Evaluating Time Series Predictability via Transition Graph Analysis

This study is focused on exploring time series intrinsic predictability using transition graph analysis. The goal is to find out whether a special graph that reproduces system transition along its trajectory in the state space is useful for distinguishing time series of “good” and “bad” predictability. We perform a state space clustering to construct a weighted and directed transition graph and then to calculate different graph characteristics. We train several predictive models (in particular, the well-known auto-regression, singular spectrum analyses, artificial neural network and specific dynamic models of local approximation and maximal similarity) for time series and apply k-means algorithm to divide the set of the series into two parts using the properties of the corresponding transition graph. As a result we have artificial and real-world datasets divided into two clusters in one of which the mean forecasting error is much less than in the other. The F1-score value (≈ 0.87) for this clustering shows that our approach performs better than those in some related works. We also train several classification models on a set of artificial series so that they are able to distinguish real-world time series of “good” and “bad” predictability. The results of this work can be used for data engineering in time series forecasting tasks and for predictive model design and evaluation. The datasets, the framework implementation and the results related to our study are publicly available on GitHub.