Quantile Autoregression-based Non-causality Testing

TL;DR

This paper develops new statistical tests based on quantile autoregression to identify non-causal processes in time series, with applications to financial market data and extensions to heteroskedastic models.

Contribution

It introduces three novel non-causality testing strategies within the QAR framework, exploiting properties of non-causal processes' conditional quantiles.

Findings

QAR estimates vary across quantiles for non-causal processes.

Proposed tests effectively detect non-causality in simulated and real data.

Method performs well at extreme quantiles and with heteroskedastic innovations.

Abstract

Non-causal processes have been drawing attention recently in Macroeconomics and Finance for their ability to display nonlinear behaviors such as asymmetric dynamics, clustering volatility, and local explosiveness. In this paper, we investigate the statistical properties of empirical conditional quantiles of non-causal processes. Specifically, we show that the quantile autoregression (QAR) estimates for non-causal processes do not remain constant across different quantiles in contrast to their causal counterparts. Furthermore, we demonstrate that non-causal autoregressive processes admit nonlinear representations for conditional quantiles given past observations. Exploiting these properties, we propose three novel testing strategies of non-causality for non-Gaussian processes within the QAR framework. The tests are constructed either by verifying the constancy of the slope coefficients or by applying a misspecification test of the linear QAR model over different quantiles of the process. Some numerical experiments are included to examine the finite sample performance of the testing strategies, where we compare different specification tests for dynamic quantiles with the Kolmogorov-Smirnov constancy test. The new methodology is applied to some time series from financial markets to investigate the presence of speculative bubbles. The extension of the approach based on the specification tests to AR processes driven by innovations with heteroskedasticity is studied through simulations. The performance of QAR estimates of non-causal processes at extreme quantiles is also explored.