We would like to sincerely thank Reviewer xofX for providing a detailed review and insightful comments. Based on the suggestions, we have revised our paper accordingly.

W1:Use of linking words

Thank you for your suggestions. We have made the corresponding modifications in the article to enhance its clarity and coherence.

W2:Ambiguous connection

We apologize for any confusion caused by our choice of words. Here, "complexity" does not refer to computational complexity, but rather to the difficulty of constructing an appropriate method for transforming time series into images. Our intention is to convey that existing methods that directly map time series into scatter plots can lead to information loss, and designing a method that avoids such loss is challenging.

W3:Clarification of model objectives

The reason we utilize the periodicity and trend of the predicted output is closely related to the characteristics of the image reconstruction model. Image reconstruction refers to the process of restoring a degraded image, where "degraded" indicates that the geometric structure of the image has been compromised. Given the limitations of image reconstruction models in capturing temporal dynamics, it is crucial to employ existing time series modeling techniques to predict the output's periodicity and trends. Consequently, the degraded image we maintain must reflect these predicted structural periodicity and trends. In other words, we need to use segments of the predicted results from the time series as the foundation for the image reconstruction process.

W4:Expanding in Y-dimension

We need to extend the Y-axis because this adjustment provides a more accurate representation of the computed loss. Considering this scenario, when the predicted values are close to the actual values, in the time series modality, the corresponding loss should be small. However, in the image modality, these values do not correspond to the same pixel if the Y-axis is not expanded, resulting in a significantly larger loss in the image MSE, which does not align with our understanding and requirements regarding the errors in actual predictive results.

By extending the Y-axis, we can ensure that as the predicted points get closer to the points in the ground truth (GT), the loss becomes smaller, which aligns with our expectations.

W5:The computational costs of proposed method

In our model, the DTFE component includes a Transformer block, whereas the V2T component does not incorporate this block, as it serves as a conversion method that does not require training. We will first present the theoretical analysis of the computational complexity of the Transformer block in the DTFE component, where the sequence length is denoted as L, the patch size as P, the number of variables as N, and the number of Transformer layers as 1.

When modeling with variables as tokens, the number of tokens is N and the dimensionality is L, resulting in a complexity of $O(N^2L)$. In contrast, when modeling using patches of time series, we consider patches as tokens, with the patch size defining the dimensionality, leading to a complexity of $O(\frac{L^2}{P})$. The computational complexity for the periodic prediction part is denoted as $O(\frac{L^2}{P})$, while that for the trend prediction part is denoted as $O(N^2L)$, resulting in an overall computational complexity for DTFE represented as $O(N^2L+\frac{L^2}{P})$. We have selected commonly used models, iTransformer and patchTST, for comparison, with their respective computational complexities denoted as $O(2N^2L)$and $O(2\frac{L^2}{P})$. The factor of 2 is included because both models have two layers.

It is important to note that the specific values of these computational complexities are influenced by different datasets and prediction lengths. Therefore, we tested the computational complexity on a specific dataset, namely the ETTh2 dataset, with a prediction length of 96, using GMac as the unit of measurement for the computational complexity.

Our model achieves the best prediction results, with computational costs positioned between the two provided baselines.

Dear Reviewer xofX,

We would like to sincerely thank you for your time and efforts in reviewing our paper.

We have made an extensive effort to try to address your concerns. In our response:

• We revise the manuscript to reduce the use of inappropriate terminology and ambiguous expressions.
• We provide a detailed explanation of why we use the output features as the prediction target.
• We supplement our analysis with a comparison of the computational costs associated with our model and the baseline models.

We hope our response can effectively address your concerns, If you have any further concerns or questions, please do not hesitate to let us know, and we will respond timely.

All the best,

Authors

W3:The introduction of the SSIM metric

We introduce the SSIM because existing evaluation metrics for time series lack a focus on structural assessment. Continuing with the previously mentioned example in response to W1, both Time Series One and Time Series Two have the same MSE value compared to the ground truth (GT), yet their geometric structures are entirely different. To evaluate their geometric structural similarity with the GT, we converted this example into images and conducted SSIM testing. Specifically, the SSIM value between Time Series One and the GT is 0.5866, while the SSIM value between Time Series Two and the GT is only 0.2722.

