QuanTAlib/lib/momentum/mom/Mom.md

MOM: Momentum (Absolute Price Change)

The market's simplest question answered: how much has price moved in N bars? No ratios, no percentages. Just the raw delta.

Property	Value
Category	Momentum
Inputs	Source (close)
Parameters	period (default 10)
Outputs	Single series (Mom)
Output range	Varies (see docs)
Warmup	period + 1 bars
PineScript	mom.pine

• MOM (Momentum) calculates the absolute price difference between the current value and the value N periods ago.
• Similar: ROC, Vel | Complementary: Moving average for smoothing | Trading note: Raw momentum: Price(t) − Price(t−n). Simplest momentum measure.
• Validated against TA-Lib, Skender, and Tulip reference implementations where available.

MOM (Momentum) calculates the absolute price difference between the current value and the value N periods ago. It is the purest expression of directional price movement, returning a signed value in the same units as the input. Positive MOM indicates rising prices; negative indicates falling. This is functionally identical to ROC but with a configurable lookback period (default 10 vs ROC's convention), and maps directly to TA-Lib's MOM function.

Historical Context

Momentum is arguably the oldest quantitative concept in technical analysis. Before oscillators, before moving averages, traders measured "how much has price changed" by simple subtraction. The term appears in Gerald Appel's work on MACD (1979) and in Martin Pring's "Technical Analysis Explained" as a foundation concept.

Different libraries handle the naming inconsistently:

• TA-Lib / Tulip: MOM = absolute change (this calculation)
• TradingView / PineScript: ta.mom = absolute change
• QuanTAlib: Mom = absolute change, Roc = absolute change (same formula, different default period), Change = percentage change

The implementation uses a ring buffer of size period + 1 for O(1) streaming with zero allocations on the hot path.

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}, \ldots, v_{t-1}, v_t]

where n is the lookback period. Only the oldest and newest values participate in the calculation.

2. Absolute Change Calculation

\text{MOM}_t = v_t - v_{t-n}

The result is in the same units as the input (dollars, points, ticks). No normalization is applied.

3. State Management

The indicator uses record struct State with _state / _p_state pairs for bar correction:

if isNew:
    _p_state = _state       // snapshot for rollback
else:
    _state = _p_state        // restore on correction

NaN/Infinity inputs are sanitized via last-valid-value substitution stored in State.LastValid.

Mathematical Foundation

Core Formula

\text{MOM}_t = P_t - P_{t-n}

where:

• P_t = current price
• P_{t-n} = price from n periods ago
• Default n = 10

Relationship to Other Momentum Variants

Indicator	Formula	Output
MOM	P_t - P_{t-n}	Absolute (price units)
ROC	P_t - P_{t-n}	Absolute (same formula)
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 fraction

Conversions

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

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

Performance Profile

Operation Count (Streaming Mode)

Operation	Count	Notes
SUB	1	current - past
Buffer add	1	O(1) ring buffer
State copy	1	rollback support
Total	~3 ops	Extremely lightweight

Batch Mode (Span-based)

Operation	Complexity	Notes
Per-element	O(1)	Single subtraction
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 subtraction

Validation

Library	Status	Notes
Skender	✅	Matches exactly
TA-Lib	✅	MOM function matches
Tulip	✅	MOM matches exactly
Ooples	✅	Matches within tolerance

Common Pitfalls

1. Unit confusion: MOM returns absolute values in price units, not percentages. A MOM of 5 means price moved 5 dollars/points, not 5%.

2. Scale dependency: MOM values are not comparable across instruments with different price levels. Use ROCP or CHANGE for normalized comparisons.

3. Warmup period: The first period values return 0.0 because there is no historical reference point yet. IsHot becomes true after period + 1 bars.

4. Zero handling: Unlike percentage-based variants, MOM has no division-by-zero risk.

5. Sign interpretation: Positive MOM indicates price increase over the lookback window; negative indicates decrease. The magnitude indicates the size of the move.

6. ROC vs MOM naming: In QuanTAlib, both Mom and Roc compute the same formula (P_t - P_{t-n}). The difference is the default period (MOM=10, ROC=10) and naming convention alignment with different library ecosystems.

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.
• Appel, G. (2005). "Technical Analysis: Power Tools for Active Investors." FT Press.
• TA-Lib documentation: MOM function reference
• TradingView PineScript Reference: ta.mom