Bridging Time and Linguistics: LLMs as Time Series Analyzer through Symbolization and Segmentation

W1, Q1: More Discussion and Comparison of Related LLM-based Methods

1. Discussion

   A: We will include more discussions on LLM-based related works in the revised version. Specifically, TimeCMA aims to enhance forecasting performance by leveraging LLM-generated text as an augmentation to time series data. To this end, it retrieves and selects textual information highly relevant to the time series, constructing disentangled and robust cross-modal embeddings for prediction. Unlike TimeCMA, which uses LLMs as external modules, our S$^2$TS-LLM tokenizes time series into textual descriptions, providing prompts to directly help LLMs better capture temporal dynamics during forecasting. FSCA addresses the cross-modal alignment problem in LLMs by representing time series and textual prompts as hierarchical graph nodes. It constructs a directed graph to characterize structural relationships between time series and prompts, and then uses graph convolution to fuse their representations for forecasting. In contrast, our S$^2$TS-LLM does not model the relationship between time series and textual prompts. Instead, we captures internal temporal context by reassigning the position indices of time-series patches, making the time-series representation more akin to linguistic context and thus easier for LLMs to interpret.

2. Comparison

   A: In light of your suggestions, we add TimeCMA for further long-term forecasting comparison, as listed below. Although both our method and TimeCMA achieve cross-modal alignment, they differ in direction: TimeCMA adopts an LLMs-for-Time-Series strategy, using LLM-generated text to augment time-series features without adapting LLMs to temporal understanding. In contrast, we adopt a Time-Series-for-LLMs strategy that transforms time series into language-like representations by tokenizing frequency patterns and learning temporal context. This bridges the gaps between LLMs and time series, leading to improved performance of our method.

   Method	Metric	Weather	ECL	ETTh1	ETTh2	ETTm1	ETTm2
   TimeCMA	MSE↓	0.250	0.174	0.423	0.372	0.380	0.275
   	MAE↓	0.276	0.269	0.431	0.397	0.392	0.323
   S$^2$TS-LLM(Ours)	MSE↓	0.225	0.164	0.404	0.321	0.344	0.258
   	MAE↓	0.265	0.256	0.429	0.376	0.380	0.318

W2: More Ablation Study of Short-term Forecasting and Classification Tasks

A: To further evaluate the capability of designed components, we conduct additional ablation study on short-term forecasting and classification tasks as follows. The results consistently show that each module contributes positively across different tasks. Notably, although reduced input length in short-term forecasting limits available frequency information, our method still effectively distinguishes temporal patterns by dynamically selecting top-$k$ components, providing valuable prompts to guide LLMs in forecasting. For classification, contextual segmentation proves most effective, likely because it transforms raw signals into discrete semantic units by reassigning index, making LLMs easier to capture local patterns and improving performance.

W3, Q2: Clarify Tokenization Example and Motivation of Using ASCII Symbol

1. Clarify Tokenization Example

   A: The example of time-domain tokenization in lines 162-164 aims to convey a message similar to the motivation illustrated in Fig. 1(a), but its simplified expression may lead to ambiguity. To clarify, consider the sequence $[66, 45, 24, 32, 27, 33, 16, 8]$. A time-domain tokenization that captures only the global trend might represent this sequence as "decreasing from 66 to 8," thereby omitting intermediate fluctuations such as 24→32→27→33. To provide a clearer description, more words are required. For example, GPT-3.5 generates: "The series starts at 66 and drops quickly to 24 over the first three points. After reaching 24, it briefly rises to 32 and 33, then drops again to 16 and finally 8." However, such a verbose textual description significantly exceeds the length of the original sequence. Using such long-sequence prompts to train LLMs for time series forecasting would result in significant computational overhead, making it impractical. Therefore, tokenizing a time series for prompting LLMs requires striking a balance between accuracy and efficiency, which is highly challenging.

