Direct answer
You can use the U.S. Dollar Index (often called DXY) with forex by treating it as its own time series and then measuring how its market behavior changes relative to a forex pair. In the Fractal Dimension Index (FDI) approach, the practical idea is to compare “fractal dimension/roughness” shifts across (1) the dollar index and (2) a currency pair, and then look for consistent, testable relationships—without assuming that the dollar index directly predicts price moves.
Mechanics: what to compute and what to compare
Start by defining two synchronized datasets: the DXY series and the forex pair series (for example, EUR/USD or USD/JPY). FDI-style indicators typically estimate how “complex” or “rough” recent price movement is, based on how price changes across different time scales. The key workflow is:
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Choose a consistent time scale Pick a bar interval for both series (for example, daily or 1-hour). Fractal/FDI estimates depend on the sampling frequency, so mixing timeframes can create misleading comparisons.
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Compute an FDI (or FDI-like) value for each series Run the same FDI calculation on DXY and on the forex pair. Even if you implement FDI differently in tools, the comparison only makes sense if the measurement logic is consistent within each series.
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Align and compare changes, not just levels Rather than assuming a static relationship, compare whether shifts in FDI (for example, moving from lower to higher values) occur around the same periods for DXY and the pair. This can be framed as regime detection: “rougher” behavior may cluster in certain market conditions.
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Add a simple dependency check Use an out-of-sample test of association between FDI changes in DXY and FDI changes in the forex pair. For example, you can check whether periods where DXY FDI rises are followed by a higher frequency of elevated FDI on the pair, compared with random baselines.
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Interpret direction carefully FDI does not provide a direction signal by itself; it describes structure/complexity of movement. Any direction inference must come from separately measured price-response statistics, and those must be validated.
Example checks you can run without assuming a prediction
Consider two approaches you can evaluate independently.
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FDI co-movement (structure alignment): Compute FDI for DXY and for a forex pair. Then measure how often both indicators move into “high-roughness” states around the same dates.
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Regime-conditioned behavior: Split history into windows where DXY FDI is relatively higher versus lower. Within each regime, check how the forex pair’s own FDI behaves. If the relationship changes dramatically across regimes, the dollar index may be acting more as a regime context than a stable driver.
These checks answer whether the dollar index provides useful context for volatility/complexity rather than a direct forecasting rule.
Limitations and risks
- FDI/FDI-like estimates are noisy and sensitive to parameters (window length, sampling frequency, and calculation details). Small implementation differences can change results.
- Correlations between DXY behavior and forex pairs can shift over time. A relationship found in one period may not hold in another.
- Complexity measures describe structure, not direction. Any attempt to infer buy/sell timing from FDI must be validated with strict, out-of-sample testing.
- No real-time guarantees: this framework is observational and uncertain, especially near turning points. Market microstructure and news-driven jumps can distort fractal estimates.
- Always separate what is measurable (index values, computed FDI values, statistical associations) from what is not guaranteed (future outcomes).