Quantile Correlations and Quantile Autoregressive Modeling

By Guodong Li, Yang Li, Chih-Ling Tsai. 2012

260 citations recorded by the source corpus.

In this article, 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 Box–Jenkins three-stage procedure (model identification, model parameter estimation, and model diagnostic checking) from classical autoregressive models 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 and QPCOR, but also show the large sample results of QACF, QPACF, and the quantile version of the Box–Pierce test. Moreover, we obtain the bootstrap approximations to the distributions of parameter estimators and proposed measures. Simulation studies indicate that the proposed methods perform well in finite samples, and an empirical example is presented to illustrate usefulness. Supplementary materials for this article are available online.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3467316226d02e2d2fb2a52119f6f488fe5c29e7

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Citations in the corpus

Quantile coherency: A general measure for dependence between cyclical economic variables (2015, unknown): “More recently, quantile correlation Schmitt et al. (2015), and quantile autocorrelation functions Li et al. (2015) together with cross-quantilograms Han et al. (2016) have been proposed as a fundamental tool for analysing dependence in quantiles of the distribution.”
Partial martingale difference correlation (2015, methodology): “[6], quantile partial correlation was introduced to measure the conditional quantile dependence of a random variable Y given X in a linear way, controlling for the linear effect of Z.”
Network quantile autoregression (2019, background): “(Robust Estimation) General vector autoregression models are usually sensitive to outliers, which leads to a serious distortion of the estimation (Abello et al., 2013; Li et al., 2015).”