ADX (Average Directional Index)¶

Overview¶

The Average Directional Index (ADX) is a technical indicator that measures the strength of a trend, regardless of its direction. Developed by J. Welles Wilder Jr. as part of the Directional Movement System, ADX is one of the most reliable and widely-used trend strength indicators in technical analysis. Unlike most momentum indicators, ADX does not indicate trend direction—only the strength of the current trend.

Parameters¶

Parameter	Type	Default	Description
`high`	Array	Required	Array of high prices
`low`	Array	Required	Array of low prices
`close`	Array	Required	Array of close prices
`period`	Integer	14	Number of periods for ADX calculation

Parameter Details¶

Note: Array elements should be ordered from oldest to newest (chronological order)

high, low, close - Requires complete OHLC data (open not needed) - Arrays must be of equal length - Minimum data points needed: (period * 2) + 1 for meaningful results - Works on any timeframe (intraday, daily, weekly, monthly)

period (time_period) - Wilder's original recommendation: 14 periods - Shorter periods (7-10) create more responsive but noisier signals - Longer periods (21-28) create smoother signals with fewer false readings - Recommended ranges: - Day trading: 7-10 periods for faster signals - Swing trading: 14 periods (standard) - Position trading: 21-28 periods for long-term trend identification

Usage¶

Basic Usage¶

require 'sqa/tai'

high =  [48.70, 48.72, 48.90, 48.87, 48.82, 49.05, 49.20, 49.35,
         49.92, 50.19, 50.12, 50.10, 50.00, 49.75, 49.80, 50.00,
         50.20, 50.30, 50.50, 50.70]
low =   [47.79, 48.14, 48.39, 48.37, 48.24, 48.64, 48.94, 49.03,
         49.50, 49.87, 49.20, 49.00, 48.90, 49.00, 49.10, 49.20,
         49.30, 49.40, 49.50, 49.60]
close = [48.20, 48.61, 48.75, 48.63, 48.74, 49.03, 49.07, 49.32,
         49.91, 50.13, 49.53, 49.50, 49.25, 49.20, 49.45, 49.60,
         49.80, 50.00, 50.20, 50.40]

# Calculate 14-period ADX (standard)
adx = SQA::TAI.adx(high, low, close, period: 14)

puts "Current ADX: #{adx.last.round(2)}"

With Custom Parameters¶

# More sensitive 10-period ADX for day trading
adx_fast = SQA::TAI.adx(high, low, close, period: 10)

# Smoother 21-period ADX for position trading
adx_slow = SQA::TAI.adx(high, low, close, period: 21)

puts "Fast ADX (10): #{adx_fast.last.round(2)}"
puts "Standard ADX (14): #{adx.last.round(2)}"
puts "Slow ADX (21): #{adx_slow.last.round(2)}"

Understanding the Indicator¶

What It Measures¶

The ADX measures the strength of a trend by analyzing the directional movement of price:

Trend Strength: How powerful the current trend is, regardless of direction
Market Condition: Whether the market is trending or ranging
Trend Quality: The reliability of the current directional movement
Trend Sustainability: Whether a trend is strong enough to follow

ADX answers the question: "Is this market worth trading with trend-following strategies, or should I use range-bound strategies?"

Calculation Method¶

ADX is derived from the Directional Movement System through several steps:

Calculate Directional Movement (+DM and -DM): Measure upward and downward price movement
Calculate True Range (TR): Measure price volatility
Smooth +DM, -DM, and TR: Apply Wilder's smoothing over the period
Calculate Directional Indicators (+DI and -DI): Normalize directional movement
Calculate DX: Measure difference between +DI and -DI
Calculate ADX: Smooth DX values using Wilder's smoothing

Formula:

+DM = Current High - Previous High (if positive, else 0)
-DM = Previous Low - Current Low (if positive, else 0)

+DI = 100 × (Smoothed +DM / Smoothed TR)
-DI = 100 × (Smoothed -DM / Smoothed TR)

DX = 100 × |+DI - -DI| / (+DI + -DI)

ADX = Smoothed Average of DX

Where smoothing uses Wilder's method:
First value = Simple average of period values
Subsequent values = (Previous × (period-1) + Current) / period

Indicator Characteristics¶

Range: 0 to 100 (theoretically unbounded but rarely exceeds 100)
Type: Trend strength oscillator (non-directional)
Lag: High lag due to multiple smoothing operations (typically 2× period lag)
Best Used: Identifying trending vs ranging markets, filtering trades, confirming trend strength
Limitations: Does not indicate direction; high lag means late signals

Interpretation¶

Value Ranges¶

Specific guidance on what different ADX values indicate:

0-20: Weak or absent trend. Market is ranging, consolidating, or moving sideways. Trend-following strategies are unreliable. Consider oscillators and range-bound strategies.
20-25: Developing trend. A trend may be forming but is not yet established. Watch for ADX to continue rising for confirmation.
25-50: Strong trend. Good conditions for trend-following strategies. The trend has clear direction and momentum. Most profitable zone for trend traders.
50-75: Very strong trend. Excellent trending environment with sustained directional movement. Rare but highly profitable for trend followers.
75-100: Extremely strong trend. Very rare and indicates exceptional directional movement. Often seen during major breakouts or market moves.

