LightGTS: A Lightweight General Time Series Forecasting Model

Q1: Discussions and experimental comparisons with Tiny Time Mixers (TTMs).

A1: Thank you for mentioning TTMs, which are also lightweight TSFMs like LightGTS. We will differentiate LightGTS from TTMs in the following two aspects:

• Flexibility: TTMs have fixed input and output formats, which imposes limitations in downstream applications. In contrast, LightGTS supports flexible input and output configurations.
• Adaptive Patching: While TTMs employ adaptive patching through CV-inspired patch merging techniques to capture multi-scale features, they remain constrained by predefined patch sizes. LightGTS, however, leverages periodical patching that adaptively segments time series based on the intrinsic periods. This approach enables LightGTS to achieve unified modeling across datasets with varying scales.

Based on your suggestions, we add a comparison experiment with TTMs. The following table shows the average MSE in zero shot setting, and LightGTS outperforms TTMs on most datasets.

Q2: The article's expression and description need some revision.

A2: Thank you for your detailed suggestions, we will correct the errors you mentioned in the revised paper.

Q3: Need a diagram illustrating the differences between the Periodical Patching and Periodical Parallel Decoding techniques and traditional practices.

A3:

• As shown in Figure 2 (a), the key difference of Periodical Patching from other patching techniques is its ability to adaptively perform consistent modeling on multivariate time series datasets with varying scales.
• The differences between Periodical Parallel Decoding and other decoding techniques are shown in the table below.

Q1: The zero-shot evaluation requires further validation for generalizability to unseen scales and periods, such as an ablation study on cycle-length estimation.

A1: To further evaluate the generalizability of LightGTS, we add experiments on Chronos Benchmark II which contains 27 evaluation datasets with different scales and periods. As shown in the table below, LightGTS shows outstanding performance, second only to Moirai-large whose training corpus overlap is much higher. In addition, LightGTS also exhibits superior efficiency compared to other foundation model.

Q2: Cycle-length detection ablation is unclear; limited discussion of failure modes (e.g., non-periodic series).

A2: Actually, for datasets with little periodicity, LightGTS is insensitive to the prediction of trends with the selection of patch size. Take the exchange dataset which exhibits little periodicity as an example, the performance of LightGTS in zero-shot setting remains stable when the patch size is set to 1, 4, 6, 8, 16 and 24, respectively. In the paper, we use fft-extracted period: 6.

Q3: Clarify the detection and effectiveness of intrinsic periods across datasets. The periods determined for datasets with unknown/noisy periodicities?

A3: For datasets with prior knowledge of period, we use known period. For datasets where the period is not known, we use Fast Fourier Transform (FFT) to extract the period, which we have discussed in the Appendix B.1.

In Table 8, we give the cycle lengths of the evaluation dataset. For traffic and electricity dataset with two cycle lengths: 24 (one day) and 168 (one week), we choose the smaller cycle length 24 as the patch size. For the exchange dataset with insignificant periodicity, we use fft to extract the cycle length of 6.

In Table 4 of paper, we perform an ablation study against periodical patching on seven datasets. After replacing periodical patching with a fixed patching, the model’s performance decreases significantly, validating the effectiveness of periodical patching.

Q1: Larger benchmark datasets should be used for evaluating the pretrained TSF model.

A1: We use Chronos Benchmark II to further evaluate the effectiveness of LightGTS. As shown in the table below, LightGTS shows outstanding performance, second only to Moirai-large whose training corpus overlap is much higher. In addition, LightGTS also exhibits superior efficiency compared to other foundation model.

Q2: Light-weight time series models [1] [2] or even non-parametric models [3] that use periodical information to improve forecasting should be discussed.

A2:

• CycleNet, SparseTSF, and OneShotSTL all propose explicit periodicity decomposition methods to enhance the accuracy and lightweight nature of time series forecasting models. However, LightGTS not only explicitly models periodicity through periodic patching but also adapts to multivariate time series pretraining via flex resizing technique. This allows the model to leverage the scale-invariant periodicity inductive bias in multivariate time series, achieving strong zero-shot performance with fewer parameters.
• Experiment (MSE)：

Q3: Specific experimental settings should be given. For instance, which period is used for training and evaluation? How long is the context length?

