AugurCoin, and Ripple. With the exception of Dashcoin, the latter subsample is the one for which
Table2.6:In-SampleFitVARModelforReturns Thetableliststherootmean-squarederror(RMSE)multipliedby100ofthein-samplepredictionsofthemodelsaswellastheR2ofaMincer-Zarnowitzregression MincerandZarnowitz(1969)inpercentages.Usingtheforecastevaluationtestof?fornestedmodels,theRMSEofModels1-5canbetestedwhetheronwhether theyresultinsmallerRMSEthantheoneofModel0,ourbenchmarkmodel.OnestarindicatesthatthenullhypothesisthattheRMSEofourbenchmarkmodel issmallercanberejectedona10%significancelevel,twostarssignifyrejectiononthe5%significancelevel.FortheRMSEandtheQL,thesmallestvalue,for eachcryptocoin,acrossthemodelsistypesetinbold.FortheR2 MZ,thehighestvalueisreportedboldfaced. Model0Model1Model2Model3Model4Model5 RMSER2 MZRMSER2 MZRMSER2 MZRMSER2 MZRMSER2 MZRMSER2 MZ BitcoinCash8.961.668.892.148.771.418.771.478.892.198.892.24 Bitcoin4.300.004.27**0.904.26**1.56––4.26**1.44–– Dashcoin6.770.006.74**1.496.74**1.216.73**1.296.73**1.446.72**1.62 EOSToken15.240.0015.11**0.6715.03**1.7815.00*1.2615.03**1.7815.03**1.78 EthereumClassic7.300.007.27**0.737.27**1.007.26**1.237.26**1.007.25**1.36 Ethereum8.050.006.90**1.026.79**1.986.93**0.366.90**1.286.90**1.09 Gnosis6.600.006.54**1.406.54**1.396.54**1.286.58*0.276.57*0.40 Litecoin7.170.006.99**1.676.99**1.717.01**0.947.09**1.087.07**1.66 AugurCoin8.600.558.560.418.570.238.531.198.560.528.51*1.66 Monero7.060.006.98**1.206.98**1.226.96**1.796.97**1.276.95**1.88 Ripple8.210.008.08**3.528.09**3.288.14**2.038.05**4.028.03**4.48 zCash14.4519.448.36**9.778.37**9.568.39**9.108.34**10.208.33**10.53
we also document Granger causality (cp. Table 2.5). With the exception of Litecoin, the addition of general interest SVIs can further reduce theRM SE and improve the model fit.
For Monero, the best fitting model is Model 2 which contains the SVI for the search-term cryptocurrency, but not the SVI for its name. Lastly, for Bitcoin cash, Model 4 (which includes search-terms for the coin’s name and cryptocurrency) is selected unanimously.
In general, the comparison of the in-sample fit across models is only clear for a few coins.
In summary, according to the in-sample results, the search volume of yesterday (for one term or another) helps to predict today’s volatility for the majority of coins, but is not a reliable predictor of today’s return.