Graph Learning for FX Rate Prediction

• The paper demonstrates that GNN-based models and tensor-train compression outperform traditional approaches in forecasting FX rates with improved accuracy and risk-adjusted returns.
• Graph learning is defined as the application of network representations and geometric deep learning to capture multi-currency interdependencies and market dynamics.
• Innovative techniques such as spatiotemporal graphs, structural embeddings, and dual-stage attention models enhance FX trading strategies and statistical arbitrage optimization.

Graph learning for foreign exchange (FX) rate prediction encompasses a collection of methodologies that exploit the relational and temporal structure of financial markets by representing currencies, rates, and associated features as graphs. These approaches leverage modern developments in geometric deep learning, complex networks, and tensor-based compression to forecast FX rates, identify arbitrage opportunities, and construct high-performing trading agents. The field has advanced with bespoke graph-construction pipelines, message-passing graph neural networks (GNNs), graph-theoretic embeddings, and hybrid integration with reinforcement learning. Recent empirical evidence demonstrates that graph-learning approaches outperform standard recurrent or fully-connected models in both predictive accuracy and portfolio risk-adjusted return, particularly when modeling multi-currency dependencies and market microstructure constraints (Hong et al., 20 Aug 2025, Xu et al., 2020, Wu et al., 2021).

1. Graph Representations of Foreign Exchange Markets

FX markets are naturally multi-relational: currencies form nodes and pairs (exchanges) define edges. Distinct graph construction strategies have emerged:

• Currency-graph construction: Nodes represent currencies, and edges represent tradable pairs with associated attributes such as spot/forward rate differentials ("carry"). Adjacency matrices encode magnitude of economic signals, e.g., $a_{i,j} = |c_{i,j}|$ with $c_{i,j}$ quantifying the FX carry between currencies $i$ and $j$ (Xu et al., 2020).
• Spatiotemporal graphs: Extend static FX graphs over discrete time, so each timestep $t$ holds a graph $G_t = (V, E_t, X_t^v, X_t^e)$ where $X_t^v$ (node features) includes government bond yields and $X_t^e$ (edge features) contains spot rates (Hong et al., 20 Aug 2025).
• Visibility graphs for time series: Constructs nodes for each timepoint in an FX rate series, connecting timepoints $(i, j)$ by a visibility criterion based on price trajectory convexity, capturing long-range temporal dependencies (Wu et al., 2021).

Graph formation can incorporate multi-modal data (prices, volumes, volatilities), fundamental economic priors (interest rates), or statistical features (structural influence scores).

2. Graph-based Feature Extraction and Embedding Methodologies

Graph learning in FX prediction employs a range of embedding and compression techniques to reduce dimensionality and retain structural information.

• Graph neural network (GNN) layers: Message-passing GNNs update both node and edge features by aggregating information from neighbors. For each layer $l$, node and edge embeddings are iteratively refined:

$$n^l_i = \frac{1}{|N(i)|} \sum_{j \in N(i)} \textrm{MLP}_{N,l}[n_i^{l-1}; e_{ji}^{l-1}; n_j^{l-1}], \quad e^l_{ij} = \textrm{MLP}_{E,l}[n_i^l; e_{ij}^{l-1}; n_j^l]$$

capturing both direct and indirect (multi-leg) relationships among currencies (Hong et al., 20 Aug 2025).

• Tensor-train (TT) compression: Multi-modal tensors representing FX data (prices, volumes, volatility) are compressed using the TT format, reducing parameter complexity from exponential in the tensor's order to linear in modes and TT ranks. All dense layers in the Multi-Graph Tensor Network (MGTN) can be tensorized for tractable training and inference (Xu et al., 2020).
• Structural graph embeddings: The struc2vec algorithm encodes nodes' structural equivalence using random walks over a hierarchy of auxiliary graphs, yielding embeddings amenable to downstream neural prediction, particularly effective with visibility or temporal graphs (Wu et al., 2021).
• Node weighting via structural centrality: The collective influence (CI) statistic, computed over local balls in the graph, serves as a priori knowledge to direct attention in temporal models (Wu et al., 2021).

These methodologies enable the encoding of complex multi-currency, temporal, and structural relationships that underlie FX market dynamics.

3. Learning and Prediction Frameworks

• FX rate prediction as edge-level regression: The prediction task is formalized as minimizing, over network parameters $\theta$,

$$\min_{\theta} \sum_{t=1}^T \sum_{(i,j) \in \Upsilon_t} \|f_{\theta}(G_{1:t-1}; i,j) - r_{t+\Delta}^{(i \rightarrow j)}\|^2 + \lambda\|\theta\|^2$$

where $f_\theta$ is a GNN-based predictor, and $\Upsilon_t$ is the subset of edges targeted at time $t$ (Hong et al., 20 Aug 2025).

• Trading agent architectures: Predictive features extracted from MGTN or graph-attention RNNs can be integrated into Deep Q-Network (DQN) agents, producing Q-values for buy/sell decisions on each currency pair. The RL agent is trained using Double DQN with experience replay, Bellman-error loss, and periodically updated target networks (Xu et al., 2020).
• Dual-stage attention models: CI-weighted temporal attention in LSTM decoders enhances the selection of influential timepoints, improving the modeling of chaotic bursts and long-range memory in FX time series (Wu et al., 2021).
• Statistical arbitrage optimization: Predicted rates inform a portfolio allocation problem (FXSA) that maximizes risk-adjusted return under budget, zero-net holding, and no-direct-arbitrage constraints, solved by projecting unconstrained flows onto a feasible subspace and applying ReLU for non-negativity (Hong et al., 20 Aug 2025).