2. More Explanation of Frequency-domain Tokenization

   A: Compared to time-domain tokenization, representing compact frequency-domain information in textual form is more tractable. For the same sequence $[66, 45, 24, 32, 27, 33, 16, 8]$, applying a real-valued FFT yields the frequency-domain components $[251+0j, 30.5-33.4j, 53.0-38.0j, 47,5-17.5j, 15+0j]$, which respectively represents the DC component and the 1/8 to 4/8 frequency bands. By selecting the top 2 components with the largest magnitudes for reconstruction, we obtain the sequence $[56.5, 35.6, 13.8, 33.4, 32.8, 46.2, 22.5, 10.4]$. Although the reconstructed values are not numerically accurate, the sequence successfully preserves the three key trends of the original: an initial decline, a fluctuation, and a subsequent drop. This demonstrates that the temporal pattern of a sequence can be effectively captured by tokenizing only a small number of dominant frequency components. In doing so, frequency-domain tokenization mitigates the limitations of time-domain approaches, which may introduce noise when overly concise or lead to high computational costs when overly verbose.

3. The Motivation of Using ASCII Symbols

   A: The motivation for using ASCII symbols to tokenize frequency components lies in the observation that different temporal patterns can be effectively characterized by combinations of salient frequency components. By assigning each frequency component a unique ASCII symbol, we can represent the top-k components of a sequence as a compact symbolic string. For example, combinations dominated by low-frequency symbols typically indicate smooth and stable trends of time series, while those containing more high-frequency symbols suggest volatile or rapidly changing patterns of time series.

   Although ASCII symbols do not carry semantic meaning in natural language, LLMs can still learn their distributional statistics after fine-tuning[1]. In this way, ASCII tokens function similarly to foreign-language or domain-specific tokens, allowing the LLMs to associate certain patterns of symbols with frequency characteristics. As shown in our ablation study (Section 4.6), using ASCII symbols to represent frequency components achieves comparable forecasting performance to using natural-language words, demonstrating their effectiveness as interpretable and learnable tokens for LLMs.

[1] W. J. Su, et al. Do Large Language Models (Really) Need Statistical Foundations? arXiv, 2025

W4, Q3: Confusing Design of Time-Linguistic Fusion

A: To clarify, our time-linguistic fusion (TLF) design is inspired by the Gated TCN module in GraphWavelet[2], which uses a gating mechanism of the form: $h = g(\Theta \star \mathcal{X} + b) \odot \sigma (\Theta \star \mathcal{X} + c)$. The sigmoid function $\sigma(\cdot)$ controls the proportion of information from $\mathcal{X}$ that is propagated to the next layer.

In a similar spirit, we apply a sigmoid transformation to the frequency-domain output, which acts as a gating signal. This gate determines which parts of the time-series information should be preserved or suppressed during the fusion process. Following the gating, we incorporate cosine similarity to further modulate the fusion weights, emphasizing components of the time-domain signal that are more semantically aligned with the frequency-domain patterns.

We intentionally do not fuse the raw frequency-domain output directly with the time-domain representation, as the prediction task is inherently defined in the time domain. The frequency-domain output is instead treated as a complementary signal that guides the fusion process without shifting the prediction space. To evaluate the effectiveness of our fusion mechanism, we further conduct comparisons with several alternative fusion strategies, including bilinear fusion ($z = x^T W y$), gated fusion ($z = \alpha x + (1 - \alpha)y$), and attention-based fusion. The following experimental results show that our proposed TLF fusion achieves the best performance, consistently yielding lower prediction errors than the alternatives.

[2] Z. H. Wu, et al. Graph WaveNet for Deep Spatial-Temporal Graph Modeling. IJCAI, 2019

W1:Limited Novelty

A: We respectfully clarify that the novelty of our S$^2$TS-LLM lies in two aspects:

• Frequency-domain Tokenization: We adapt LLMs to time-series tasks from a frequency-domain perspective, setting it apart from prior time-domain methods like Time-LLM, TEST, CALF, and S$^2$IP-LLM. Based on the insight that top-k frequency components can capture key temporal trends, we tokenize them as textual prompts to help LLMs in distinguish different time-series patterns. This dominant-frequency tokenization is conceptually akin to keypoint detection in CV, where a few salient features (e.g., tires) can represent the whole object (e.g., car). This makes our method be more flexible and efficient for cross-modal alignment than time-domain methods that rely on comparing token discrepancies between text and time series one by one.

