## 4 Results  
In this section, we examine the predictive performance of the proposed confidence indicators in tracking economic activity in a nowcasting exercise. We used the last 17 quarters (2016.Q1 to 2020.Q1) as the out-of-sample period, and the root mean square forecasting error (RMSFE) as a measure of forecast accuracy. First, we compared the forecasts obtained with the evolved confidence indicators (Exp.IND and Exp.CONS) to those obtained with the corresponding confidence indicators constructed by the EC, previously re-scaled (Cof.IND and Cof.CONS). Because the output of the evolved indicators is directly expressed as expected annual GDP growth rates, we re-scaled the indicators presented in expressions (1) and (2), by regressing the GDP growth of each country on the components of the indicators during the in-sample period (2003.Q1 to 2015.Q4). In Figure 2, we graphically compare the evolution of the two GP-generated indicators to that of the GDP of each country. The last seventeen quarters of the sample are used as the out-of-sample period, in which we use the results of the surveys to estimate the period-to-period economic growth prior to the publication of official data. The EC publishes one composite indicator for the industry (_ICI_) and another one for households (_CCI_). Both indicators are obtained from the arithmetic mean of the balance series of a subset of questions. \[ICI_{t}=\frac{B2_{t}+B5_{t}-B4_{t}}{3} \tag{1}\]  
\[CCI_{t}=\frac{C2_{t}+C4_{t}+C11_{t}-C7_{t}}{4} \tag{2}\]  
The in-sample OLS estimates of the weights of each of the components of the confidence indicators published by the EC allow us to compute the scaled confidence indicators that are directly comparable with the evolved confidence indicators. This experiment can be regarded as a nowcasting exercise, given that for each period, the indicators provide an estimation of the current state of the economy before the official figures are released, making exclusive use of the latest survey data published by the EC. For further discussion of nowcasting, one can refer to [47,48], and the references cited therein. To test whether the reduction in accuracy is statistically significant, we computed the Harvey-Leybourne-Newbold (HLN) statistic [49], which is a modification for small samples of the Diebold-Mariano (DM) statistic [50]. Under the null hypothesis that there is no significant difference in precision, the statistic follows a Student's-\(t\) distribution. A negative sign indicates that the second model has larger forecast errors. The results are presented in Table 3.  
In Table 3, we can observe that in most countries, the lowest forecast errors are obtained using the evolved indicators contained in Tables 1 and 2, although the difference in accuracy is not always statistically significant. For the industry, we obtained significantly lower forecast errors for Bulgaria, Germany, the Netherlands, Poland and Sweden; however, for consumers, we obtained these errors in Belgium, Germany, Hungary, Italy, the Netherlands, Poland, Sweden, and the UK. We also observed notable differences in accuracy between firms and households in countries such as the Czech Republic and Greece. The EC weights the confidence indicators obtained for each of the surveys to calculate an aggregate index, the economic sentiment indicator (_ESI_). In [51,52], the authors showed that letting the aggregation weights of each component of the ESI be data-driven improves its forecasting performance. Hence, we next combined the estimations obtained from the evolved industry and consumer confidence indicators by means of constrained optimization. We used a generalized reduced gradient non-linear algorithm to minimize the summation of squared forecast errors and imposed the following two restrictions: (a) the sum of both weights must equal one, and (b) the weights must be equal to or larger than zero. The resulting weights are annexed in Appendix B (Table A2).