A Note on A Priori Forecasting and Simplicity Bias in Time Series

TL;DR

This paper explores a method for forecasting time series patterns without fitting to historical data by leveraging simplicity bias and Kolmogorov complexity, achieving high accuracy in predicting pattern likelihoods.

Contribution

It introduces a novel approach to a priori time series forecasting based on complexity bounds, bypassing traditional data fitting methods.

Findings

Predicted pattern probabilities without data fitting.

Achieved ~80% accuracy in likelihood comparisons.

Demonstrated practical potential for complexity-based forecasting.

Abstract

To what extent can we forecast a time series without fitting to historical data? Can universal patterns of probability help in this task? Deep relations between pattern Kolmogorov complexity and pattern probability have recently been used to make \emph{a priori} probability predictions in a variety of systems in physics, biology and engineering. Here we study \emph{simplicity bias} (SB) -- an exponential upper bound decay in pattern probability with increasing complexity -- in discretised time series extracted from the World Bank Open Data collection. We predict upper bounds on the probability of discretised series patterns, without fitting to trends in the data. Thus we perform a kind of `forecasting without training data', predicting time series shape patterns \emph{a priori}, but not the actual numerical value of the series. Additionally we make predictions about which of two discretised series is more likely with accuracy of $\sim$80\%, much higher than a 50\% baseline rate, just by using the complexity of each series. These results point to a promising perspective on practical time series forecasting and integration with machine learning methods.