• New Context Alignment: We go beyond prior work by introducing a contextual alignment, which endows temporal segments with language-like contextual structures. This alignment is done externally by reassigning positional indices of time series, without altering LLM's internal architecture, making our design plug-and-play and more friendly for LLMs' cross-modal adaptation.

W2,W1,Q1:Motivation, Challenge and Effectiveness of Spectral Symbolization (SS)

1. Motivation of SS

   A: Our motivation is to leverage the sparsity of frequency signals to improve the clarity of textual prompts for LLMs. Prior studies [1][2] show that prompts are most effective when they are clear and precise, not necessarily long. Time-domain prompts, while rich in information, often require verbose language to detailedly express trends, local variations, etc., which may overwhelm or confuse LLMs. In contrast, frequency signals are often sparse and quantifiable, with key temporal features concentrated in a few dominant components (as shown in Fig. 1). This sparsity enables the generation of compact and unambiguous prompts that help LLMs distinguish global temporal patterns such as periodicity, volatility, or smoothness.

2. Not Address the Core Challenge

   A: We respectfully clarify that our goal is not to "losslessly capture the infinite variability of the time domain," but to appropriately preserve essential patterns that support LLMs' cross-modal adaptation. The core challenge lies in the trade-off between accuracy and efficiency when tokenizing time series as prompts for LLMs. We address this by shifting tokenization from the time domain to the frequency domain.

   To illustrate, consider tokenizing a sequence $[66,45,24,32,27,33,16,8]$:

   • Time-domain Tokenization: When aiming for efficiency, it tends to oversimplify temporal dynamics (e.g., describing a sequence as "decreasing from 66 to 8"), which ignores local variations and thus lacks accuracy. When seeking for accuracy, it needs to capture fine-grained changes, which often requires lengthy descriptions and hurts efficiency. For example, a precise description-"The series starts at 66 and drops to 24 over the first three points. After reaching 24, it briefly rises to 32 and 33, then drops again to 16 and finally 8"-far exceeds the length of the original sequence.

   • Frequency-domain Tokenization: Through FFT, we reduce the sequence length by half, improving the efficiency due to less information needed to be tokenized. Meanwhile, since using top-2 frequency component can reconstruct a sequence $[57,36,14,33,32,46,23,10]$ with original "drop→flucuation→drop" trends, our frequency-domain tokenization can preserve global patterns to ensure accuracy.

   Based on these observation, our method can leverage the sparsity of frequency features to generate compact yet informative prompts, balancing accuracy and efficiency more effectively than time-domain tokenization.

3. Effectivenss of SS

   A: While the frequency domain contains less information than the time domain, prior work [3] have shown that frequency features are effective for modeling time-series. These successes support the potential of frequency learning to address LLMs' cross-modal adaptation. Importantly, our method does not rely solely on frequency features. We combine frequency-domain prompts with raw time-domain series, allowing LLMs to benefit from complementary information: the frequency prompts helps LLMs perceive global trends, while raw series allows attention mechanisms to capture local variations. As shown in Section 4 and Appendix Table 7, our method outperforms time-domain methods, like Time-LLM and S$^2$IP-LLM, in both prediction accuracy and computational efficiency, highlighting the benefits of our method.

[1]Chen.Unleashing the potential of prompt engineering for large language models.arXiv
[2]Kusano.Are Longer Prompts Always Better? Prompt Selection in Large Language Models for Recommendation Systems.arXiv
[3]Zhou.Fedformer:Frequency enhanced decomposed transformer for long-term series forecasting.ICML

W3,Q4:Point-level Mismatches Patch-level in Segmentation

A: We believe that the term 'time points' may have unintentionally caused some misunderstanding. We appreciate the reviewer's observation and will revise ambiguous terms like "time points" to improve clarity. As stated in lines 147-150 and 188-191, our method, like Time-LLM, first applies a patching strategy to preprocess time series and then performs contextual segmentation at the patch level, not at individual time points. The detailed process is listed below:

• A univariate time series $X \in \mathbb{R}^{L}$ is divided into $Q$ non-overlapping patches, resulting in $X \in \mathbb{R}^{Q \times M}$.

