br Building measures that are representative of

Building measures that are representative of the panel of inflation forecasts Aggregate measures such as the mean, median and standard deviation of the expectations panel surveyed by the Central Bank of Brazil, and others derived from these three, are reported daily at the central bank\'s website (https://www3.bcb.gov.br/expectativas/publico/en/serieestatisticas). The survey currently encompasses over 100 registered participants. The first core measure built for this inositol phosphatase study was the symmetric trimmed mean (Fig. 1 and Appendix A). Its computation involved ordering all projections according to their magnitude at each sampling day, and excluding those placed in the outer 10% ranges. The remaining 80% of the individual forecasts were used to calculate the mean. Second, we built an asymmetric median and mean core of inflation expectations. To this end, we carried out two asymmetry tests at each surveyed date: one based on Pearson\'s asymmetry coefficient and another based on the third moment of the sampling distribution. In both tests, distributions are classified as asymmetric when the absolute value of the resulting asymmetry coefficient is larger than 0.3. The results of this initial identification test of asymmetry in the expectations series are reported in Fig. 2. The direction of the asymmetry does not always coincide in both tests. In fact, there was contradiction in 40% of the sample. After determining whether the distribution of expectations at each survey date is symmetric or not according to each type of asymmetry test, we removed the outliers as follows: There is an important degree of arbitrariness in the construction of asymmetric core measures. First, the size of the trim (5%) in the distribution tails, regardless of the degree of asymmetry found, does not necessarily imply that the remaining distribution will be void of asymmetry. Second, the methodology requires computation of the sample mode, which also bears an important degree of arbitrariness. The resulting asymmetric core series are presented in Fig. 3 and in Appendix A. Finally, we built a series of modes for each survey date (Fig. 4 and Appendix A). The mode is more representative of a “consensus” measure than the median. However, its computation is not straightforward. To compute the mode, we first built distribution histograms of the forecasts at each survey date. Next, we identified the mean point of the interval with the highest concentration of forecasts. This calculation, however, is sensitive to the size of the bin chosen to slice the sample. The choice of the size of the bin for each survey date was arbitrary, and had the purpose of obtaining only one modal bin.
Comparing the alternative measures to the median and testing its predictive power We carried out statistical tests to investigate whether the alternative measures representative of inflation forecasts were statistically different from the median. These tests are inspired in the unbiasedness tests traditionally used in the literature (e.g., Marimon and Sunder, 1993; Zarnowitz, 1985; Keane and Runkle, 1990). The tests consist of assessing the joint null H0: c(1)=0 and c(2)=1 in the equation: Rejecting H0 implies skeletal muscle the alternative measure under evaluation is statistically different from the median. The results are reported in Tables A1 and A3 in Appendix A. Comparing the alternative measures with the realized value of consumer inflation (IPCA), we tested the null H0: c(1)=0 at the equationwhere the bias present in the alternative measure corresponds to the difference between the headline consumer inflation and the considered alternative measure of inflation forecasts. Rejecting H0 implies that there is evidence of bias in the forecasts. In addition, we used a Newey–West covariance matrix with MA(12) errors, as suggested by Keane and Runkle (1990), since the forecast errors for a 12-month-ahead horizon accumulate along these months in face of unexpected shocks.