This article presents a general method for studentizing weighted sums of a linear process where weights are arrays of known real numbers and innovations form a martingale difference sequence. Asymptotical normality for such sums was established in Abadir et al. (2013). This article centres on the estimation of the standard deviation, to make the normal approximation operational. The proposed studentization is easy to apply and robust against unknown types of dependence (short range and long range) in the observations. It does not require the estimation of the parameters controlling the dependence structure. A finite‐sample Monte Carlo simulation study shows the applicability of the proposed methodology for moderate sample sizes. Assumptions for studentization are satisfied by the Nadaraya–Watson kernel type weights used for inference in non‐parametric regression settings.