Quantile correlations and quantile autoregressive modeling

TL;DR

This paper introduces quantile correlation measures and extends classical time series modeling techniques to the quantile domain, enabling better analysis of distributional characteristics and model adequacy.

Contribution

It proposes new quantile-based correlation measures and functions, extending the Box-Jenkins approach to quantile autoregressive models with theoretical and practical validation.

Findings

Quantile autocorrelation and partial correlation functions effectively identify model order.

Proposed methods perform well in finite sample simulations.

Empirical example demonstrates practical usefulness of the methods.

Abstract

In this paper, we propose two important measures, quantile correlation (QCOR) and quantile partial correlation (QPCOR). We then apply them to quantile autoregressive (QAR) models, and introduce two valuable quantities, the quantile autocorrelation function (QACF) and the quantile partial autocorrelation function (QPACF). This allows us to extend the classical Box-Jenkins approach to quantile autoregressive models. Specifically, the QPACF of an observed time series can be employed to identify the autoregressive order, while the QACF of residuals obtained from the fitted model can be used to assess the model adequacy. We not only demonstrate the asymptotic properties of QCOR, QPCOR, QACF, and PQACF, but also show the large sample results of the QAR estimates and the quantile version of the Ljung-Box test. Simulation studies indicate that the proposed methods perform well in finite samples, and an empirical example is presented to illustrate usefulness.