The DFA (Detrended Fluctuation Analysis) Index Calculator is used to analyze time series data for long-term correlations and fractal-like behavior. This tool is widely applied in fields such as finance, neuroscience, and physics to measure the complexity and predictability of datasets. By using DFA, researchers can determine whether a time series exhibits self-similarity and scaling properties over different time intervals.
Formula of Dfa Index Calculator
The DFA Index is calculate using the following formula:
where:
- F(n) (Fluctuation Function) is the root-mean-square fluctuation of the time series over different window sizes.
- n (Window Size) is the segment length use in the detrending process.
This formula helps researchers assess the degree of correlation and scaling behavior in a dataset, making it useful for studying trends and variability.
DFA Index Reference Table
This table provides estimated DFA index values for different types of time series behavior.
| DFA Index Value | Interpretation |
|---|---|
| < 0.5 | Anti-persistent, mean-reverting behavior |
| 0.5 | Random (uncorrelated, white noise) |
| 0.5 - 1.0 | Long-range correlated, fractal behavior |
| > 1.0 | Strongly correlated, possible non-stationarity |
These values help researchers classify time series data based on their fractal properties and correlation strength.
Example
A financial analyst examines stock market fluctuations over various time windows. Using detrended fluctuation analysis, the fluctuation function F(n) for different window sizes n is calculate. If the DFA Index is find to be 0.8, this indicates long-term correlations in the stock price movements, suggesting a fractal-like behavior in market trends.
Most Common FAQs
The DFA Index helps identify underlying patterns in complex datasets, making it valuable for detecting trends, correlations, and self-similarity in fields such as finance, medicine, and climate science.
A DFA Index of 0.5 indicates that the dataset follows a purely random pattern (white noise) with no significant long-term correlations.
Yes, DFA is commonly apply in biological sciences to analyze heart rate variability, brain activity, and other physiological time series to assess health conditions and predict anomalies.