The integration of structural graph information, tensor network layers, and reinforcement learning forms a core methodological advancement in graph-based FX forecasting.

4. Empirical Results and Comparative Performance

Comprehensive benchmarking across recent studies supports the effectiveness of graph-learning approaches in FX rate prediction and trading:

Model/Method	Return (%)	Sharpe	Sortino	Hit Rate (%)	Parameters	Notes
fMGTN-DQN (Xu et al., 2020)	0.80	0.0445	—	52.8	531	FX-9c basket, minutely
GRU (Xu et al., 2020)	0.03	0.0012	—	50.4	3107
TTNN (Xu et al., 2020)	0.16	0.0064	—	50.6	—
GCN (Xu et al., 2020)	-0.05	-0.0032	—	50.2	5891
GNN FXSA (Hong et al., 20 Aug 2025)	—	43.80	47.38	—	—	10 currencies, daily, 1995–24

• The fMGTN–DQN framework achieves higher returns (+0.80%) and Sharpe ratios (0.0445) with just 531 trainable parameters, constituting a 90% reduction compared to standard GCNs (Xu et al., 2020).
• In a 10-currency statistical arbitrage (FXSA) setting, graph learning with GNNs yields 61.9% higher information ratio and 45.5% higher Sortino ratio versus a linear-programming benchmark, with 52% lower volatility and 44% reduced maximum drawdown; all improvements are statistically significant (Hong et al., 20 Aug 2025).
• Visibility-graph LSTM pipelines report classification accuracies of 62–64% on hourly EUR/USD, maintaining positive P&L after realistic round-trip costs (Wu et al., 2021).

These outcomes indicate the capacity of graph-learning models to outperform sequence-based and fully-connected network baselines, both in predictive accuracy and in portfolio-level risk metrics.

5. Practical Considerations and Domain-Specific Adaptations

Graph-learning models for FX forecasting incorporate several FX market aspects:

• Multi-currency coupling: Edge-level GNNs allow dynamic modeling of triangular (tri-currency) arbitrage, cross-currency influences, and indirect hedges (Hong et al., 20 Aug 2025).
• Interest rate integration: Node features commonly include sovereign interest rates, critical for accounting for carry trade effects (Hong et al., 20 Aug 2025, Xu et al., 2020).
• Market microstructure constraints: Proposals enforce unit budget, zero net holdings (for all non-home currencies), and prohibit direct two-leg arbitrage within allocation optimization (Hong et al., 20 Aug 2025).
• Temporal structure: Time-lag modeling distinguishes between observation and execution, reflecting market mechanics (e.g., overnight settlement) and enabling proper out-of-sample evaluation (Hong et al., 20 Aug 2025).
• Liquidity and regime changes: Different window lengths and graph features may be required to capture high-frequency, 24×5 trading and macroeconomic regime shifts (Wu et al., 2021).

Empirical protocols for evaluation include rolling out-of-sample tests, matched-trade historical backtests, and reporting of returns, risk (Sharpe/Sortino), drawdown, and trade hit rates.

6. Connections to Related Fields and Extensions

Graph learning in FX prediction is anchored in broader developments:

• Message-passing and geometric deep learning: Building upon GNNs for dynamic networks, these methods bridge time series modeling and relational reasoning.
• Tensor network compression: The use of tensor-train and related decompositions aligns with efforts to compress deep learning architectures without sacrificing accuracy, allowing deployment in high-frequency, low-latency FX settings (Xu et al., 2020).
• Complex network theory: Techniques such as visibility graphs and collective influence scores import tools from statistical physics and network science into financial time series analysis (Wu et al., 2021).
• Statistical arbitrage and portfolio optimization: The explicit enforcement of arbitrage constraints and maximization of risk-adjusted return relate to classical market making, but enhanced by contemporaneous predictive and structural learning.

A plausible implication is that such frameworks could generalize to other asset classes with networked dependencies (e.g., cryptocurrencies, commodity pairs) or be adapted for regime-aware trading under changing macroeconomic conditions.

7. Limitations and Outlook

Current graph-based FX rate prediction approaches face:

• Scalability: As the currency universe grows, so does the edge set. Tensor compression alleviates parameter bloat but may introduce trade-offs in representation (Xu et al., 2020).
• Data requirements and regime sensitivity: Changing micro- and macrostructure, such as central bank interventions, necessitate frequent recalibration and careful feature engineering (Wu et al., 2021).
• Transaction costs and liquidity constraints: Realistic backtesting highlights the need to model bid/ask spreads and finite market depth; predictions must be robust to microstructure noise (Wu et al., 2021).
• Model interpretability and regulatory context: The complexity of GNNs and tensor networks can obscure the economic rationale for signals, an active area for explainable AI research.

Future research may explore adaptive graph architectures, online learning under non-stationarity, and the integration of exogenous signals (e.g., macroeconomic news) into graph-based FX trading frameworks.

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Graph learning establishes a rigorous framework for modeling and predicting FX rate dynamics by encoding currencies, exchange rates, economic covariates, and market structure into graph-structured data subjected to advanced neural and statistical learning algorithms. Empirical evidence supports its superiority over traditional sequence and tabular models in both accuracy and risk-adjusted performance for FX rate prediction and statistical arbitrage (Hong et al., 20 Aug 2025, Xu et al., 2020, Wu et al., 2021).