Time series forecasting is critical across various domains, such as weather, finance and real estate forecasting, as accurate forecasts support informed decision-making and risk mitigation. While recent deep learning models have improved predictive capabilities, they often overlook time-lagged cross-correlations between related sequences, which are crucial for capturing complex temporal relationships. To address this, we propose the Time-Lagged Cross-Correlations-based Sequence Prediction framework (TLCCSP), which enhances forecasting accuracy by effectively integrating time-lagged cross-correlated sequences. TLCCSP employs the Sequence Shifted Dynamic Time Warping (SSDTW) algorithm to capture lagged correlations and a contrastive learning-based encoder to efficiently approximate SSDTW distances. Experimental results on weather, finance and real estate time series datasets demonstrate the effectiveness of our framework. On the weather dataset, SSDTW reduces mean squared error (MSE) by 16.01% compared with single-sequence methods, while the contrastive learning encoder (CLE) further decreases MSE by 17.88%. On the stock dataset, SSDTW achieves a 9.95% MSE reduction, and CLE reduces it by 6.13%. For the real estate dataset, SSDTW and CLE reduce MSE by 21.29% and 8.62%, respectively. Additionally, the contrastive learning approach decreases SSDTW computational time by approximately 99%, ensuring scalability and real-time applicability across multiple time series forecasting tasks.