Time Series Quantile Regression

Abstract

In this chapter, we explore a topic that has gained considerable attention in the academic literature during the latter years, namely quantile regression for time series data. We will illustrate how to use conditional quantile regression to model the dynamics of electricity prices as a function of the price of an input and also substitute energy commodity such as natural gas. We will also illustrate how to estimate different conditional quantiles of electricity prices using lags of the same prices, in the vein of traditional autoregressive processes in time series analysis. This exercise when conducted to estimate the tail quantiles (i.e., very low or very high quantiles) allows us to recover a modified value at risk statistic on the price distribution, which is asymmetric conditional on each tail, and which can be used to monitor the market risk for consumers and producers of electricity.