• Contextual segmentation is performed over these $Q$ patches. It groups adjacent and semantically similar patches into the same segment for assigning a shared position index, with each segment composed of one or more consecutive patches. For example, GPT-2 assigns sequential indices $[0,1,2,3,4]$ to 5 patches, while our segmentation may group patches 0, 1, 2 into one segment, assigning indices $[0,0,0,1,2]$ to reflect contextual continiuty.

• Segment-level indices are fed into the the LLM's positional encoding, allowing patches within the same segment to share positional embeddings. This helps the attention mechanism fuse related patches, better capturing local trend continuity.

Q2:Why ASCII Symbol Works?

A: Thank you for the insightful question. ASCII symbols help LLMs understand spectral patterns for two main reasons: 1) they offer a compact and discriminative encoding of frequency components, and 2) LLMs, as statistical models, can learn meaningful patterns from symbolic inputs even without explicit semantics.

• Discriminative representation: By mapping each component to a unique ASCII symbol, dynamically selecting top-k components can form a specific symbolic sequences that differentiate between spectral patterns. For example, sequences dominated by low-frequency symbols reflect smooth trends, while high-frequency symbols indicate volatility.

• Statistical nature of LLMs: LLMs rely on statistical patterns rather than semantic meaning[4]; for example, [5] shows ASCII separators act as structural cues in LLMs. Thus, LLMs can interpret ASCII symbols as frequency-related tokens (like foreign language) via fine-tuning.

Our ablation (Section 4.6) further confirms that ASCII tokens perform comparably to natural language words, validating their utility in frequency-domain prompting.

[4]Su.Do Large Language Models (Really) Need Statistical Foundations?arXiv
[5]Chen.SepLLM:Accelerate Large Language Models by Compressing One Segment into One Separator.ICML

Q3:Contextual Segmentation may Destroy Temporal Order

A: We respectfully clarify that our segmentation preserves the temporal order of patches. Only adjacent and semantically similar patches are grouped into the same segment, and later patches never get lower position indices than earlier ones, making the sequence in order. This ensures the LLMs perceive the correct sequence structures; for example, a peak (upward followed by downward), won't be mistaken for a valley.

Q5:More LLM-based Comparison

A: Per your suggestions, we add TEST and CALF as baselines for comparison. Both of them perform cross-modal alignment from the time domain. In contrast, our method achieves better results by using frequency-domain alignment, which guides LLMs through simpler and clearer prompts. Additionally, our contextual segmentation endows time series with language-like structure. Assume that time series can be treated as character-like sequence, $[x_0,x_1,x_2,x_3,x_4,x_5] =$ ["c","a","t","d","o","g"]. Our method assigns grouped indices [0,0,0,1,1,1], forming semantic units like "cat" and "dog." Compared to LLMs' default sequential indexing [0,1,2,3,4,5], this grouping helps preserve trend continuity, enabling LLMs better modeling of time-series patterns.

Q6:Backbone Fairness

A: We follow GPT4TS and S$^2$IP-LLM in using GPT-2 as the backbone. As noted in Appendix (lines 41-42), the Time-LLM results reported are also based on GPT-2, ensuring fair comparison. To verify the robustness of our method across backbones, our ablation (Fig. 6) has included a BERT-based variant. Here, we further compare with Time-LLM using LLaMA, and results show that our method achieves comparable performance with fewer layers (4 vs. 8), verifying its architectural robustness.

W1:Lack Citations of Similar Idea of FreqTST and FreEformer

A: We appreciate the reviewer's suggestion and will add a more detailed discussion of related frequency-domain works in the revised manuscript. While FreqTST and FreEformer all adopts frequency learning, our approach is conceptually and technically distinct from both:

• FreEformer is a non-LLM-based method that focuses on improving the rank of attention matrices to better handle the sparsity in frequency data for forecasting. In contrast, our S$^2$TS-LLM, a LLM-based framework, aims to bridging the representational gap between time series and language for LLMs. Thus, our method transforms spectral signals to generate textual descriptions, prompting LLMs to capture time-series patterns for downstream tasks.

