QuanTAlib/lib/momentum/rocp/Rocp.md

ROCP: Rate of Change Percentage

Property	Value
Category	Momentum
Inputs	Source (close)
Parameters	period (default 9)
Outputs	Single series (Rocp)
Output range	Varies (see docs)
Warmup	period + 1 bars

TL;DR

• ROCP (Rate of Change Percentage) calculates the percentage change between the current value and the value N periods ago.
• Parameterized by period (default 9).
• Output range: Varies (see docs).
• Requires period + 1 bars of warmup before first valid output (IsHot = true).
• Validated against TA-Lib, Skender, and Tulip reference implementations where available.

"The percentage form of momentum: by what percent has price changed? The most intuitive momentum measure."

ROCP (Rate of Change Percentage) calculates the percentage change between the current value and the value N periods ago. This is the most commonly used form of rate of change, expressing change in percentage terms that are directly interpretable (e.g., 5.0 = 5% increase).

Historical Context

ROCP is the standard way of expressing price momentum in percentage terms. It's widely used in technical analysis because percentage changes are comparable across different instruments regardless of their price levels.

The terminology varies by platform:

• TA-Lib: Uses ROCP for percentage change / 100 (decimal form)
• TradingView/PineScript: Often uses change for this calculation
• QuanTAlib: Uses ROCP for percentage (5.0 = 5%), CHANGE for decimal (0.05 = 5%)

Architecture & Physics

1. Ring Buffer Storage

The indicator maintains a sliding window of period + 1 values:

\text{buffer} = [v_{t-n}, v_{t-n+1}, ..., v_{t-1}, v_t]

where n is the lookback period.

2. Percentage Calculation

\text{ROCP}_t = 100 \times \frac{v_t - v_{t-n}}{v_{t-n}}

where:

• v_t = current value
• v_{t-n} = value from n periods ago
• Result is in percentage units (5.0 = 5%)

Mathematical Foundation

Core Formula

\text{ROCP}_t = 100 \times \frac{P_t - P_{t-n}}{P_{t-n}}

Relationship to Other Rate of Change Variants

Indicator	Formula	Output
ROC	P_t - P_{t-n}	Absolute (price units)
ROCP	\frac{P_t - P_{t-n}}{P_{t-n}} \times 100	Percentage (%)
ROCR	\frac{P_t}{P_{t-n}}	Ratio (dimensionless)
CHANGE	\frac{P_t - P_{t-n}}{P_{t-n}}	Decimal (0.10 = 10%)

Conversions

\text{ROCP} = \text{CHANGE} \times 100

\text{ROCP} = (\text{ROCR} - 1) \times 100

\text{CHANGE} = \text{ROCP} / 100

Performance Profile

Operation Count (Streaming Mode)

Operation	Count	Notes
SUB	1	current - past
DIV	1	change / past
MUL	1	× 100
Buffer add	1	O(1) ring buffer
Total	~4 ops	Very lightweight

Quality Metrics

Metric	Score	Notes
Accuracy	10/10	Exact arithmetic
Timeliness	10/10	Zero lag
Smoothness	3/10	Reflects raw volatility
Simplicity	10/10	Basic arithmetic

Interpretation

• ROCP = 0.0: No change from N periods ago
• ROCP > 0: Price increased (e.g., 5.0 = 5% increase)
• ROCP < 0: Price decreased (e.g., -3.0 = 3% decrease)
• ROCP = 100: Price doubled
• ROCP = -50: Price halved

Validation

Library	Status	Notes
TA-Lib	✅	Note: TA-Lib ROCP returns decimal (0.05), multiply by 100
TradingView	✅	Matches PineScript calculation

Common Pitfalls

1. Scale: ROCP returns percentage values directly. A return of 5.0 means 5%, not 0.05.

2. Division by zero: If the historical price is zero, ROCP returns 0.0 as a safe default.

3. TA-Lib difference: TA-Lib's ROCP returns decimal form (0.05 for 5%), while this implementation returns percentage form (5.0).

4. Compounding: Unlike ROCR, ROCP values cannot be directly multiplied for multi-period changes.

5. Warmup period: The first period values return 0.0.

References

• Pring, M. J. (2014). "Technical Analysis Explained." McGraw-Hill.
• Murphy, J. J. (1999). "Technical Analysis of the Financial Markets."
• TA-Lib Documentation: ROCP function