Recent studies have shown that deep learning models such as RNNs and Transformers have brought significant performance gains for long-term forecasting of time series because they effectively utilize historical information. We found, however, that there is still great room for improvement in how to preserve historical information in neural networks while avoiding overfitting to noise present in the history. Addressing this allows better utilization of the capabilities of deep learning models. To this end, we design a Frequency improved Legendre Memory model, or FiLM: it applies Legendre polynomial projections to approximate historical information, uses Fourier projection to remove noise, and adds a low-rank approximation to speed up computation. Our empirical studies show that the proposed FiLM significantly improves the accuracy of state-of-the-art models in multivariate and univariate long-term forecasting by (19.2%, 22.6%), respectively. We also demonstrate that the representation module developed in this work can be used as a general plugin to improve the long-term prediction performance of other deep learning modules.

Time series data is ubiquitous, with forecasting applications spanning from finance to healthcare. Beyond popular deterministic methods, generative models are gaining attention due to advancements in areas like image synthesis and video generation, as well as their inherent ability to provide probabilistic predictions. However, existing generative approaches mostly involve recurrent generative operations or repeated denoising steps, making the prediction laborious, particularly for long-term forecasting. Most of them only conduct experiments for relatively short-term forecasting, with limited comparison to deterministic methods in long-term forecasting, leaving their practical advantages unclear. This paper presents TARFVAE, a novel generative framework that combines the Transformer-based autoregressive flow (TARFLOW) and variational autoencoder (VAE) for efficient one-step generative time series forecasting. Inspired by the rethinking that complex architectures for extracting time series representations might not be necessary, we add a flow module, TARFLOW, to VAE to promote spontaneous learning of latent variables that benefit predictions. TARFLOW enhances VAE's posterior estimation by breaking the Gaussian assumption, thereby enabling a more informative latent space. TARFVAE uses only the forward process of TARFLOW, avoiding autoregressive inverse operations and thus ensuring fast generation. During generation, it samples from the prior latent space and directly generates full-horizon forecasts via the VAE decoder. With simple MLP modules, TARFVAE achieves superior performance over state-of-the-art deterministic and generative models across different forecast horizons on benchmark datasets while maintaining efficient prediction speed, demonstrating its effectiveness as an efficient and powerful solution for generative time series forecasting.

Then, we propose FreTS, a simple yet effective architecture built upon Fre quency-domain MLPs for T ime S eries forecasting.

Recent advances have investigated the use of pretrained large language models (LLMs) for time-series forecasting by aligning numerical inputs with LLM embedding spaces. However, existing multimodal approaches often overlook the distinct statistical properties and temporal dependencies that are fundamental to time-series data. To bridge this gap, we propose MAP4TS, a novel Multi-Aspect Prompting Framework that explicitly incorporates classical time-series analysis into the prompt design. Our framework introduces four specialized prompt components: a Global Domain Prompt that conveys dataset-level context, a Local Domain Prompt that encodes recent trends and series-specific behaviors, and a pair of Statistical and Temporal Prompts that embed handcrafted insights derived from autocorrelation (ACF), partial autocorrelation (PACF), and Fourier analysis. Multi-Aspect Prompts are combined with raw time-series embeddings and passed through a cross-modality alignment module to produce unified representations, which are then processed by an LLM and projected for final forecasting. Extensive experiments across eight diverse datasets show that MAP4TS consistently outperforms state-of-the-art LLM-based methods. Our ablation studies further reveal that prompt-aware designs significantly enhance performance stability and that GPT-2 backbones, when paired with structured prompts, outperform larger models like LLaMA in long-term forecasting tasks.

The recent development of foundation models for time series data has generated considerable interest in using such models across a variety of applications. Although foundation models achieve state-of-the-art predictive performance, their calibration properties remain relatively underexplored, despite the fact that calibration can be critical for many practical applications. In this paper, we investigate the calibration-related properties of five recent time series foundation models and two competitive baselines. We perform a series of systematic evaluations assessing model calibration (i.e., over- or under-confidence), effects of varying prediction heads, and calibration under long-term autoregressive forecasting. We find that time series foundation models are consistently better calibrated than baseline models and tend not to be either systematically over- or under-confident, in contrast to the overconfidence often seen in other deep learning models.

This work was done during the internship at Microsoft Research Asia.

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