Forecasting multivariate time series remains challenging due to complex cross-variable dependencies and the presence of heterogeneous external influences. This paper presents Spectrogram-Enhanced Multimodal Fusion (SEMF), which combines spectral and temporal representations for more accurate and robust forecasting. The target time series is transformed into Morlet wavelet spectrograms, from which a Vision Transformer encoder extracts localized, frequency-aware features. In parallel, exogenous variables, such as financial indicators and macroeconomic signals, are encoded via a Transformer to capture temporal dependencies and multivariate dynamics. A bidirectional cross-attention module integrates these modalities into a unified representation that preserves distinct signal characteristics while modeling cross-modal correlations. Applied to multiple commodity price forecasting tasks, SEMF achieves consistent improvements over seven competitive baselines across multiple forecasting horizons and evaluation metrics. These results demonstrate the effectiveness of multimodal fusion and spectrogram-based encoding in capturing multi-scale patterns within complex financial time series.
Figures & tables
Figure 1: Overall framework of Spectrogram-Enhanced Multimodal Fusion (SEMF).
Type
Variable
Target
Closing price of target commodity futures
Exogenous
US 10-year Treasury yield
US 2-year Treasury yield
US 3-month Treasury bill yield
US Dollar Index (DXY)
USD to CNY exchange rate
Table 1: Input variables for commodity price forecasting.
Category
Model
Commodity
RMSE ↓
RMAE ↓
MAPE ↓
R2↑
Time series-based
LSTM
Coal
18.86
0.1230
11.4718
-0.1821
Gold
538.60
0.2220
0.2139
-1.5574
Steel
570.24
0.1491
15.6967
-2.6951
iTransformer
Coal
104.09
0.5663
55.7048
-37.7016
Gold
112.52
0.0408
0.0407
0.9660
Steel
183.48
0.0419
4.1703
0.5649
Table 2: Performance comparison across multiple forecasting horizons. Results are averaged over all horizons. Red and blue denote the best and second-best results, respectively.
Model
H
RMSE
RMAE
MAPE
TimesNet
1
73.88
0.0269
0.0262
3
89.43
0.0325
0.0316
7
99.13
0.0363
0.0353
14
116.28
0.0426
0.0415
21
116.14
0.0418
0.0407
35
130.53
0.0469
0.0459
Table 3: Horizon-wise forecasting performance for Gold price forecasts. Best results are shown in red .
Image
RMSE
RMAE
MAPE
Line
187.98
0.0634
0.0617
STFT
173.20
0.0554
0.0544
CMOR
129.93
0.0495
0.0495
Morlet
107.05
0.0361
0.0358
Table 4: Forecasting performance of SEMF with different time-frequency representations.
RMSE
RMAE
MAPE
MLP
273.17
0.1097
0.1095
Transformer
107.05
0.0361
0.0358
Table 5: Comparison of SEMF performance using different Exogenous Feature Encoders (MLP vs. Transformer).
Fusion
RMSE
RMAE
MAPE
Single CA
200.66
0.0766
0.0776
Bi-CA
107.05
0.0361
0.0358
Table 6: Forecasting performance of SEMF with different cross-attention fusion strategies.
Patch
Scale
RMSE
RMAE
MAPE
8
64
199.32
0.0696
0.0670
16
64
142.79
0.0536
0.0524
8
128
107.05
0.0361
0.0358
16
128
181.61
0.0615
0.0587
Table 7: Forecasting performance of SEMF under varying patch sizes and Morlet wavelet scales.
Seq Length
RMSE
RMAE
MAPE
30
269.94
0.1092
0.1101
60
270.05
0.1090
0.1094
90
244.43
0.0848
0.0821
120
107.05
0.0361
0.0358
Table 8: Forecasting performance with different input sequence lengths.
Time series forecasting predicts future values from ordered observations using statistical, neural, and probabilistic models to support decisions under uncertainty.