A3:

• For datasets with prior knowledge of period, we use known period. For datasets where the period is not known, we use Fast Fourier Transform (FFT) to extract the period.
• We use a variable context length, keeping the number of tokens at 10. For example, for a dataset with a period of 24, we set the context length to 240.

Q4: How would the proposed model perform trend forecasting? Does it go back to point patch? Then the model size would be significantly affected, if there are many non-periodic time series in the pretraining datasets, right? Emperically, how does the proposed model perform on such datasets?

A4: Actually, for datasets with little periodicity, LightGTS is insensitive to the prediction of trends with the selection of patch size, and the the model size would be affected by the selection of patch size. Take the exchange dataset which exhibits little periodicity as an example, the performance of LightGTS in zero-shot setting remains stable when the patch size is set to 1, 4, 6, 8, 16 and 24, respectively. In the paper, we use fft-extracted periods: 6.

Q5: How to deal with different cycle lengths.

A5: For the case where a time series is known to have different cycle lengths, we pick the smallest cycle as the patch size. For example, traffic and electricity dataset both have two cycle lengths, 24 (one day) and 168 (one week), and we choose 24 as the patch size. For the case where the cycle length is not well known, FFT can be used for cycle length extraction, which we have discussed in the Appendix B.1.

Q1: Improve the quality of evaluation

A1: We use Chronos Benchmark II you mentioned to further evaluate the generalizability of LightGTS. As shown in the table below, LightGTS shows outstanding performance, second only to Moirai-large whose training corpus overlap is much higher. In addition, LightGTS also exhibits superior efficiency compared to other foundation model.

Q2: Periodical Patching vs. Multi-Patching

A2: While MOIRAI's predefined patch sizes based on sampling frequency offer some solution for consistent modeling across different frequencies, they are still fixed and lack flexibility in certain scenarios. In contrast, Periodical Patching adaptively divides patches according to scale-invariant periodicity, enabling more flexible and unified modeling for datasets with varying frequencies.

Q3: Some works such as TinyTimeMixers have made similar claims as LightGTS and should be discussed as part of related work.

A3: Thank you for mentioning TTMs, which are also lightweight TSFMs like LightGTS. We will differentiate LightGTS from TTMs in the following two aspects:

• Flexibility: TTMs have fixed input and output formats, which imposes limitations in downstream applications. In contrast, LightGTS supports flexible input and output configurations.
• Adaptive Patching: While TTMs employ adaptive patching through CV-inspired patch merging techniques to capture multi-scale features, they remain constrained by predefined patch sizes. LightGTS, however, leverages periodical patching that adaptively segments time series based on the intrinsic periods. This approach enables LightGTS to achieve unified modeling across datasets with varying scales.

We would update it in the related work of the revised paper.

Q4: LightGTS is only a point forecaster, whereas most existing pretrained models (Chronos, Moirai, TimesFM, Chronos-Bolt) support probabilistic forecasting. Uncertainty quantification is critical feature for downstream decision making based on a forecast.

A4: We are developing an enhanced version of LightGTS with quantile regression pre-train task to support probabilistic forecasting (uncertainty quantification), which will be released in future updates.

Q5: Replace non-standard terms (e.g., "scale" for frequency, "cycle length" for seasonality) with established conventions.

A5: We sincerely appreciate your feedback regarding terminology alignment. In the revised manuscript, we will systematically replace non-standard terms with established terminology from time series.

Q6: Was the model only trained on the ETTh1 dataset? How does the model perform quantitatively when trained on a single seasonality?Why does the pretraining corpus include diverse seasonalities, and how were they selected?

A6:

• Yes, we found that pre-training on a single seasonality dataset can enable effective transfer learning.
• Experiment: LightGTS-single was pre-trained on ETTh1 and directly tested on downstream datasets in a zero-shot setting. As shown in the table below, LightGTS-single achieved strong transfer performance on datasets with single seasonality (e.g., Solar), while its performance was less optimal on datasets with multiple seasonalities (e.g., Electricity). By pre-training on multi-seasonalities datasets, LightGTS-mini significantly improved its performance on datasets with multiple seasonalities.

• Pre-training corpus selection: We did not explicitly filter datasets based on seasonality. Instead, we collected datasets from diverse domains (e.g., energy, weather, traffic), assuming that time-series data from different domains inherently contain distinct seasonal patterns. This approach ensures broader generalizability while retaining domain-specific characteristics.