autoformer 非周期性的数据

https://openreview.net/forum?id=J4gRj6d5Qm

 

Q1: For time series without clear periodicity, whether Auto-Correlation still works or not?

In Table 3 of main paper―, we have shown that Auto-Correlation outperforms the self-attention family on the ETT dataset (with clear periodicity), by replacing the Auto-Correlation in Autoformer with different self-attention modules. As per your suggestion, we repeat the experiment on the Exchange dataset (without clear periodicity). Here are more results:

Exchange (without clear periodicity) input-96-predict-336MSEMAE
Auto-Correlation + Autoformer architecture (deep decomposition) 0.488 0.510
Full Self-Attention + Autoformer architecture (deep decomposition) 0.632 0.584
LogSparse Attention + Autoformer architecture (deep decomposition) 0.569 0.592
LSH Attention + Autoformer architecture (deep decomposition) 0.553 0.549
PropSparse Attention + Autoformer architecture (deep decomposition) 0.958 0.729

As shown in the above table, for series without clear periodicity, Auto-Correlation still outperforms other self-attention mechnisms in both MSE and MAE. Therefore, Auto-correlation is a robust deep learning module for general-pattern series data.

We have also provided some visualization results on the Exchange dataset (without clear periodicity) in Section 4.2 of supplementary material―, which shows that Autoformer can make meaningful long-term forecasting for series without clear periodicity. It is notable that both the Auto-Correlation and the decomposition architecure contribute substantially to Autoformer's predicative power for complex series.

 

 

Q3: More baselines for comparison, including ARIMA, DeepGLO, and N-BEATS.

We have provided in Table 4 of supplementary material―​ the results of ARMIA, as well as the well-known deep learning model (DeepAR) and a strong statistical model (Prophet, open-sourced by FaceBook). Here are more results of Autoformer comparing with ARIMA, DeepGLO, and N-BEATS.

(1) Results of input-96-predict-O under the univariate setting.

ETT (MSE | MAE)Predict 96Predict 192Predict 336Predict 720
ARIMA 0.568 | 0.572 0.804 | 0.720 1.438 | 1.010 3.291 | 1.569
DeepGLO 0.199 | 0.341 0.223 | 0.360 0.245 | 0.400 0.328 | 0.462
N-BEATS 0.257 | 0.389 0.298 | 0.424 0.320 | 0.445 0.363 | 0.480
Autoformer 0.065 | 0.189 0.110 | 0.258 0.145 | 0.295 0.182 | 0.335
Exchange (MSE |MAE)Predict 96Predict 192Predict 336Predict 720
ARIMA 0.308 ｜ 0.396 1.305 ｜ 1.178 1.762｜1.445 5.017 ｜ 1.893
DeepGLO 0.850 | 0.786 1.825 | 1.185 2.210 | 1.330 5.818 | 2.232
N-BEATS 0.319 | 0.433 0.706 | 0.651 1.282 | 0.879 2.757 ｜1.341
Autoformer 0.126 | 0.268 0.530 | 0.565 0.586 | 0.572 1.838 | 1.201

(2) Results of input-96-predict-O under the multivariate setting. For ARIMA, N-BEATS (univariate predictive model), we predict the multivariate series dimension by dimension.

ETT (MSE |MAE)Predict 96Predict 192Predict 336Predict 720
ARIMA 0.267 | 0.382 2.414 | 0.588 10.083 | 0.896 15.338 | 1.183
DeepGLO 0.288 | 0.395 0.510 | 0.551 0.872 | 0.734 2.173 | 1.208
N-BEATS 0.313 | 0.395 0.392 | 0.440 0.464 | 0.473 0.571 | 0.521
Autoformer 0.194 | 0.284 0.261 | 0.323 0.351 | 0.384 0.491 | 0.470
Exchange (MSE |MAE)Predict 96Predict 192Predict 336Predict 720
ARIMA 0.327｜ 0.417 0.656 | 0.568 0.970 | 0.572 4.808 | 1.182
DeepGLO 0.928 | 0.751 1.142 | 0.861 1.512 | 1.013 1.542 | 1.097
N-BEATS 0.316 | 0.409 0.328 | 0.444 1.203 | 0.819 1.672 | 1.013
Autoformer 0.134 | 0.270 0.272 | 0.374 0.488 | 0.510 1.367 | 0.901

We will make Table 1 of main paper―​ more complete by adding the above results for all datasets and forecasting horizons.

 

posted @ 2023-10-08 08:03  emanlee  阅读(13)  评论(0)  编辑  收藏  举报