Absolute

$|x| = \begin{cases} x, & \text{if } x \geq 0 \\ -x, & \text{if } x < 0 \end{cases}$

Converts all values to their non-negative magnitude. Positive values stay positive, negative values become positive, zero remains zero.

Input	Output
5	5
-3	3
0	0
-7.5	7.5

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Missing Data

A datapoint can be missing (null) — a data gap, or a closed-market slot such as a weekend on a stock series.

• A missing input produces a null output at the same position. The math is never faked: no zero or other substitute is invented for a slot that has no data.
• ABS itself has no invalid inputs — every real number has an absolute value — so a null output always means "no input datapoint here", never a math error.
• In live execution the module returns exactly one datapoint (the newest slot), which is null when that slot has no input value.

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When to Use

Absolute value is essential when you care about how much something moved, not which direction:

Use Case	Example
Volatility measurement	Size of daily returns regardless of direction
Distance from baseline	How far price is from a moving average
Error magnitude	Tracking error, deviation from target

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Practical Example: Movement Magnitude

Take absolute value of daily returns to measure activity intensity:

Day	Return	|Return|
Mon	+2.5%	2.5%
Tue	-1.8%	1.8%
Wed	-4.2%	4.2%
Thu	+0.3%	0.3%

The average of these magnitudes (2.2%) describes how much the asset typically moves per day—the foundation of volatility metrics like Average True Range.

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Volatility Compression Detection

A creative application of absolute value is detecting periods of low volatility—often a precursor to significant moves. When the average absolute return falls to its lowest percentile over a lookback period, the market may be "coiling" for a breakout.

flowchart LR
    subgraph Pipeline["Volatility Compression Pipeline"]
        DR["Daily Return"]
        ABS["ABS Module"]
        SMA["Simple Moving Average"]
        PERC["Percentile"]
        SIGNAL["Low Percentile = Alert"]
    end
    
    DR --> ABS
    ABS --> SMA
    SMA --> PERC
    PERC --> SIGNAL
    
    style ABS fill:#4a90d9,stroke:#333,color:#fff
    style SIGNAL fill:#e74c3c,stroke:#333,color:#fff

When the average absolute return falls to its lowest 10th percentile over the past year, consider it a warning: the market might be coiling for a significant move. This phenomenon is well-documented in options pricing (see volatility clustering) and can inform both directional bets and options strategies.

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Related Modules

• SUB — Calculate differences (then apply ABS for unsigned distance)
• SQRT — Another transformation that constrains output
• POW — Use exponent 0.5 for dampened magnitude

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Key Takeaways

Use Case	What ABS Does	Why It Matters
Volatility analysis	Converts returns to magnitudes	Measures movement intensity
Deviation measurement	Removes directional sign	Focuses on distance from reference
Symmetric indicators	Equal treatment of up/down	Ideal for oscillators
Risk metrics	Absolute drawdown/deviation	Direction-agnostic risk assessment

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Further Reading

• Absolute Value - Khan Academy — Foundational math concepts
• Average True Range (ATR) - Fidelity — A popular volatility indicator built on absolute values
• Mean Absolute Deviation - Khan Academy — Statistical measure using absolute values
• Volatility Clustering - Wikipedia — The phenomenon of clustered volatility in financial markets