Time Series Quantile Regression Using Random Forests

We discuss an application of Generalized Random Forests (GRF) proposed to quantile regression for time series data. We extended 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 and trees, we show that the tsQRF (time series Quantile Regression Forest) estimator is consistent. Compare with existing article, 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 capture volatility more efficiently, thus preventing underestimation of uncertainty.