TY - JOUR
T1 - Unit root quantile autoregression inference
AU - Koenker, Roger
AU - Xiao, Zhijie
N1 - Roger Koenker is Professor of Economics and Statistics (E-mail: rkoenker@ uiuc.edu) and Zhijie Xiao is Associate Professor of Economics (E-mail: [email protected]), University of Illinois, Urbana-Champaign, IL 61820. This research was supported in part by National Science Foundation grant SES-02-40781. The authors thank the editor, an associate editor, and three referees for their detailed and constructive comments.
PY - 2004/9
Y1 - 2004/9
N2 - 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.
AB - 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.
KW - Brownian bridge
KW - Kolmogorov-Smirnov tests
KW - Quantile regression process
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U2 - 10.1198/016214504000001114
DO - 10.1198/016214504000001114
M3 - Article
AN - SCOPUS:4944231551
SN - 0162-1459
VL - 99
SP - 775
EP - 787
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 467
ER -