help liqcoint_fc

Title

liqcoint_fc -- Functional-coefficient quantile cointegrating regression
with stationary covariates (Li, Zhang & Zheng 2025).

Syntax

liqcoint_fc depvar indepvars [if] [in],
tau(#) zvar(varname)
[options]

where indepvars are I(1) regressors and zvar is a stationary covariate.

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

zvar(varname) stationary covariate z_t; required

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

ngrid(#) number of grid points; default 25

bandwidth(#) bandwidth h; default 1.06·sd(z)·n^(-1/5)

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

fm apply NFMQR (Nonparametric Fully-Modified) endogeneity correction (Li 2025 eq 2.7)

graph plot β̂(z) curves with 95% CIs

notable suppress table

save(name) save β̂(z) matrix

Description

liqcoint_fc fits the functional-coefficient quantile cointegration model
of Li, Zhang & Zheng (2025):

y_t = α + x_t' β(τ, z_t) + u_t

where the coefficient β(τ, z) is an unknown smooth function of the
stationary covariate z_t. For each grid point z_0, a local-linear quantile
regression is fitted:

β̂(z_0) = argmin_b Σ_t ρ_τ(y_t - x_t'(b_0 + b_1·(z_t-z_0))) · K((z_t-z_0)/h)

Pointwise 95% confidence intervals use the asymptotic sandwich variance
(Cai, Li & Park 2009 / Li et al. 2025 Theorem 1).

NOTE: The double-sup Kolmogorov-Smirnov stability test with
fixed-regressor wild bootstrap (Li et al. 2025 Section 3 and Theorem 4) is
NOT included in this implementation. For parametric structural tests, see
qpolycoint or fqardl with type(qcoint).

Examples

. tsset t

. liqcoint_fc y x, tau(0.5) zvar(z) ngrid(20) graph

. liqcoint_fc y x1 x2, tau(0.25) zvar(zindex) gridz(0(0.1)1)

Reference

Li, H., Zhang, J. & Zheng, C. (2025). Functional-coefficient quantile
cointegrating regression with stationary covariates.
Statistics and Probability Letters 219, 110344.

Author

Dr Merwan Roudane

merwanroudane920@gmail.com

February 2026

Also see

xqcoint, qpolycoint, tuqcoint, qcointall