Estimating Predictability: Redundancy and Surrogate Data Method

TL;DR

This paper introduces a method to estimate the predictability of time series using information-theoretic measures and surrogate data, enabling classification of series as predictable or unpredictable and assessing the nature of predictability.

Contribution

The paper presents a novel approach combining redundancy measures and surrogate data techniques to evaluate the theoretical predictability of time series.

Findings

Method effectively distinguishes predictable from unpredictable series.

Application to foreign exchange data demonstrates practical utility.

Comparison with nonlinear predictor shows consistent results.

Abstract

A method for estimating theoretical predictability of time series is presented, based on information-theoretic functionals---redundancies and surrogate data technique. The redundancy, designed for a chosen model and a prediction horizon, evaluates amount of information between a model input (e.g., lagged versions of the series) and a model output (i.e., a series lagged by the prediction horizon from the model input) in number of bits. This value, however, is influenced by a method and precision of redundancy estimation and therefore it is a) normalized by maximum possible redundancy (given by the precision used), and b) compared to the redundancies obtained from two types of the surrogate data in order to obtain reliable classification of a series as either unpredictable or predictable. The type of predictability (linear or nonlinear) and its level can be further evaluated. The method is demonstrated using a numerically generated time series as well as high-frequency foreign exchange data and the theoretical predictability is compared to performance of a nonlinear predictor.