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Multivariate Time Series Forecasting on Exchange

0.007MAEDA-SPS
-0.0050.0760.1570.238Feb 26, 2024Jul 12, 2024Nov 27, 2024Apr 14, 2025Aug 30, 2025Jan 15, 2026Jun 2, 2026

Evaluation results

MethodLinks
DA-SPSHorizon=32026.010.007—0.00980.10090.9957——
TS-Conv-LSTMHorizon=32026.010.0084—0.0110.11030.9962——
DA-Conv-LSTMHorizon=32026.010.0088—0.01130.11350.9962——
DA-SPSHorizon=62026.010.0098—0.01310.13450.9933——
TS-Conv-LSTMHorizon=62026.010.0109—0.01390.14030.9932——
TCLNHorizon=62026.010.0112—0.01470.14820.9907——
DA-Conv-LSTMHorizon=62026.010.0118—0.01460.14680.9902——
DA-SPSHorizon=122026.010.0122—0.01540.15850.9889——
TS-Conv-LSTMHorizon=122026.010.0127—0.01650.16580.9891——
LSTMHorizon=32026.010.0128—0.01510.15180.9959——
DA-Conv-LSTMHorizon=122026.010.0128—0.0160.16080.9882——
TCLNHorizon=32026.010.0141—0.01740.17510.9944——
CNNHorizon=32026.010.0146—0.01710.17190.9932——
DA-RNNHorizon=32026.010.0159—0.01860.18680.9951——
DA-RNNHorizon=62026.010.0194—0.02260.22740.9922——
CNNHorizon=62026.010.0214—0.0290.29240.9792——
DA-SPSHorizon=242026.010.0218—0.02830.29120.9734——
LSTMHorizon=62026.010.0221—0.02520.25330.9916——
TCLNHorizon=122026.010.024—0.0290.29160.984——
CNNHorizon=122026.010.0261—0.03150.31720.9722——
TS-Conv-LSTMHorizon=242026.010.0262—0.03380.34060.979——
LSTNetHorizon=32026.010.0281—0.03620.36440.9831——
DA-Conv-LSTMHorizon=242026.010.0283—0.03660.36820.9692——
CNNHorizon=242026.010.0299—0.0350.3520.9696——
LSTMHorizon=122026.010.0312—0.03510.35310.9855——
LSTNetHorizon=62026.010.0317—0.04020.40490.9726——
TCLNHorizon=242026.010.0355—0.04140.41680.9622——
LSTMHorizon=242026.010.0387—0.0440.44280.9713——
LSTNetHorizon=122026.010.0408—0.0480.48320.9607——
LSTNetHorizon=242026.010.0465—0.05430.54620.9537——
DA-RNNHorizon=122026.010.0491—0.05370.54090.9756——
DA-RNNHorizon=242026.010.056—0.06130.61720.9729——
TimesFMHorizon=24, Input sequence length=96, Training strategy=Separately trained for each horizon2026.050.1170.03—————
TimesFM2.5Horizon=24, Input sequence length=96, Training strategy=Separately trained for each horizon2026.050.1180.029—————
ChronosHorizon=24, Input sequence length=96, Training strategy=Separately trained for each horizon2026.050.1240.034—————
LeapTSInput length=96, Horizons=P ∈ {18, 24, 36, 48, 60}2026.050.1250.035—————
PatchTSTInput length=96, Horizons=P ∈ {18, 24, 36, 48, 60}2026.050.1260.036—————
FSAHorizon=24, Input sequence length=96, Training strategy=Once-trained (autoregressive step size 3)2026.050.1260.033—————
AMDInput length=96, Horizons=P ∈ {18, 24, 36, 48, 60}2026.050.1280.036—————
PatchTSTHorizon=24, Input sequence length=96, Training strategy=Separately trained for each horizon2026.050.1280.034—————
TimeMixerInput length=96, Horizons=P ∈ {18, 24, 36, 48, 60}2026.050.1290.037—————
AmplifierInput length=96, Horizons=P ∈ {18, 24, 36, 48, 60}2026.050.1320.039—————
iTransformerInput length=96, Horizons=P ∈ {18, 24, 36, 48, 60}2026.050.1360.04—————
Na¨ıveForecast length (H)=48, Lookback length (T)=962025.060.1390.042—————
DeepEDMForecast length (H)=48, Lookback length (T)=962025.060.1420.042—————
DLinearInput length=96, Horizons=P ∈ {18, 24, 36, 48, 60}2026.050.1520.044—————
TimesNetInput length=96, Horizons=P ∈ {18, 24, 36, 48, 60}2026.050.1530.047—————
TimesFM2.5Horizon=48, Input sequence length=96, Training strategy=Separately trained for each horizon2026.050.160.052—————
TimesFMHorizon=48, Input sequence length=96, Training strategy=Separately trained for each horizon2026.050.170.061—————
PatchTSTHorizon=48, Input sequence length=96, Training strategy=Separately trained for each horizon2026.050.1760.062—————
