QuanTAlib/lib/momentum/rocr/Rocr.md

ROCR: Rate of Change Ratio

"The ratio form of momentum: how many times larger is the current price compared to the past? A multiplier view of market movement."

ROCR (Rate of Change Ratio) calculates the ratio between the current value and the value N periods ago. Values hover around 1.0, with values above 1.0 indicating price increase and values below 1.0 indicating price decrease. Unlike ROC (absolute) or ROCP (percentage), ROCR provides a dimensionless multiplier that directly shows the price ratio.

Historical Context

ROCR belongs to the family of momentum indicators that measure price change over time. The ratio form is particularly useful when comparing relative movements across instruments with different price scales. The terminology varies by platform and library:

• TA-Lib: Uses ROCR for ratio (price / past_price)
• Tulip: Uses ROCR for ratio
• TradingView/PineScript: Uses source / source[n] pattern
• QuanTAlib: Uses ROCR for ratio, ROC for absolute, ROCP for percentage

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. Only the oldest and newest values are needed for calculation.

2. Ratio Calculation

\text{ROCR}_t = \frac{v_t}{v_{t-n}}

where:

• v_t = current value
• v_{t-n} = value from n periods ago
• Result is dimensionless (ratio around 1.0)

3. State Management

The indicator uses state rollback for bar correction:

if isNew:
    save current state as previous
else:
    restore previous state

This enables real-time bar updates without corrupting historical calculations.

Mathematical Foundation

Core Formula

\text{ROCR}_t = \frac{P_t}{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{ROCR} = \text{CHANGE} + 1 = \frac{P_t}{P_{t-n}}

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

\text{CHANGE} = \text{ROCR} - 1

Performance Profile

Operation Count (Streaming Mode)

Operation	Count	Notes
DIV	1	current / past
Buffer add	1	O(1) ring buffer
State copy	1	rollback support
Zero check	1	division safety
Total	~4 ops	Very lightweight

Batch Mode (Span-based)

The span-based calculation is a simple loop with no dependencies between iterations.

Operation	Complexity	Notes
Per-element	O(1)	Single division
Total	O(n)	Linear scan
Memory	O(1)	No additional allocation

Quality Metrics

Metric	Score	Notes
Accuracy	10/10	Exact arithmetic, no approximation
Timeliness	10/10	Zero lag by definition
Smoothness	3/10	No smoothing, reflects raw volatility
Simplicity	10/10	Single division

Interpretation

• ROCR = 1.0: No change from N periods ago
• ROCR > 1.0: Price increased (e.g., 1.05 = 5% increase)
• ROCR < 1.0: Price decreased (e.g., 0.95 = 5% decrease)
• ROCR = 2.0: Price doubled
• ROCR = 0.5: Price halved

Validation

Library	Status	Notes
TA-Lib	✅	ROCR matches exactly
Tulip	✅	Matches ratio calculation
TradingView	✅	Matches PineScript division

Common Pitfalls

1. Value interpretation: ROCR returns values around 1.0, not percentages. A ROCR of 1.05 means 5% increase, not 105% increase.

2. Division by zero: If the historical price is zero, ROCR returns 1.0 as a safe default.

3. Warmup period: The first period values return 1.0 as there's no historical reference point.

4. Scale invariance: ROCR is comparable across instruments since it's a ratio.

5. Compounding: ROCR values can be multiplied across periods: total_change = ROCR_1 × ROCR_2 × ...

References

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