Abstract
We study statistical inference in quantile auto-regression models when the largest autoregressive coefficient may be unity. The limiting distribution of a quantile autoregression estimator and its t-statistic is derived. The asymptotic distribution is not the conventional Dickey-Fuller distribution, but rather a linear combination of the Dickey-Fuller distribution and the standard normal, with the weight determined by the correlation coefficient of related time series. Inference methods based on the estimator are investigated asymptotically. Monte Carlo results indicate that the new inference procedures have power gains over the conventional least squares-based unit root tests in the presence of non-Gaussian disturbances. An empirical application of the model to U.S. macroeconomic time series data further illustrates the potential of the new approach.
Original language | English (US) |
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Pages (from-to) | 775-787 |
Number of pages | 13 |
Journal | Journal of the American Statistical Association |
Volume | 99 |
Issue number | 467 |
DOIs | |
State | Published - Sep 2004 |
Externally published | Yes |
Keywords
- Brownian bridge
- Kolmogorov-Smirnov tests
- Quantile regression process
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty