Often, in the analysis of time series and digital signals, a smoothing procedure is required to filter undesired random perturbations as noise and outliers in data. Among the most widely known techniques for time series smoothing, we have convolutional filters, simple exponential smoothing, triple exponential smoothing (Holt-Winters method) and linear adaptive filters, such as the Wiener filter. In this paper, we propose the NoLAW filter (Non-Linear Adaptive Wiener filter), a higher-order nonlinear extension for the adaptive Wiener filter, which is a linear statistical smoothing technique that assumes the hypothesis that the underlying series is corrupted by a zero mean, additive and independent Gaussian noise. Numerical experiments show that the proposed method is a computationally efficient and viable approach for filtering time series. Quantitative metrics show that the NoLAW filter is capable of producing better results than the usual linear Wiener filter, simple exponential smoothing and Holt-Winters method. Moreover, the computational cost of the proposed NoLAW is linear in the number of samples, which means that, asymptotically, it is equivalent to the regular Wiener filter.