A symbolic analysis of observed time series requires a discrete partition of a continuous state space containing the dynamics. A particular kind of partition, called "generating," preserves all deterministic dynamical information in the symbolic representation, but such partitions are not obvious beyond one dimension. Existing methods to find them require significant knowledge of the dynamical ...

With time series data, there is often the issue of finding accurate approximations for the variance of such quantities as the sample autocovariance function or spectral estimate. Smith and Field (1993) proposed a variance estimate motivated by resampling in the frequency domain. In this paper we present some results on the cumulants of this and other frequency domain estimates obtained via symb...

Macro-economic models describe the dynamics of economic quantities. The estimations and forecasts produced by such models play a substantial role for financial and political decisions. In this contribution we describe an approach based on genetic programming and symbolic regression to identify variable interactions in large datasets. In the proposed approach multiple symbolic regression runs ar...

This is an investigation of forecasting stock returns using genetic programming. We first test the hypothesis that genetic programming is equally successful in predicting series produced by data generating processes of different structural complexity. After rejecting the hypothesis, we measure the complexity, of thirty-two time series representing four different frequencies of eight stock retur...

In this paper we investigate new methods to build and evaluate interpretable predictive models for time series data using symbolic regression and generalized additive models. We propose a novel framework to iteratively build a model while maintaining model interprebility as accuracy and complexity increase. We also propose multiple methods that ease interpretation of the built model, the model ...

Analysis of finite, noisy time series data leads to modern statistical inference methods. Here we adapt Bayesian inference for applied symbolic dynamics. We show that reconciling Kolmogorov's maximum-entropy partition with the methods of Bayesian model selection requires the use of two separate optimizations. First, instrument design produces a maximum-entropy symbolic representation of time se...

Positively charged: We look back at the developments of 2021 and give a glimpse to what our readers authors can expect in 2022. The past few years have been very exciting for field electrochemical energy storage. Batteries particular become an essential technology achieving carbon neutrality as well key component next-generation transport renewable solutions. It has real pleasure witness rapid ...