Scaling Law for Large-Scale Pre-Training Using Chaotic Time Series and Predictability in Financial Time Series

Time series forecasting plays a critical role in decision-making processes across diverse fields including meteorology, traffic, electricity, economics, finance, and so on. Especially, predicting returns on financial instruments is a challenging problem. Some researchers have proposed time series foundation models applicable to various forecasting tasks. Simultaneously, based on the recognition that real-world time series exhibit chaotic properties, methods have been developed to artificially generate synthetic chaotic time series, construct diverse datasets and train models. In this study, we propose a methodology for modeling financial time series by generating artificial chaotic time series and applying resampling techniques to simulate financial time series data, which we then use as training samples. Increasing the resampling interval to extend predictive horizons, we conducted large-scale pre-training using 10 billion training samples for each case. We subsequently created test datasets for multiple timeframes using actual Bitcoin trade data and performed zero-shot prediction without re-training the pre-trained model. The results of evaluating the profitability of a simple trading strategy based on these predictions demonstrated significant performance improvements over autocorrelation models. During the large-scale pre-training process, we observed a scaling law-like phenomenon that we can achieve predictive performance at a certain level with extended predictive horizons for chaotic time series by increasing the number of training samples exponentially. If this scaling law proves robust and holds true across various chaotic models, it suggests the potential to predict near-future events by investing substantial computational resources. Future research should focus on further large-scale training and verifying the applicability of this scaling law to diverse chaotic models.