• FreqTST aims to construct a new token dictionary that can generalizably represent frequency features across datasets to enhance Transformer-based forecasting. To achieve this, it designs a pretraining strategy to vectorize frequency amplitudes into token embeddings. In contrast, our method avoids creating a new dictionary, as LLMs struggle to understand newly introduced token vocabularies. Instead, we leverage the existing token vocabulary of LLMs to represent time series, enabling seamless and efficient adaptation to time-series tasks without additional pretraining. To this end, we propose a frequency-domain tokenization that maps each frequency component to a unique character and dynamically selects dominant frequency components to form distinctive textual descriptions for different time series. Our approach is conceptually akin to keypoint detection in CV, where identifying a few salient features (e.g., car tires) is sufficient to recognize the entire object (e.g., car).

W2,L1:Potential Information Loss Problem of Spectral Symbolization Module

A: We thank the reviewer for pointing out potential information loss problem of FFT in certain cases, such as curved trajectories. Although our Spectral Symbolization (SS) module is built upon FFT, its design helps mitigate this limitation. First, SS primarily uses FFT to generate textual descriptions of frequency-domain features, which serve as supplementary inputs alongside the original time-domain data for LLM training. Second, the SS module dynamically selects top-k frequency components for encoding, enabling it to capture discriminative patterns through varying combinations of dominant frequencies, even when the signal energy is concentrated in narrow frequency bands.

Below, we provide an ablation study of short-term forecasting on the M4 datasets to support the effectiveness of our SS module. Although FFT intensifies the information compression problem in short-term forecasting, which may limit the relative contribution of the SS module compared to the other two modules, it still offers valuable frequency patterns that effectively help LLMs understand temporal dynamics.

Additionally, we further evaluate the magnitude sensitivity and trend preservation capabilities of our method, in comparison with two representative frequency-based models (FEDformer[1] and FiLM[2]). Regarding magnitude sensitivity, we compute cosine similarity and Pearson correlation between the frequency components of predictions and ground truth. For trend preservation, we measure the dominant frequency overlap to assess how well each model captures underlying trends. The results listed below show that our method achieves better performance in both magnitude and trend measures, indicating the effectiveness of our method in frequency learning.

Based on the above results and the strong performance of our method across 23 datasets (as shown in Section 4), we believe that our method retains good generalization ability in real-world applications.

[1]T. Zhou, et al. Fedformer: Frequency enhanced decomposed transformer for long-term series forecasting. ICML [2]T. Zhou, et al. FiLM: Frequency improved Legendre Memory Model for Long-term Time Series Forecasting. NIPS

W3:GPT-2 Gets Per-set LR Sweeps While Classic Models Use Canned Configs

A: As described in Appendix B.3, our method follows the standard setup of existing time-series LLM methods [3][4][5] by fine-tuning the LLM with a fixed and small learning rate (e.g., 0.0001) for time-series analysis.

[3]T. Zhou, et al. One fits all: Power general time series analysis by pretrained lm. NIPS [4]M. Jin, et al. Time-llm: Time series forecasting by reprogramming large language models. ICLR [5]Z. J. Pan, et al. s2ip-llm: Semantic space informed prompt learning with llm for time series forecasting. ICML

Q1:Contextual Segmentation vs. Long-Context Tricks

A: We clarify that our segmentation and long-context modeling (the position encoding such as relative positions in RoPE) are two distinct components to address different problems: the former is an LLM-independent module that captures temporal dependencies from time series (as shown in Fig. 3), while the latter is part of the LLM used to model contextual relationships among input tokens. By default, if no inputs' indices are provided, the LLM automatically generates sequential indices (e.g., $P = [0,...,n-1]$) for inputs and pass them into the position encoding module to learn contextual relationships. Our method instead creates grouped indices $P$ and feeds them to the LLM. To illustrate why our segmentation works, we can consider treating each time-series patch as a character, such as $[x_0, x_1, x_2, x_3, x_4, x_5] =$ ["c", "a", "t", "d", "o", "g"]. A standard LLM would assign sequential indices [0,1,2,3,4,5], treating each patch independently. In contrast, our segmentation assigns grouped indices [0,0,0,1,1,1], effectively grouping $x_0$ to $x_2$ as "cat" and $x_3$ to $x_5$ as "dog". This narrows the structural gap between text and time series, allowing the LLM to better capture trend continuity in time series, without compromising its ability to model long-context dependencies.

