QuanTAlib/lib/volume/efi/Efi.md

EFI: Elder's Force Index

Force Index combines price movement with volume to measure the power behind every move. It's the market's polygraph test.

Property	Value
Category	Volume
Inputs	OHLCV bar (TBar)
Parameters	period (default 13)
Outputs	Single series (EFI)
Output range	Unbounded
Warmup	> period bars
PineScript	efi.pine

• Elder's Force Index (EFI) quantifies the buying and selling pressure behind price movements by multiplying price change by volume.
• Similar: FI, MFI | Complementary: EMA for smoothing | Trading note: Elder Force Index; price change × volume. Smoothed version identifies trend changes.
• Validated against TA-Lib, Skender, and Tulip reference implementations where available.

Elder's Force Index (EFI) quantifies the buying and selling pressure behind price movements by multiplying price change by volume. Large positive values indicate strong buying pressure (bulls in control), while large negative values reveal strong selling pressure (bears dominant).

The genius of EFI lies in its integration of three essential market elements: direction (price change sign), extent (price change magnitude), and conviction (volume). A $1 move on 1 million shares tells a very different story than the same move on 10,000 shares.

Historical Context

Developed by Dr. Alexander Elder and introduced in his seminal book "Trading for a Living" (1993), the Force Index emerged from Elder's quest to measure market momentum more accurately. Unlike oscillators that focus solely on price, Elder recognized that volume provides crucial context—it measures the crowd's emotional commitment to a price move.

Elder originally used a 2-period EMA for short-term signals and a 13-period EMA for intermediate trends. The raw force (price change × volume) is smoothed with an exponential moving average to filter noise while preserving responsiveness.

This implementation uses bias-corrected EMA during warmup, ensuring accurate values from the first calculation rather than waiting for exponential decay to stabilize.

Architecture & Physics

EFI operates as a two-stage pipeline:

1. Raw Force Calculation

The raw force measures instantaneous buying or selling pressure:

F_t = (Close_t - Close_{t-1}) \times Volume_t

• Positive when price rises (buying pressure)
• Negative when price falls (selling pressure)
• Magnitude proportional to both price change and volume

2. EMA Smoothing with Bias Correction

The raw force is smoothed using an exponential moving average:

\alpha = \frac{2}{period + 1}

EMA_t = \alpha \times F_t + (1 - \alpha) \times EMA_{t-1}

During warmup, bias correction compensates for the EMA's initial underestimation:

e_t = e_{t-1} \times (1 - \alpha)

EFI_t = \frac{EMA_t}{1 - e_t}

Once e_t \leq 10^{-10}, the correction factor approaches 1 and is disabled.

Mathematical Foundation

Raw Force

F_t = \Delta P_t \times V_t

where:

• \Delta P_t = Close_t - Close_{t-1} (price change)
• V_t = Volume at time t

Smoothed Force Index

Standard EMA form:

EFI_t = \alpha \times F_t + (1 - \alpha) \times EFI_{t-1}

Using FMA optimization:

EFI_t = \text{FMA}(\alpha, F_t - EFI_{t-1}, EFI_{t-1})

Interpretation Thresholds

• Strong buying pressure: EFI >> 0 with increasing trend
• Strong selling pressure: EFI << 0 with decreasing trend
• Zero line crossover: Potential trend change signal
• Divergence: Price makes new high/low but EFI doesn't confirm

Performance Profile

Operation Count (Streaming Mode)

Operation	Count	Notes
SUB	1	Price change
MUL	1	Force calculation
FMA	1	EMA smoothing
MUL	1	Bias decay (warmup only)
DIV	1	Bias correction (warmup only)
Total	~3-5	Per bar

Memory Footprint

Component	Size	Notes
State record	48 bytes	6 doubles/flags
Previous state	48 bytes	For bar correction
Total	~96 bytes	Per instance

Quality Metrics

Metric	Score	Notes
Accuracy	10/10	Bias-corrected EMA matches reference
Timeliness	8/10	EMA lag increases with period
Overshoot	7/10	Can spike on volume surges
Smoothness	7/10	Smoother than raw force, responsive to extremes
Allocation	10/10	Zero heap allocations in hot path

Validation

Library	Status	Notes
QuanTAlib	✅	Bias-corrected EMA implementation
TA-Lib	N/A	No Force Index implementation
Skender	N/A	Has ElderRay (different indicator)
Tulip	N/A	No Force Index implementation
Ooples	✅	Matches after warmup period

Note: Most libraries use standard EMA without bias correction, causing warmup divergence. After the warmup period, values converge.

Common Pitfalls

1. First Bar: No previous close exists, so raw force = 0. The implementation handles this gracefully.

2. Volume Scale: EFI is not bounded—values depend on volume magnitude. Comparing EFI across securities with vastly different volume levels requires normalization.

3. Zero Volume: When volume is zero, raw force is zero regardless of price change. This can create misleading readings during low-liquidity periods.

4. Period Selection:

   • Short periods (2-3): More sensitive, more noise, good for short-term signals
   • Standard period (13): Balance of responsiveness and smoothness
   • Long periods (20+): Smoother, slower, better for trend confirmation

5. Divergence Interpretation: EFI divergence from price is a warning, not a signal. Confirm with other indicators before acting.

6. isNew Parameter: When correcting a bar (isNew=false), the implementation properly restores previous state. Failure to handle this causes cumulative EMA errors.

7. NaN/Infinity Handling: Implementation substitutes last valid close for NaN inputs and treats infinite volume as zero to prevent propagation of invalid values.

References

• Elder, A. (1993). "Trading for a Living." John Wiley & Sons.
• Elder, A. (2002). "Come Into My Trading Room." John Wiley & Sons.
• StockCharts. "Force Index." Technical Indicators
• Investopedia. "Force Index Definition." Technical Analysis