Time Series Forecasting (TSF) is an important application across many fields. There is a debate about whether Transformers, despite being good at understanding long sequences, struggle with preserving temporal relationships in time series data. Recent research suggests that simpler linear models might outperform or at least provide competitive performance compared to complex Transformer-based models for TSF tasks. In this paper, we propose a novel data-efficient architecture, \textit{Gaussian-activated Linear model (GLinear)}, for multivariate TSF that exploits periodic patterns to provide better accuracy. It achieves higher prediction accuracy while requiring less historical data than other state-of-the-art linear predictors. Four different datasets (ETTh1, Electricity, Traffic, and Weather) are used to evaluate the performance of the proposed predictor. A performance comparison with state-of-the-art linear architectures (such as NLinear, DLinear, and RLinear) and transformer-based time series predictors (Autoformer) shows that the GLinear, despite being data efficient, outperforms the existing architectures in most cases of multivariate TSF while being competitive in others. We hope that the proposed GLinear model opens new fronts of research and development of simpler and more sophisticated architectures for data and computationally efficient time-series analysis. The source code is publicly available on GitHub.