EQUIVALENCE BETWEEN OUT-OF-SAMPLE FORECAST COMPARISONS AND WALD STATISTICS

• 成果类型: Article
• 署名作者: Hansen, Peter Reinhard; Timmermann, Allan
• 署名单位: European University Institute; University of North Carolina; University of North Carolina Chapel Hill; CREATES; University of California System; University of California San Diego; University of California System; University of California San Diego
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA10581
• 发表日期: 2015
• 页码: 2485-2505
• 关键词: STOCHASTIC INTEGRALS; predictive ability; tests; accuracy; CONVERGENCE; models

摘要

We demonstrate the asymptotic equivalence between commonly used test statistics for out-of-sample forecasting performance and conventional Wald statistics. This equivalence greatly simplifies the computational burden of calculating recursive out-of-sample test statistics and their critical values. For the case with nested models, we show that the limit distribution, which has previously been expressed through stochastic integrals, has a simple representation in terms of chi(2)-distributed random variables and we derive its density. We also generalize the limit theory to cover local alternatives and characterize the power properties of the test.