Wavelet ATR (WATR)

A novel volatility measurement tool that applies wavelet decomposition to True Range values, providing multi-scale volatility analysis superior to traditional ATR. Uses the Hybrid Multi-Scale algorithm for robust, practical volatility measurement.

Overview

WATR solves a critical problem with pure energy-based wavelet indicators: they go to zero with constant True Range, making them impractical for trading. WATR maintains meaningful values in all market conditions.

Key Innovation: Blends two complementary signals from wavelet decomposition:

1. Baseline Magnitude: Energy of low-frequency approximation (underlying volatility level)
2. Regime Component: Weighted energy of high-frequency details (volatility changes)

Algorithm

Step 1: True Range Calculation
  TR_t = max{H_t - L_t, |H_t - C_(t-1)|, |L_t - C_(t-1)|}

Step 2: Wavelet Decomposition
  SWT(TR) → {A_J, D_J, D_(J-1), ..., D_1}

Step 3: Baseline Energy
  E_baseline = RMS(A_J)

Step 4: Regime Energy
  E_regime = Σ(w_j × RMS(D_j)) / Σ(w_j)
  where w_j = decay^(j-1)

Step 5: Hybrid Blending
  WATR_raw = α × E_baseline + (1-α) × E_regime

Step 6: Wilder's Smoothing
  WATR_t = WATR_(t-1) + β × (WATR_raw_t - WATR_(t-1))

Result: With constant TR=20 and α=0.75, WATR reports ~15.0 (not zero), making it usable for real trading.

Studies

Wavelet ATR (Panel)

• Display: WATR line in separate panel below price
• Use Case: Volatility measurement, stop-loss calculation, position sizing
• Context Options: Moving Average, Bollinger Bands, Percentile Lines

Wavelet ATR Bands (Overlay)

• Display: Dynamic upper/lower bands on price chart
• Calculation: Upper = Close + (WATR × multiplier), Lower = Close - (WATR × multiplier)
• Use Case: Volatility-adjusted support/resistance, breakout confirmation

Settings

Volatility Profile

Pre-configured blend ratios for different use cases:

Profile	Blend (α)	Best For
Balanced	0.75	General trading, good default
Magnitude Focused	0.95	Stable stop placement, position sizing
Regime Focused	0.50	Detecting volatility changes

ATR Settings

Setting	Default	Description
Period	14	Wilder's smoothing period
Multiplier	2.0	Band distance (for overlay study)

Wavelet Settings

Setting	Default	Description
Wavelet Type	DB4	Wavelet family
Decomposition Levels	4	Analysis depth
Energy Decay	0.5	Weight decay for regime calculation

Context Lines (Panel Study)

Setting	Default	Description
Show MA	false	Moving average of WATR
MA Period	20	MA lookback
Show Bollinger	false	Volatility bands on WATR itself
Show Percentiles	false	Historical percentile lines

Usage

Stop-Loss Placement

Use WATR for volatility-adjusted stops:

Stop Distance = WATR × multiplier

Long Entry:  Stop = Entry - (WATR × 2.0)
Short Entry: Stop = Entry + (WATR × 2.0)

Multiplier Guide:

• 1.5x: Tight stop, more frequent stops
• 2.0x: Standard, balanced approach
• 2.5x: Wide stop, ride through noise
• 3.0x: Very wide, swing trading

Position Sizing

Calculate position size based on risk:

Risk Amount = Account × Risk%
Position Size = Risk Amount / (WATR × multiplier)

Breakout Confirmation

Using WATR Bands:

• Price closes outside band → potential breakout
• Confirm with volume/momentum
• WATR expanding → increasing volatility confirms move

Regime Detection

With Regime Focused profile:

• WATR rising → volatility expanding (trend or chaos)
• WATR falling → volatility contracting (consolidation)
• Watch for WATR breakouts from tight ranges

Pattern Detection

WATR can automatically detect volatility patterns:

Pattern	Description	Trading Implication
Spike	Sudden WATR surge	Major event, wait for settle
Collapse	WATR falls sharply	Consolidation, expect breakout
Regime Transition	Sustained change in WATR level	Adjust stops and position sizes

Comparison to Standard ATR

Aspect	Standard ATR	WATR
Input	True Range	True Range
Analysis	Simple EMA	Multi-scale wavelet decomposition
Information	Single volatility value	Baseline + regime components
Edge Cases	Works everywhere	Never goes to zero
Responsiveness	Fixed	Configurable via profile

Troubleshooting

WATR Seems Too High/Low

• Adjust Volatility Profile to match your use case
• Check Decomposition Levels — more levels = smoother
• Verify instrument has sufficient liquidity

Bands Too Wide/Narrow

• Adjust Multiplier setting
• Consider instrument's typical range
• Use historical percentiles for calibration

See Also

• WEV (Wavelet Energy Volatility) - Energy-based volatility with trailing stops
• SWT Trend + Momentum - Combine with trend for complete system