Operator Analysis of MACD
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916970632314880 |
|---|---|
| author | Li, Yuelong |
| author_facet | Li, Yuelong |
| contents | This paper develops a rigorous functional-analytic framework for the MACD (Moving Average Convergence Divergence) indicator, a classical tool in technical analysis. We show that MACD, commonly defined as the difference between two moving averages, can be precisely interpreted as a phase-corrected, smoothed derivative operator. By analyzing nested and recursive moving averages, we establish that MACD is structurally equivalent to a band-pass filter and derive exact formulas expressing it as a finite difference of delayed and doubly averaged signals. We prove new operator identities demonstrating that MACD corresponds to the derivative of a phase-centered, double-smoothed average, appropriately delayed to correct for asymmetries introduced by causal averaging. This characterization unifies MACD with concepts from harmonic analysis and operator theory, providing a principled basis for understanding its role in signal detection, filtering, and trend analysis. The framework naturally generalizes to recursive decompositions, culminating in an expansion that expresses MACD as a weighted sum of delayed, smoothed derivatives, thereby revealing the true analytical structure underlying this widely used yet traditionally heuristic indicator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21326 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Operator Analysis of MACD Li, Yuelong Mathematical Finance This paper develops a rigorous functional-analytic framework for the MACD (Moving Average Convergence Divergence) indicator, a classical tool in technical analysis. We show that MACD, commonly defined as the difference between two moving averages, can be precisely interpreted as a phase-corrected, smoothed derivative operator. By analyzing nested and recursive moving averages, we establish that MACD is structurally equivalent to a band-pass filter and derive exact formulas expressing it as a finite difference of delayed and doubly averaged signals. We prove new operator identities demonstrating that MACD corresponds to the derivative of a phase-centered, double-smoothed average, appropriately delayed to correct for asymmetries introduced by causal averaging. This characterization unifies MACD with concepts from harmonic analysis and operator theory, providing a principled basis for understanding its role in signal detection, filtering, and trend analysis. The framework naturally generalizes to recursive decompositions, culminating in an expansion that expresses MACD as a weighted sum of delayed, smoothed derivatives, thereby revealing the true analytical structure underlying this widely used yet traditionally heuristic indicator. |
| title | Operator Analysis of MACD |
| topic | Mathematical Finance |
| url | https://arxiv.org/abs/2509.21326 |