Direct answer
Timeframe affects the Fractal Dimension Index (FDI) because the index measures how complex a time series looks at a specific observation scale. Changing the timeframe changes which data points are included and over what window you estimate “roughness,” so the computed FDI can move even when the underlying process is unchanged. This means FDI values are best understood as scale-dependent descriptions of the series you used, not as fixed properties of “the market” in general.
Mechanism or definition
FDI is an estimate of fractal dimension for a time series, often interpreted as a proxy for how “rough,” “irregular,” or space-filling the series path appears when viewed at the chosen scale. In practical terms, your timeframe affects at least two parts of the computation:
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The observation window (sampling length). A “short” timeframe includes fewer points and emphasizes short-term fluctuations. A “long” timeframe aggregates more history, which can smooth some micro-variations and expose different structure.
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The scale at which detail is judged. Fractal-dimension ideas are inherently multi-scale. If the estimator uses multiple window sizes or a rule that maps window sizes to complexity, then changing timeframe effectively changes the scale relationships the estimator sees.
Because of this, two analysts using different holding periods or data windows on the same type of instrument can obtain different FDI results. That difference is not automatically an error—it can be a sign that the series has different complexity at different scales.
Evidence or example (with explicit assumptions)
Assume a time series has short bursts of rapid movement followed by quieter periods. Consider two observation choices:
- Assumption A (short timeframe): You compute FDI using only a recent window that includes several bursts. The series path contains sharper turns over that window, so the estimated complexity can appear higher.
- Assumption B (long timeframe): You compute FDI using a longer window that includes both bursts and quieter periods. The same bursts still exist, but the longer window introduces additional structure and averaging effects. The estimated complexity can shift lower or become more stable, depending on how the estimator treats scale and noise.
In both cases, the “change in FDI” reflects the fact that the estimator is describing the data at the chosen scale. It does not, by itself, identify whether any future movement will be more or less complex.
A further realistic scenario is estimator sensitivity: the computed FDI can depend on choices like how you preprocess the series (for example, transforming it into returns or using raw prices) and how you handle missing data or outliers. Those choices interact with timeframe.
Limitations and risks
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Scale dependence is not prediction. Even if FDI changes when timeframe changes, that does not establish that FDI explains or forecasts future prices. It is a descriptive statistic, not a standalone signal.
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Noise and microstructure effects. Short timeframes can be dominated by irregularities caused by measurement noise, gaps, or bid/ask effects (where applicable). That can inflate apparent roughness. Longer timeframes may reduce some noise influence, but they can also blend distinct regimes.
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Estimation failure modes. If the chosen window is too short for the estimator’s requirements, or if the series contains abrupt regime shifts, the FDI estimate may become unstable. Comparisons across timeframes can then be misleading.
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Cross-study comparability. If different studies use different preprocessing, parameter settings, or windowing rules, their FDI values may not be directly comparable. Without matched settings, “higher” FDI may mean different things.
Verification or next question
To independently verify how timeframe affects FDI in a specific context, you can treat timeframe as a controlled variable:
- Recompute FDI on the same instrument-like time series using multiple window lengths, keeping preprocessing and estimator settings fixed.
- Check whether the direction and magnitude of FDI changes are consistent across nearby window sizes, or whether results flip erratically.
- Repeat the exercise on different segments (earlier vs later periods) to see whether the sensitivity is stable or regime-dependent.
A useful next question is: **Which preprocessing and estimation settings are used, and do they change with timeframe?