Statistical Comparison of Forecasts Made at Different Frequencies
提出一种两样本t型检验，用于比较不同频率下对同一经济变量的预测，通过块平均方差估计解决混合频率数据的方差计算问题，模拟显示小样本下优于传统方法。
Current forecast evaluation tests can only assess forecasts generated at the same frequency. However, in real-world scenarios, predictions for the same economic variable may be made at different frequencies. The existing literature lacks statistical tests for evaluating such forecasts. This paper introduces a new evaluation test for comparing these forecasts. We propose a two-sample t-type test designed to test the equality of means between two potentially correlated time series that are sampled at different frequencies. No current estimator can compute the variance needed to studentize the difference in the sample means, given the potential temporal and cross-correlations, alongside the mixed-frequency nature of the related data. To address this, we propose a block-average-based variance estimator for this purpose. We derive the asymptotic null distribution of our new two-sample t statistic and analyze the test’s local power. Through extensive Monte Carlo simulations, our two-sample test demonstrates favorable size and power properties in finite samples. Notably, in cases with small sample sizes, our approach outperforms existing heuristic methods, which involve discarding data to align forecasts and applying conventional tests. Additionally, we uncover interesting connections with relevant methods in the literature.