Widespread applications of IoT generate massive periodic time series data. The time series forecasting (TSF) enables people to perceive things before hand. Inspired by the classical autoregressive TSF models, we conclude that the future sequences are influenced by the regular periodic variations, the long-term trend changes, the short-term trend changes, and the noises. In this paper, a novel lightweight interpretable deep time series forecasting model, 2D Convolution and Linear mapping-based model (CLinear), is proposed. CLinear decomposes time series into periods, and models the periodic patterns, long-term trends, short-term trends and noise in a progressive manner. The model extracts features with 2D convolution, and then generates periodic patterns and long-term trends with fully connected layers. Combining short-term trends generated from the nearest sequence, preliminary predictions are produced. Finally, the model generates the prediction noise according to the feedback noise from the preliminary predictions. Short-term trend enhances the model’s adaptability for non-periodic datasets. The feedback noise is utilized to fit complex factors that cannot be effectively expressed in complex environments. Experiments on 5 time series datasets and 3 raw meteorological datasets demonstrate the superior performance of our method while maintaining a smaller parameter scale. Ablation experiments validate the necessity of each component. Finally, experiments on the meteorological temperature dataset demonstrate the practical significance of each component, and visualize the interpretability. CLinear verifies that classical methods are referential for constructing deep learning models. Code is available at https://github.com/LoneLoser/CLinear.