2012/09/28 by Guodong Li, Yang Li, Li, Guodong +3 · 2 citations
Economics, Econometrics and Finance · Mathematics · #FOS: Computer and information sciences #Financial Risk and Volatility Modeling #Methodology (stat.ME) #Statistical Distribution Estimation and Applications #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1209.6487
openalex publication_date 2012/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.