Journal of Investment Strategies
ISSN:
2047-1238 (print)
2047-1246 (online)
Editor-in-chief: Ali Hirsa
Need to know
- This paper discusses an application of information-theoretic concepts to moving averages of time series.
- Moving average weighting functions are defined as maximum entropy distributions subject to constraints.
- Constraining the width yields the simple moving average, while constraining the time scale yields the exponential moving average.
- Generalised constraints and entropies define a wide family of moving average weighting functions.
Abstract
This paper discusses the application of information-theoretic concepts to the backward filtering of time series using moving averages. We identify moving averages as time-dependent expectation values derived from maximum entropy probability kernels that are subject to relevant constraints. Constraining the width of the kernel results in the simple moving average, while constraining the typical timescale yields the exponential moving average. With a martingale constraint, we derive a moving average corresponding to a risk-neutral valuation scheme for financial time series. By expanding this framework to generalized forms of entropy, we introduce a broad family of maximum-entropy-based moving averages.
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