Profile least squares estimation of a partially linear time trend model with weakly dependent data

•We propose a semiparametric method to estimate a partially linear time trend model.•The semiparametric estimator for the time trend coefficient is shown be semiparametrically efficient.•The Monte Carlo simulations strongly support our theoretical analysis.

We consider a partially linear time trend model with weakly dependent data. We show that the semiparametric estimator for the time trend coefficient has the same rate of convergence as in the parametric time trend model case. We also show that the asymptotic variance reaches the semiparametric efficient bound. The Monte Carlo simulations strongly support our theoretical analysis.