Using Fractal Dimension and Recurrence Analysis to Study Market Regimes
Summary
The article presents nonlinear time-series tools for examining financial-market structure. It explains estimating fractal dimension with a box-counting procedure: cover a price series at several scales, count the required boxes, and fit a line to the logarithms of scale and count. Changes in the estimate are proposed as clues to transitions among smoother, trending, and more irregular market conditions. It also introduces recurrence plots, built by reconstructing states in phase space and marking pairs of sufficiently similar states, with recurrence rate, determinism, and laminarity used to summarize patterns. MQL5 indicator implementations and an expert-advisor example are discussed, and the conclusion reports tests across currency pairs with profitability varying by instrument. The text gives no detailed numerical results or robust validation protocol, so those claims do not establish general predictive value. It acknowledges that markets have many interacting influences and that chaotic dynamics limit long-range forecasts; the measures are best treated as exploratory inputs alongside other methods.
Key ideas
- Box counting estimates fractal dimension from how the number of covering boxes changes across scales.
- Fractal-dimension shifts may help identify changes in market behavior, though they do not prove predictability.
- Recurrence plots compare reconstructed time-series states to reveal repeated structures and possible regime changes.
- Recurrence rate, determinism, and laminarity summarize distinct aspects of recurrence patterns.
- The article reports uneven currency-pair test results and emphasizes the limits of long-term forecasting.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.