Q2:Effectiveness of Time-Linguistic Fusion

A: To clarify, the proposed time-linguistic fusion (TLF) is designed in a simple yet effective way by combining cosine similarity with a gating mechanism. Specifically, the design of TLF is inspired by the Gated TCN module in GraphWavelet[6], which uses a gating mechanism of the form: $h = g(\Theta \star \mathcal{X} + b) \odot \sigma (\Theta \star \mathcal{X} + c)$. The sigmoid function $\sigma(\cdot)$ controls the proportion of information from $\mathcal{X}$ that is propagated to the next layer. In a similar spirit, we apply a sigmoid function to the frequency-domain output, generating a gating signal that controls the retention or suppression of time-series information during fusion. This gating is then complemented by a cosine similarity measure. It refines the fusion process by assigning higher weights to time-domain information that are more closely aligned with frequency-domain semantics.

Below, we compare the proposed TLF with several other fusion techniques, including bilinear fusion ($z = x^T W y$), gate fusion ($z = \alpha x + (1-\alpha)y$), and attention-based fusion. The results show that TLF achieves the best performance, yielding lower prediction errors than the alternatives.

[6]Z. Wu, et al. Graph WaveNet for Deep Spatial-Temporal Graph Modeling. IJCAI

Q3:Lack of Justification for GPT-2's Benefit from ASCII Symbols

A: The effectiveness of ASCII symbols lies in that different combinations of ASCII symbols can reflect different distributional patterns of the time series and can be understood by LLMs. Specifically, we assign an ASCII symbol to each frequency component and encode the top-k components into a textual description of time series. When the resulting text is dominated by symbols representing low-frequency components, it indicates smooth and stable trends of time series; when high-frequency components dominate, it reflects more volatile changes of time series. Although ASCII symbols lacks semantic meaning in natural language, LLMs can, after fine-tuning, learn statistical patterns in ASCII sequences and interpret them as foreign-language tokens representing frequency [7]. As shown in the ablation study in Section 4.6, using ASCII symbols to represent frequency components achieves comparable performance to using natural-language words, demonstrating that ASCII symbols can effectively serve as interpretable tokens for LLMs.

[7]W. Su, et al. Do Large Language Models (Really) Need Statistical Foundations? arXiv

W1, Q1: More Experimental evaluation

1. Anomaly Detection

   A: We clarify that our S$^2$TS-LLM can be applied on anomaly detection tasks, and the results provided below showing its reasonable performance. However, S$^2$TS-LLM currently falls short of state-of-the-art models such as the LLM-based GPT4TS. One possible reason is that our top-k frequency selection mechanism is designed to capture dominant and generalizable patterns in the time series, rather than rare or subtle deviations. While this focus aligns well with forecasting or classification tasks, it may overlook the sparse and abnormal signals that are essential for anomaly detection. In future work, we plan to explore alternative selection strategies and anomaly-sensitive frequency encodings to better adapt our method to this task.

   F1-Score ↑	S$^2$TS-LLM (Ours)	GPT4TS	PatchTST	ETS	DLinear
   SMD	83.93	86.89	84.62	83.13	77.10
   MSL	82.16	82.45	78.70	85.03	84.88
   SWaT	92.65	94.23	85.72	84.91	87.52
   PSM	96.71	97.13	96.08	91.76	93.55
   Average	88.61	90.18	86.28	86.21	85.76

2. Experiments on all UEA Datasets

   A: Following prior work [1][2], we select 10 representative datasets from the UEA time-series classification archive to strike a balance between experimental diversity and computational feasibility, as LLM-based methods are relatively resource-intensive. These 10 datasets span a wide range of application domains, including biomedical signals (e.g., Heartbeat, SelfRegulationSCP1, SelfRegulationSCP2), chemical signals (e.g., EthanolConcentration), human activity (e.g., UWaveGestureLibrary, PEMS-SF), speech and audio (e.g., JapaneseVowels, SpokenArabicDigits), and visual tasks (e.g., FaceDetection, Handwriting). We believe this selection supports both comparability and meaningful evaluation.

