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

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.