Estimation and test for quantile nonlinear cointegrating regression

- A quantile nonlinear cointegration model is proposed.
- The parameter estimator follows a nonstandard distribution asymptotically.
- A fully modified estimator and a test for linearity are developed.
- Monte Carlo results show that the test has good finite sample performance.

In order to investigate the nonlinear relationship among economic variables at each quantile level, this paper proposes a quantile nonlinear cointegration model in which the nonlinear relationship at each quantile level is approximated by a polynomial. The parameter estimator in the proposed model is shown to follow a nonstandard distribution asymptotically due to serial correlation and endogeneity. Therefore, this paper develops a fully modified estimator which follows a mixture normal distribution asymptotically. Moreover, a test statistic for the linearity and its asymptotic distribution are also derived. Monte Carlo results show that the proposed test has good finite sample performance.