3. More Evaluation on UCR Dataset

   A: We believe that the results on the UEA datasets provide meaningful insights into the method's potential generalizability to the UCR archive. According to [3], the UEA archive is developed as an extension of the UCR archive, offering more challenging and diverse benchmarks with multivariate and longer time series, in contrast to the mostly univariate and short-sequence nature of UCR datasets.

4. Study of Model's Performance Gain

   A: To investigate when our S$^2$STS-LLM works well and when it fails, we follow prior work [4][5] to evaluate model performance under different lookback lengths $\{512, 336, 192, 96, 48\}$. The detailed results are as follows.

   We observe that S$^2$STS-LLM outperforms the other two LLM-based methods, S2IP-LLM and GPT4TS, when the lookback length is between 512 and 96. However, as the lookback length decreases to 48, S$^2$STS-LLM experiences a significant performance drop and underperforms compared to the S2IP-LLM and GPT4TS. This is consistent with our paper's observation that S$^2$STS-LLM achieves suboptimal results on short-term forecasting tasks. The main reason is that S$^2$STS-LLM uses FFT to extract dominant frequency components, which leads to further information compression when the lookback window is short. As a result, the generated compact textual descriptions may not provide LLMs with sufficient prompts to bridge the semantic gap between linguistics and time series.

   Therefore, our method is better suited for long-sequence scenarios. For example, our model shows significant gains in both long-term forecasting and zero-shot learning tasks, where it can capture enough dominant frequency components to distinguish different temporal patterns.

   	Lookback Length	512	336	192	96	48
   	Metric	MSE↓ , MAE↓	MSE↓ , MAE↓	MSE↓ , MAE↓	MSE↓ , MAE↓	MSE↓ , MAE↓
   ETTh1	S$^2$TS-LLM (Ours)	0.355, 0.387	0.365, 0.389	0.372, 0.391	0.378, 0.391	0.398, 0.411
   	S2IP-LLM	0.368, 0.403	0.367, 0.398	0.368, 0.393	0.379, 0.394	0.390, 0.401
   	GPT4TS	0.376, 0.397	0.378, 0.399	0.380, 0.401	0.383, 0.401	0.385, 0.403
   ETTh2	S$^2$TS-LLM (Ours)	0.260, 0.329	0.281, 0.335	0.288, 0.338	0.291, 0.336	0.310, 0.350
   	S2IP-LLM	0.284, 0.345	0.282, 0.343	0.288, 0.343	0.293, 0.343	0.301, 0.344
   	GPT4TS	0.285, 0.342	0.286, 0.345	0.294, 0.349	0.295, 0.349	0.299, 0.350

[1] T. Zhou, et al. One fits all: Power general time series analysis by pretrained lm. NIPS, 2023
[2] H. X. Wu, et al. Long. Timesnet: Temporal 2d-variation modeling for general time series analysis. ICLR, 2023
[3] A. J. Bagnall, et al. The uea multivariate time series classification archive. arXiv, 2018
[4] M. Jin, et al. Time-llm: Time series forecasting by reprogramming large language models. ICLR, 2024
[5] W. Z. Yue, et al. FreEformer: Frequency Enhanced Transformer for Multivariate Time Series Forecasting. arXiv, 2025

W2: More Literature Review

A: Thanks for the comments. We will expand the discussion of related work by incorporating [6][7], to provide useful preliminaries on frequency-domain modeling and further demonstrate the potential of frequency-based representations in time-series applications with LLMs.

[6] R. Liu, et al. Frequency-aware masked autoencoders for multimodal pretraining on biosignals. arXiv 2023.
[7] X. Zhang, et al. Self-supervised contrastive pre-training for time series via time-frequency consistency. NIPS, 2022