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Measure of predictability
Weiguang Yao1, Christopher Essex, Pei Yu
1Applied Mathematics Department, University of Western Ontario, London, Ontario, Canada N6A 5B7. wgyao@uwo.ca
Summary
This study introduces forecast entropy, a new measure for time series predictability. It quantizes how predictable a time series is, aiding in analyzing chaotic and random systems.
Area of Science:
- * Data Science
- * Chaos Theory
- * Time Series Analysis
Background:
- * Existing methods for measuring time series forecasting difficulty are numerous.
- * Quantifying the inherent predictability of time series data remains a challenge.
Purpose of the Study:
- * To introduce a novel measure, forecast entropy, for quantifying time series predictability.
- * To establish a standardized method for assessing the predictability of time series data.
Main Methods:
- * Reconstructing attractors from time series data.
- * Analyzing data distributions in regular and tangent spaces across different scales.
- * Developing a formula for calculating forecast entropy.
- * Defining an idealized random system for normalization.
Main Results:
- * Forecast entropy successfully measures the predictability of time series.
- * The measure distinguishes between chaotic and pseudorandom systems.
- * Forecast entropy aids in selecting optimal parameters for attractor reconstruction.
Conclusions:
- * Forecast entropy provides a robust tool for time series predictability assessment.
- * The method offers insights into the underlying dynamics of deterministic and random systems.
- * This measure can optimize attractor reconstruction for improved time series analysis.
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