FSAHorizon=48, Input sequence length=96, Training strategy=Once-trained (autoregressive step size 3)2026.050.180.068—————
ChronosHorizon=48, Input sequence length=96, Training strategy=Separately trained for each horizon2026.050.180.071—————
SARAFHorizon=96, Look-back window=7202026.060.2020.085—————
DB2-TransFPrediction Length=962025.120.2030.083—————
PatchTSTHorizon=962024.120.2050.088—————
PatchTSTPrediction Length=962025.120.2050.088—————
GeoCertLookback Length (L)=96, Forecast Length (T)=962026.040.2050.084———24.9—
PatchTSTLookback Length (L)=96, Forecast Length (T)=962026.040.2050.088—————
iTransformerHorizon=962024.120.2060.086—————
iTransformerPrediction Length=962025.120.2060.086—————
iTransformerLookback Length (L)=96, Forecast Length (T)=962026.040.2060.086—————
GPHTHorizon (H)=96, Lookback Window (L)=336, Method Category=Ours, Training Protocol=Fine-tuned2024.020.2070.087—————
PatchTSTHorizon (H)=96, Lookback Window (L)=336, Method Category=Self-supervised, Training Protocol=Standard2024.020.2070.088—————
S-MambaHorizon=962024.120.2070.086—————
GG-SSMHorizon=962024.120.20730.0878—————
GPHT*Horizon (H)=96, Lookback Window (L)=336, Method Category=Ours, Training Protocol=Pre-trained2024.020.2160.096—————
RLinearHorizon=962024.120.2170.093—————
RLinearPrediction Length=962025.120.2170.093—————
RLinearLookback Length (L)=96, Forecast Length (T)=962026.040.2170.093—————
TiDEHorizon=962024.120.2180.094—————
DLinearHorizon=962024.120.2180.088—————
TiDEPrediction Length=962025.120.2180.094—————
DLinearPrediction Length=962025.120.2180.088—————
TiDELookback Length (L)=96, Forecast Length (T)=962026.040.2180.094—————
DLinearLookback Length (L)=96, Forecast Length (T)=962026.040.2180.088—————
TransformerHorizon=48, Input sequence length=96, Training strategy=Separately trained for each horizon2026.050.2210.09—————
TimesFM2.5Horizon=96, Input sequence length=96, Training strategy=Separately trained for each horizon2026.050.2230.102—————
iTransformerHorizon (H)=96, Lookback Window (L)=336, Method Category=Supervised, Training Protocol=Standard2024.020.2250.099—————
TimesNetHorizon=962024.120.2340.107—————
TimesNetPrediction Length=962025.120.2340.107—————
TimesNetLookback Length (L)=96, Forecast Length (T)=962026.040.2340.107—————
PatchTSTHorizon=96, Input sequence length=96, Training strategy=Separately trained for each horizon2026.050.2450.125—————
FSAHorizon=96, Input sequence length=96, Training strategy=Once-trained (autoregressive step size 3)2026.050.2460.127—————
TSMixerInput length=96, Horizons=P ∈ {18, 24, 36, 48, 60}2026.050.2480.105—————
ChronosHorizon=96, Input sequence length=96, Training strategy=Separately trained for each horizon2026.050.2760.174—————
FEDformerPrediction Length=962025.120.2780.148—————
FEDformerLookback Length (L)=96, Forecast Length (T)=962026.040.2780.148—————
TransformerHorizon=24, Input sequence length=96, Training strategy=Separately trained for each horizon2026.050.2790.142—————
DB2-TransFPrediction Length=1922025.120.2940.169—————
GeoCertLookback Length (L)=96, Forecast Length (T)=1922026.040.2980.175———77.2—
S-MambaHorizon=1922024.120.2990.177—————
iTransformerHorizon=1922024.120.2990.177—————
iTransformerPrediction Length=1922025.120.2990.177—————
PatchTSTPrediction Length=1922025.120.2990.176—————
iTransformerLookback Length (L)=96, Forecast Length (T)=1922026.040.2990.177—————
PatchTSTLookback Length (L)=96, Forecast Length (T)=1922026.040.2990.176—————
GG-SSMHorizon=1922024.120.30290.1813—————
RLinearHorizon=1922024.120.3070.184—————
PatchTSTHorizon=1922024.120.3070.184—————
TiDEHorizon=1922024.120.3070.184—————