What is Detrended Fluctuation Analysis (DFA)?
DFA is a statistical technique that identifies trends in financial data by removing underlying trends from time series data. It helps traders and investors:
- Assess relationships between multiple assets
- Understand market trend interactions
- Analyze portfolio performance
- Uncover scale-invariant deterministic trends
Unlike traditional statistics (mean, median, mode), DFA operates under the assumption that power laws drive return distributions rather than stochastic linear distributions. This makes it particularly effective for financial markets, which are scale-free networks.
Key Properties
- Detects and removes cycles in time series data
- Sensitive enough to detect long-range dependence
- Analyzes components contributing to price movements
- Works across different time scales
- More informative than traditional statistics for financial markets
How to Calculate DFA
Calculation Process
- Select time series data
- Calculate data mean
- Create detrended time series by subtracting mean
- Divide into non-overlapping segments
- Calculate root mean square deviation (RMSD) per segment
- Average RMSD across segments
- Plot average RMSD vs segment length
- Fit power-law curve
- Calculate DFA exponent (slope of power-law curve)
Interpreting Results
The DFA exponent indicates whether a time series is:
- Trending
- Mean-reverting
- Random
Trading Strategy Applications
Bull Market:
- Long → trending (H > 0.5)
- Short → mean-reverting (0 < H < 0.5)
Bear Market:
- Long → mean-reverting (0 < H < 0.5)
- Short → trending (H > 0.5)
Why Use DFA in Trading?
Key Benefits
- Identifies robust correlations independent of trends
- Works across multiple timeframes (1-min to 1-year)
- Complements other trading strategies:
- Mean-reversion
- Momentum
- Volatility
Important Considerations
- Some relationships visible in raw price charts may disappear after detrending
- Correlations surviving DFA analysis are more likely to be robust
- DFA doesn't imply causation, only relationship strength
- Helps optimize trade entry/exit timing