arXiv 7 Jan 2023 · Econometrics
arXiv:2301.02937 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Fries, S. and Zakoian, J.-M. (2019) Mixed causal-noncausal ar proces… Econometric Theory, 35, 1234–1270 | 1.000 | 10 | 4 | 100% |
| 2 | Koenker, R. and Xiao, Z. (2002) Inference on the quantile regression… (2006) Journal of the American statistical association, 101, 980–990 | 1.000 | 5 | 4 | 100% |
| 3 | Rosenblatt, M. (2000) Gaussian and non-Gaussian linear time series a… Springer Science & Business Media | 0.843 | 3 | 3 | 100% |
| 4 | Hecq, A. and Sun, L. (2021) Selecting between causal and noncausal m… Studies in Nonlinear Dynamics & Econometrics, 25, 393–416 | 0.737 | 3 | 2 | 100% |
| 5 | Koenker, R. and Xiao, Z. (2002) Inference on the quantile regression… Econometrica, 70, 1583–1612 | 0.737 | 3 | 2 | 100% |
| 6 | Breidt, F. J., Davis, R. A., Trindade, A. A. et al. (2001) Least abs… The Annals of Statistics, 29, 919–946 | 0.644 | 2 | 2 | 100% |
| 7 | Lanne, M., Meitz, M., Saikkonen, P. et al. (2013) Testing for linear… Journal of Financial Econometrics, 11, 682–705 | 0.644 | 2 | 2 | 100% |
| 8 | Velasco, C. and Lobato, I. N. (2018) Frequency domain minimum distan… The Annals of Statistics, 46, 555–579 | 0.644 | 2 | 2 | 100% |
| 9 | Escanciano, J. C. and Velasco, C. (2010) Specification tests of para… Journal of Econometrics, 159, 209–221 | 0.585 | 3 | 1 | 100% |
| 10 | Escanciano, J. C. and Goh, S.-C. (2012) Conditional density estimati… (2014) Journal of Econometrics, 178, 495–507 | 0.585 | 3 | 1 | 100% |
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