We discuss an application of Generalized Random Forests (GRF) proposed by Athey et al.(2019) to quantile regression for time series data. We extracted the theoretical results of the GRF consistency for i.i.d. data to time series data. In particular, in the main theorem, based only on the general assumptions for time series data in Davis and Nielsen (2020), and trees in Athey et al.(2019), we show that the tsQRF (time series Quantile Regression Forests) estimator is consistent. Davis and Nielsen (2020) also discussed the estimation problem using Random Forests (RF) for time series data, but the construction procedure of the RF treated by the GRF is essentially different, and different ideas are used throughout the theoretical proof. In addition, a simulation and real data analysis were conducted.In the simulation, the accuracy of the conditional quantile estimation was evaluated under time series models. In the real data using the Nikkei Stock Average, our estimator is demonstrated to be more sensitive than the others in terms of volatility, thus preventing underestimation of risk.
翻译:我们讨论了AYEM等人(2019年)提出的通用随机森林(GRF)应用于时间序列数据的量化回归法(GRF),我们为i.d.d.数据提取了GRF一致性的理论结果,用于时间序列数据,特别是主要理论,仅以Davis和Nielsen(2020年)时间序列数据的一般假设为基础,而AAYEM等人(2019年)的树木为根据,我们表明,TSQRF(时间序列量子回归森林)估计数据是一致的。Davis和Nielsen(202020年)也讨论了时间序列数据使用随机森林(RF)的估计问题,但GRF所处理的RF构建程序基本上不同,在整个理论证据中采用了不同的想法。此外,还进行了模拟和真实数据分析。在模拟中,根据时间序列模型对有条件的定量估计的准确性进行了评估。在使用Nikkei股票平均值的实际数据中,我们的估计数据在波动方面比其他数据更加敏感,从而防止低估风险。