Ordinal Pattern Networks for Measuring Market Structure and Efficiency
Summary
The article develops an ordinal-pattern transition network as a way to characterize price shape without relying on price levels or move sizes. It converts each rolling window into a symbol representing the rank order of its values, then treats symbols as network nodes and observed transitions between them as directed edges. A Lehmer code assigns each ordering a unique index; flat windows are excluded because they contain no ranking information.
The network supports measures including permutation entropy, time irreversibility, and the fraction of forbidden transitions, which the article uses to describe efficiency and directional structure. The author reports that initial readings on EUR/USD barely moved, then describes parameter sweeps and adjustments that made the metrics more visible, including encoding returns over a short window and applying rolling-percentile normalization to entropy. These observations are exploratory rather than proof of predictive trading value. The factorial growth in possible patterns also means higher embedding dimensions require more data for reliable estimates.
Key ideas
- Ordinal patterns encode the relative ordering of prices in a rolling window while discarding their magnitudes.
- A Lehmer code maps each ordering to a distinct network node, and successive patterns define directed transitions.
- Permutation entropy, time irreversibility, and forbidden-transition share provide different measures of market structure.
- The article reports that parameter choices and normalization affected whether the metrics visibly varied on EUR/USD.
- The number of possible patterns grows factorially, increasing data needs as embedding dimension rises.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.