help tuqcoint

Title

tuqcoint -- Nonparametric quantile cointegration with stationary
covariates (Tu, Liang & Wang 2022) — local-constant kernel estimator.

Syntax

tuqcoint depvar xvar zvar [if] [in],
tau(#)
[options]

where xvar is an I(1) regressor and zvar is a stationary covariate.

tau(#) quantile level in (0,1); required (scalar)

gridx(numlist) grid of x values for fitting; default 25 equispaced

gridz(numlist) grid of z values; default 25 equispaced

ngrid(#) number of grid points if grids not given; default 25

h1(#) bandwidth on x; default sd(x)·n^(-1/6)

h2(#) bandwidth on z; default sd(z)·n^(-1/5)

kernel(name) epan (default), gauss, or uniform

graph produce m̂(x, z̄_med) curve plot

notable suppress table

save(name) save fitted surface to matrix

Description

tuqcoint estimates the unknown quantile function m(x_t, z_t) in
the nonparametric quantile cointegration model:

y_t = m(x_t, z_t) + u_t, x_t I(1), z_t stationary

For each (x_g, z_g) grid point, the local-constant quantile estimator solves:

m̂(x_g, z_g) = argmin_α Σ_t ρ_τ(y_t - α) K1((x_t-x_g)/h1) K2((z_t-z_g)/h2)

The solution is the weighted τ-th quantile of with product-kernel
weights. Pointwise asymptotic 95% CIs use the Tu et al. (2022) Theorem 2.1
sandwich formula.

NOTE: The full bootstrap Kolmogorov-Smirnov specification test of
Tu, Liang & Wang (2022) (Section 3) is computationally
heavy and NOT included in this implementation. For parametric specification
tests, see qpolycoint (linearity Wald) or fqardl with
type(qcoint) (Furno residual test).

Examples

. tsset t

. tuqcoint y x z, tau(0.5) ngrid(20)

. tuqcoint y x z, tau(0.25) gridx(-5(0.5)5) gridz(0(0.1)1) graph

Reference

Tu, Y., Liang, H.-Y. & Wang, Q. (2022). Nonparametric inference for quantile
cointegrations with stationary covariates.
Journal of Econometrics 230(2), 453–482.

Author

Dr Merwan Roudane

merwanroudane920@gmail.com

February 2026

Also see

xqcoint, qpolycoint, liqcoint_fc, qcointall