  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.
