Multivariate time series forecasting is crucial across various industries, where accurate extraction of complex periodic and trend components can significantly enhance prediction performance. However, existing models often struggle to capture these intricate patterns. To address these challenges, we propose FilterTS, a novel forecasting model that utilizes advanced filtering techniques based on the frequency domain. FilterTS introduces a Dynamic Cross-Variable Filtering Module, a key innovation that dynamically leverages other variables as filters to extract and reinforce shared variable frequency components across variables in multivariate time series. Additionally, a Static Global Filtering Module captures stable frequency components, identified throughout the entire training set. Moreover, the model is built in the frequency domain, converting time-domain convolutions into frequency-domain multiplicative operations to enhance computational efficiency. Extensive experimental results on eight real-world datasets have demonstrated that FilterTS significantly outperforms existing methods in terms of prediction accuracy and computational efficiency.