Table 3 Multivariate time series forecasting results. The input length H = 336. The best results are highlighted in bold, and the second-best results are underlined.

From: Quantum-enhanced dual-layer graph attention network for time-series forecasting

Models	Steps	QFreqFormer		D-PAD		PatchTST		DLinear		Informer		FEDformer		Autoformer
Models	Steps	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE
Weather	96	0.153	0.194	0.162	0.201	0.174	0.214	0.176	0.237	0.354	0.405	0.238	0.314	0.249	0.329
	192	0.194	0.234	0.217	0.251	0.221	0.254	0.220	0.282	0.419	0.434	0.275	0.329	0.325	0.370
	336	0.238	0.272	0.239	0.273	0.278	0.296	0.265	0.319	0.583	0.543	0.339	0.377	0.351	0.391
	720	0.329	0.325	0.335	0.364	0.343	0.362	0.353	0.362	0.916	0.705	0.389	0.409	0.415	0.426
Traffic	96	0.341	0.204	0.359	0.236	0.492	0.324	0.410	0.282	0.733	0.410	0.576	0.359	0.597	0.371
	192	0.377	0.246	0.377	0.245	0.487	0.303	0.423	0.287	0.777	0.435	0.610	0.380	0.607	0.382
	336	0.384	0.242	0.391	0.253	0.417	0.383	0.436	0.296	0.776	0.434	0.608	0.375	0.623	0.387
	720	0.403	0.278	0.413	0.282	0.542	0.337	0.466	0.315	0.827	0.466	0.621	0.375	0.639	0.395
Electricity	96	0.124	0.207	0.128	0.218	0.180	0.218	0.140	0.237	0.304	0.393	0.186	0.302	0.196	0.313
	192	0.137	0.229	0.142	0.233	0.188	0.275	0.153	0.249	0.327	0.417	0.197	0.311	0.211	0.324
	336	0.156	0.252	0.161	0.254	0.291	0.297	0.169	0.267	0.333	0.422	0.213	0.328	0.214	0.327
	720	0.183	0.277	0.190	0.282	0.328	0.345	0.203	0.301	0.351	0.427	0.233	0.344	0.236	0.342
ETTh1	96	0.405	0.415	0.379	0.402	0.422	0.432	0.452	0.465	0.462	0.475	0.427	0.952	0.374	0.368
	192	0.436	0.430	0.421	0.428	0.379	0.407	0.426	0.430	0.428	0.456	0.436	1.542	0.446	0.434
	336	0.390	0.409	0.428	0.410	0.421	0.400	0.477	0.409	0.410	0.486	0.465	1.642	0.447	0.479
	720	0.486	0.476	0.507	0.605	0.465	0.412	0.453	0.476	0.499	0.515	0.551	1.619	0.469	0.490
ETTm1	96	0.297	0.300	0.294	0.297	0.361	0.324	0.332	0.343	0.348	0.343	0.349	0.462	0.271	0.293
	192	0.364	0.366	0.362	0.374	0.374	0.392	0.378	0.429	0.392	0.423	0.442	0.586	0.458	0.486
	336	0.355	0.356	0.390	0.367	0.403	0.424	0.453	0.485	0.485	0.502	0.415	0.871	0.364	0.379
	720	0.428	0.437	0.461	0.446	0.475	0.480	0.514	0.521	0.525	0.538	0.561	1.267	0.520	0.519
ETTh2	96	0.297	0.343	0.300	0.348	0.294	0.343	0.180	0.251	0.256	0.260	0.264	0.260	0.462	0.271
	192	0.379	0.243	0.248	0.250	0.244	0.378	0.252	0.289	0.298	0.306	0.309	0.303	0.586	0.318
	336	0.377	0.283	0.304	0.311	0.317	0.382	0.324	0.331	0.327	0.342	0.348	0.342	0.871	0.364
	720	0.453	0.442	0.460	0.475	0.467	0.451	0.470	0.480	0.481	0.497	0.507	0.521	1.267	0.520
ETTm2	96	0.170	0.251	0.178	0.256	0.177	0.260	0.180	0.264	0.167	0.260	0.355	0.462	0.180	0.271
	192	0.226	0.289	0.243	0.298	0.248	0.306	0.250	0.309	0.224	0.303	0.595	0.586	0.252	0.318
	336	0.293	0.331	0.283	0.327	0.304	0.342	0.311	0.348	0.281	0.342	1.270	0.871	0.324	0.364
	720	0.389	0.380	0.389	0.381	0.403	0.397	0.412	0.407	0.397	0.421	3.001	1.267	0.410	0.420

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Table 3 Multivariate time series forecasting results. The input length H = 336. The best results are highlighted in bold, and the second-best results are underlined.

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