This clearly indicates that Time Series One, which exhibits high geometric structural similarity with the GT, achieves a higher SSIM, whereas Time Series Two has a significantly lower SSIM. This demonstrates that SSIM effectively captures the geometric structural similarity of time series. Therefore, we introduce SSIM as an evaluation metric to supplement the limitations of MSE and MAE in assessing structural integrity.

W4:Treating the image reconstruction component as a plug-in module

Our current image reconstruction model is built upon the joint reconstruction of the periodicity, trend, and features of the time series. In contrast, existing time series models predict only the time series itself, rather than their underlying cycles and trends. To transform our method into a plugin, we need to make modifications. Specifically, in TimeIR, we will continue to accept style inputs but replace the input features of periodicity and trends with the predictions from traditional time series models. We conduct experiments on iTransformer, selecting the ETTh2 dataset for our experiments. The specific experimental results are as follows:

It can be observed that after incorporating our TimeIR module, our model achieved a reduction of 0.01 in MSE, a reduction of 0.02 in MAE, and an increase of 0.0088 in SSIM. These results demonstrate that the proposed image reconstruction component provides improved predictions in accuracy and geometric structure of the time series.

We would like to sincerely thank Reviewer MNU9 for providing a detailed review and insightful comments. Based on the suggestions, we have revised our paper accordingly.

W1:The motivation for Image Transformation

We employ image reconstruction techniques for processing time series data because current time series models fail to capture the inherent geometric structural information. These models typically use MSE or MAE between corresponding time points for training, which only reflects numerical similarity. For instance, two prediction results may yield the same MSE, yet their styles can differ significantly. Consider an example where the ground truth (GT) is a sine function $y=sin(x)$ , Time Series One is a shifted sine function $y=sin(x+a)+b$, and Time Series Two is a straight line $y=0$. By adjusting the magnitude of the shift in Time Series One, Time Series One and Time Series Two may have similar MSEs compared with GT. While the MSEs are similar, Time Series Two lacks geometric details and does not convey useful information such as periodicity and trends. Thus, low MSE alone is insufficient; we need to incorporate geometric structural similarity into our predictions.

Since one-dimensional time serie sequences cannot capture two-dimensional geometric features well, we introduced image reconstruction components to our approach. This allows us to capture the combined structural similarity of time series in a two-dimensional context, where one dimension represents the time dimension and the other dimension represents the value dimension. Our experimental results demonstrate that our model can effciently capture these combined structures, as shown in the visualizations. More detailed information regarding the incorporation of images has been revised in the appendix, with further specifics available in Appendix B.1.

We conduct ablation experiments on TimeIR using the ETTh1 dataset, and the specific results are as follows:

After adding TimeIR, it can be observed that our model achieve better prediction performance on the MSE metric., while the SSIM (which ranges from 0 to 1, with higher values indicating better performance) increased by 0.0127. This indicates that the TimeIR module not only enhances the geometric structural integrity of the time series but also reduces the traditional MSE loss.

W2:The concept of style feature

The style of the time series mentioned in the article can be defined as the geometric structural information of the time series. Specific manifestations of style can be observed in our visualization results. In the example shown in the third row of Figure 5, the original input time series(the left half of each sequence) exhibits a linear style, while the ground truth for prediction (the right half of the sequence) also appears as a straight line. In contrast, the predictions made by other time series forecasting methods show fluctuating patterns, highlighting a clear stylistic difference from the original time series. This noticeable difference clearly indicates that the original time series and predicted time series do not constitute a unified time series, thus suggesting a discontinuity in their styles. However, our model successfully reconstructs the time series into a form that closely resembles a straight line, thereby preserving the style of the preceding series.

Dear Reviewer MNU9,

We would like to sincerely thank you for your time and efforts in reviewing our paper.

