Local linear kernel estimation is a fundamental tool in nonparametric regression, renowned for its bias reduction and boundary correction properties. While its asymptotic behavior is well understood for independent data and for strongly mixing processes, it remains largely unexplored under quasi-associated dependence, even in the real-valued regression setting. In this paper, we introduce a functional local linear kernel estimator for regression models with quasi-associated observations. We establish strong consistency in the sense of almost complete convergence and derive convergence rates under mild regularity conditions involving small-ball probabilities and covariance decay. To the best of our knowledge, this paper provides the first theoretical guarantees for functional local linear kernel regression under quasi-associated dependence, covering both fixed and $k$-nearest neighbor ( $k$NN) bandwidth selection procedures.

We study estimation of the relative error regression function in a functional single-index regression model under quasi-associated dependence. We introduce a $k$-nearest neighbors ( $k$-NN) estimator whose smoothing adapts to the local concentration of the covariate trajectories. Almost complete convergence rates are established under mild small-ball and dependence conditions. A simulation study compares the proposed $k$-NN estimator with its kernel counterpart, and a real data application to air quality forecasting (NOx $\to$ ozone) illustrates it's practical performance.