On a Moving Average with Internal Degrees of Freedom

TL;DR

This paper introduces a novel moving average that incorporates an eigenproblem-derived polynomial weight, enabling immediate switching without lag, unlike traditional moving averages with fixed internal time scales.

Contribution

It develops a new moving average method using polynomial weights from eigenfunctions, allowing real-time switching and improved responsiveness.

Findings

Enables immediate switching without lag

Incorporates eigenproblem-derived polynomial weights

Improves responsiveness over traditional moving averages

Abstract

A new type of moving average is developed. Whereas a regular moving average (e.g. of price) has a built-in internal time scale (time-window, exponential weight, etc.), the moving average developed in this paper has the weight as the product of a polynomial by window factor. The polynomial is the square of a wavefunction obtained from an eigenproblem corresponding to other observable (e.g. execution flow I=dV/dt , the number of shares traded per unit time). This allows to obtain an immediate "switch" without lagging typical for regular moving average.