We have made an extensive effort to try to address your concerns. In our response:

• We elucidate the motivation for using images in time series forecasting.
• We provide a detailed explanation of the specific definition of style.
• We present examples to analyze the rationale behind our introduction of SSIM.
• We supplement our findings with corresponding experiments that incorporate our model as a plugin.

We hope our response can address your concerns. If you have any further concerns or questions, please do not hesitate to let us know, and we will respond timely.

All the best,

Authors

W3:Missing dataset

Thank you for your reminder. We have supplemented evaluation of our model on these two datasets on MSE metric, and the results are as follows:

For the Solar-Energy dataset, our model surpasses the current best baseline on the MSE metric. For the Traffic dataset, which is characterized by a high number of variables, our model's performance ranks second among all baselines, just behind the iTransformer specifically designed for multivariable time series. In the future, we will further consider modeling the relationships between variables.

W4:Missing code

Thank you for your reminder. In this supplementary material, we have submitted our model's code, as well as the training code. The complete repository of our method will be made open-source in the future.

We would like to sincerely thank Reviewer pp94 for providing a detailed review and insightful comments. Based on the suggestions, we have revised our paper accordingly.

W1:The concept of style consisency

The continuity of style can be understood as a type of discrepancy measurement between the original time series and the predicted time series. Specifically, the style of the time series mentioned in the article can be defined as the geometric structural information of the time series. This can be illustrated by examining the visualization results in Figure 5. In the third row of examples, the original input time series(the left half of each sequence) exhibits a linear style, while the ground truth for prediction (the right half of the sequence) also appears as a straight line. In contrast, the predictions made by other time series forecasting methods show fluctuating patterns, highlighting a clear stylistic difference from the original time series. This noticeable difference clearly indicates that the original time series and predicted time series do not constitute a unified time series, thus suggesting a discontinuity in their styles. However, our model successfully reconstructs the time series into a form that closely resembles a straight line, thereby preserving the style of the preceding series.

W2(1):The motivation for Image Transformation in Time-Series Forecasting

We employ image reconstruction techniques for processing time series data because current time series models fail to capture the inherent geometric structural information. These models typically use MSE or MAE between corresponding time points for training, which only reflects numerical similarity. For instance, two prediction results may yield the same MSE, yet their styles can differ significantly. Consider an example where the ground truth (GT) is a sine function $y=sin(x)$ , Time Series One is a shifted sine function $y=sin(x+a)+b$, and Time Series Two is a straight line $y=0$. By adjusting the magnitude of the shift in Time Series One, Time Series One and Time Series Two may have similar MSEs compared with GT. While the MSEs are similar, Time Series Two lacks geometric details and does not convey useful information such as periodicity and trends. Thus, low MSE alone is insufficient; we need to incorporate geometric structural similarity into our predictions.

Since one-dimensional time series sequences cannot capture two-dimensional geometric features well, we introduced image reconstruction components to our approach. This allows us to capture the combined structural similarity of time series in a two-dimensional context, where one dimension represents the time dimension and the other dimension represents the value dimension. Our experimental results demonstrate that our model can effciently capture these combined structures, as shown in the visualizations.

W2(2):The distinction between Time series and image

In the image modality, the order of each patch is significant; altering this order results in changes to the image, similar to the characteristics of time series data. Additionally, our TimeIR model incorporates positional embeddings to ensure that the model comprehends the sequence of the patches. The primary distinction between these two modalities is that the image modality, while preserving the information of the time series, introduces a y-axis, thereby providing additional geometric structural information and enhancing the capability to capture style. More detailed information regarding the incorporation of images has been revised in the appendix, with further specifics available in Appendix B.1.

Dear Reviewer pp94,

We would like to express our sincere gratitude for your time and efforts in reviewing our paper.

We have made an extensive effort to try to address your concerns. In our response:

• We provide a detailed explanation of the specific definition of style.

• We elucidate the rationale behind using images for time series forecasting.

• We supplement our findings with results from our model on the Traffic and Solar Energy datasets, along with comparisons to other baseline models.

• We also provide the code used in our research.

We hope our response can address your concerns. If you have any further concerns or questions, please do not hesitate to inform us, and we will be more than happy to address them promptly.

All the best,

Authors