Beyond Historical Data: Adaptive Synthesis for Financial Time Series

Background In quantitative finance, concept drift and non‑stationary distributions cause a gap between training and real‑world performance, leading to over‑fitting of models trained on static historical data. The authors identify data management as a core obstacle and note the lack of generic time‑series augmentation benchmarks that preserve financial fidelity.

Problem Definition The goal is to design an adaptive data‑stream system that continuously manages evolving financial data, generates diverse yet realistic synthetic samples, and dynamically adjusts synthesis operations based on model feedback to enhance robustness and risk‑adjusted returns.

Method

3.1 Overall Workflow A data‑operation module M uses an operation‑selection probability matrix p and intensity parameters λ to produce augmented training samples x_{train}. A learnable planner g_{φ} models a strategy π_{φ}(p, λ | f, x_i), while a scheduler determines the proportion α of data to transform using a heuristic algorithm. Task model updates and planner updates alternate on validation feedback, preserving provenance for exact replay. The adaptive augmentation curriculum is cast as a bi‑level optimization problem.

3.2 Parametric Data‑Operation Module Designed for financial time‑series statistics, the module consists of four tightly coupled components:

Transformation Layer : Single‑stock transformations (jittering, scaling, magnitude warping, permutation, STL augmentation) with intensity λ controlling noise level, scaling factor, warping strength, segment count, and seasonal period.

Management and Normalization Layer : After transformation, the highest price feature is set as High and the lowest as Low to maintain financial consistency. Multi‑stock mixing uses rolling‑window standard normalization per feature, with inverse normalization applied when re‑entering the workflow.

Mixing Layer : Multi‑stock mixing selects the top‑ k target stocks b most cointegrated with source stock a (based on p‑value). Operation intensity λ biases the selection probability, and the normalized probability Q is sampled to choose b. Mixing strategies include CutMix, Linear Mix, Amplitude Mix, and the Demirel‑Holz method, each governed by its own λ.

Interpolation Compensation Layer : To mitigate extreme samples, a binary mix based on mutual information adjusts the interpolation ratio; lower mutual information yields higher weight for synthetic data, preserving task‑relevant structure.

3.3 Curriculum Planner The planner learns a policy that selects p and λ conditioned on the task model f_{θ} and input x_i. State features include high‑level representations of f_{θ} (extracted from the penultimate fully‑connected layer) and statistical descriptors of x_i (mean, volatility, momentum, skewness, kurtosis, trend). A Sharpe‑ratio‑inspired loss penalizes volatility, guiding the planner toward risk‑aware augmentation.

3.4 Overfitting‑Aware Scheduler The scheduler controls the data‑operation ratio α, increasing it over training epochs to form a soft curriculum. If validation loss does not improve beyond a threshold, a penalty term R_{penalty} is removed to allow more aggressive augmentation.

3.5 Planner Training Scheme Planner g_{φ} and task model f_{θ} are trained alternately: the task model updates every training step, while the planner updates every freq steps using a validation copy f_{θ'}. The planner learns p by generating all augmentation combinations, weighting them, and optimizing λ via a straight‑through gradient estimator.

Experiments

4.1 Experimental Setup Datasets include DJIA stock prices (2000‑01‑01 to 2024‑01‑01) and a cryptocurrency set (BTC, ETH, DOT, LTC, 2023‑09‑27 to 2025‑09‑26), split 60/20/20 for train/val/test. Baselines for synthetic data are TimeGAN, SigCWGAN, RCWGAN, GMMN, CWGAN, RCGAN, and Diffusion‑TS. Workflow baselines are Original, RandAugment, TrivialAugment, and AdaAug. Prediction models: GRU, LSTM, DLinear, TCN, Transformer. RL agents: DQN, PPO with a discrete action space {‑1,0,1} and transaction cost c = 10^{-3}. Evaluation metrics: MSE, MAE, STD for prediction; total return (TR) and Sharpe ratio (SR) for RL.

4.2 Main Results

Prediction Tasks The proposed system reduces MSE, MAE, and loss STD across all models. Strong models (GRU, LSTM, Transformer) benefit from random augmentation, while weaker models (DLinear, TCN) may suffer, highlighting the planner’s role in providing model‑agnostic curricula. Compared with AdaAug, performance gains confirm the scheduler’s effectiveness.

RL Trading Tasks Applying the planner trained on 1‑day return prediction to single‑stock trading (with mixing disabled) improves profit and reduces risk, demonstrating transferability. For INTC, DQN achieves slightly lower total return but markedly higher risk‑adjusted return.

Ablation Studies Removing the multi‑stock mixing module consistently worsens MSE, MAE, and STD, indicating cross‑asset information is crucial. Replacing the adaptive scheduler with a fixed one degrades performance, underscoring the importance of a learnable curriculum. Disabling both scheduler and planner (equivalent to TrivialAug/RandAug) further harms results, especially for TCN and Transformer.

Data Quality Assessment t‑SNE visualizations show progressive, controllable shifts in synthetic data distribution as λ varies, confirming tunability. Distribution comparisons reveal that augmented training samples are closer to the test distribution, addressing concept drift.

Downstream Usability Using LSTM to predict DJIA closing price direction shows all operations improve classification accuracy. A post‑hoc RNN discriminator assigns the lowest score to the proposed synthetic data, indicating high financial fidelity.

Market Real‑World Case Statistical properties (return autocorrelation, absolute‑return autocorrelation, leverage effect) of the enhanced data match those of real market data better than other baselines.

Additional Analyses Visualizing operation weights p reveals evolution with task‑model training and significant differences across models, confirming the planner’s model‑agnostic adaptation.

Conclusion The drift‑aware data‑stream framework unifies data augmentation, curriculum learning, and workflow management within a single differentiable pipeline, delivering traceable replay, continuous quality monitoring, and substantial gains in robustness and risk‑adjusted performance for both prediction and reinforcement‑learning trading tasks.