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.

While LLMs have demonstrated remarkable potential in time series forecasting, their practical deployment remains constrained by excessive computational demands and memory footprints. Existing LLM-based approaches typically suffer from three critical limitations: Inefficient parameter utilization in handling numerical time series patterns; Modality misalignment between continuous temporal signals and discrete text embeddings; and Inflexibility for real-time expert knowledge integration. We present SMETimes, the first systematic investigation of sub-3B parameter SLMs for efficient and accurate time series forecasting. Our approach centers on three key innovations: A statistically-enhanced prompting mechanism that bridges numerical time series with textual semantics through descriptive statistical features; A adaptive fusion embedding architecture that aligns temporal patterns with language model token spaces through learnable parameters; And a dynamic mixture-of-experts framework enabled by SLMs' computational efficiency, adaptively combining base predictions with domain-specific models. Extensive evaluations across seven benchmark datasets demonstrate that our 3B-parameter SLM achieves state-of-the-art performance on five primary datasets while maintaining 3.8x faster training and 5.2x lower memory consumption compared to 7B-parameter LLM baselines. Notably, the proposed model exhibits better learning capabilities, achieving 12.3% lower MSE than conventional LLM. Ablation studies validate that our statistical prompting and cross-modal fusion modules respectively contribute 15.7% and 18.2% error reduction in long-horizon forecasting tasks. By redefining the efficiency-accuracy trade-off landscape, this work establishes SLMs as viable alternatives to resource-intensive LLMs for practical time series forecasting. Code and models are available at https://github.com/xiyan1234567/SMETimes.

Long-term time series forecasting is essential in areas like finance and weather prediction. Besides traditional methods that operate in the time domain, many recent models transform time series data into the frequency domain to better capture complex patterns. However, these methods often use filtering techniques to remove certain frequency signals as noise, which may unintentionally discard important information and reduce prediction accuracy. To address this, we propose the Frequency Decomposition Mixture of Experts (FreqMoE) model, which dynamically decomposes time series data into frequency bands, each processed by a specialized expert. A gating mechanism adjusts the importance of each output of expert based on frequency characteristics, and the aggregated results are fed into a prediction module that iteratively refines the forecast using residual connections. Our experiments demonstrate that FreqMoE outperforms state-of-the-art models, achieving the best performance on 51 out of 70 metrics across all tested datasets, while significantly reducing the number of required parameters to under 50k, providing notable efficiency advantages.