ABSTRACT
This chapter provides a selective review of quantile time series analysis, with a focus on parametric models, in particular, quantile autoregression (QAR) and related processes. The QAR process can be extended to nonlinear models. Quantile regression and quantile domain analysis are important tools in the study of time series. Quantile regression provides a method of estimating the conditional quantile function, and thus the whole conditional distribution, of a time series, and also substantially expands the modeling options for time series analysis. Quantile domain analysis provides a convenient way to study time series dynamics beyond the first few moments. The chapter discusses Quantile regressions with heavy-tailed errors. It provides quantile time series regressions with deterministic and/or stochastic trend, including unit root and cointegrating regressions. The chapter examines quantile regressions on the autoregressive models, the general autoregressive moving average models, and general linear and nonlinear dynamic regressions.