Key Levels¶

Below 20: No trend or weak trend. Market is choppy. Avoid trend-following strategies. Use range-bound approaches (oscillators, support/resistance).
20 Threshold: Critical level. ADX crossing above 20 suggests a trend is developing. ADX falling below 20 suggests trend is ending.
25 Threshold: Classic trend confirmation level. Many traders only take trend-following trades when ADX > 25.
50+ Level: Indicates very strong trend but also potential exhaustion approaching. Watch for ADX to peak and decline.

Signal Interpretation¶

How to read ADX signals:

Trend Presence
ADX > 25: Strong trend exists (use +DI/-DI to determine direction)
ADX < 20: No meaningful trend (use range-bound strategies)
ADX 20-25: Trend developing or ending (watch for confirmation)
Trend Changes
ADX rising: Trend strengthening (gaining momentum)
ADX falling: Trend weakening (losing momentum)
ADX flat: Trend strength stable
Market Regime Identification
ADX consistently below 20: Ranging market regime
ADX consistently above 25: Trending market regime
ADX oscillating around 20-25: Transitional market

Trading Signals¶

Buy Signals¶

Specific conditions that generate buy signals:

Primary Signal: ADX crosses above 20 or 25 with +DI > -DI
Confirms new uptrend is developing
Best when ADX is rising from low levels
Trend Confirmation: ADX > 25 with +DI > -DI and ADX rising
Indicates strong established uptrend
Look for pullbacks to enter
Strength Filter: Use ADX > 25 as filter for other buy signals
Only take long signals when ADX confirms trend strength
Reduces false signals in choppy markets

Example Scenario:

When ADX crosses above 25 with +DI (30) > -DI (15) and ADX rising,
consider long positions. Confirm with:
- Price breaking above resistance
- +DI rising while -DI falling
- Set stop loss below recent swing low

Sell Signals¶

Specific conditions that generate sell signals:

Primary Signal: ADX crosses above 20 or 25 with -DI > +DI
Confirms new downtrend is developing
Best when ADX is rising from low levels
Trend Confirmation: ADX > 25 with -DI > +DI and ADX rising
Indicates strong established downtrend
Look for rallies to enter shorts
Exit Signal: ADX peaks above 50 then starts declining
May indicate trend exhaustion
Consider taking profits or tightening stops

Example Scenario:

When ADX crosses above 25 with -DI (35) > +DI (12) and ADX rising,
consider short positions. Confirm with:
- Price breaking below support
- -DI rising while +DI falling
- Set stop loss above recent swing high

Divergence Analysis¶

Trend Weakening: - Pattern: Price makes new high/low but ADX makes lower high/low - Identification: Compare price extremes with corresponding ADX peaks - Significance: Trend losing strength despite price extension - Reliability: High when ADX was previously above 40 - Example: Stock rallies to new high at $120, but ADX peaks at 35 vs previous peak of 42. Uptrend weakening.

Trend Strengthening: - Pattern: ADX making higher lows while in uptrend or downtrend - Identification: Track ADX lows during pullbacks - Significance: Trend retaining strength during corrections - Reliability: Strongest when ADX stays above 25 during pullbacks - Example: During pullbacks in uptrend, ADX bottoms at 28, 30, 32 successively. Strong persistent uptrend.

Best Practices¶

Optimal Use Cases¶

When ADX works best:

Market conditions: Most effective in all conditions as a filter. Identifies when to trend-follow vs when to range-trade. Not affected by volatility.
Time frames: Works on all timeframes but most reliable on daily and 4-hour charts. Higher timeframes produce more reliable trend identification.
Asset classes: Excellent for all asset classes—stocks, forex, commodities, cryptocurrencies. Universal applicability.

Combining with Other Indicators¶

Recommended indicator combinations:

With Directional Indicators (+DI/-DI): Essential combination. ADX shows strength, DI shows direction. Together they provide complete trend picture. Enter long when ADX > 25 and +DI > -DI.
With Moving Averages: Use 50/200 MA for trend direction, ADX for trend strength. Only trade MA crossovers when ADX > 25. Avoids false crossovers in ranging markets.
With Oscillators (RSI, Stochastic): Use ADX to determine strategy. When ADX < 20, use RSI/Stochastic overbought/oversold signals. When ADX > 25, ignore oscillator extremes and trade with trend.

Common Pitfalls¶

What to avoid:

Trading Without Direction: ADX alone doesn't show direction. Always combine with +DI/-DI or trend indicator. Trading on ADX strength without knowing direction leads to losses.
Chasing High ADX: When ADX exceeds 50-60, trend may be near exhaustion. Entering late into very high ADX can result in buying/selling at extremes.
Ignoring Time Lag: ADX has significant lag (2× period). By the time ADX confirms trend, much of the move may be over. Use with other leading indicators for earlier entry.
Using Wrong Threshold: Traditional 25 threshold may not suit all markets. High-volatility markets (crypto) may need 30-35. Low-volatility markets may use 20.

Parameter Selection Guidelines¶

How to choose optimal parameters:

Short-term trading (day trading):
Period: 7-10 for faster trend detection
Threshold: 20-25 (lower threshold for more signals)
Focus: Quick identification of intraday trends
Medium-term trading (swing trading):
Period: 14 (standard Wilder setting)
Threshold: 25 (classic confirmation level)
Focus: Multi-day trend identification and following
Long-term trading (position trading):
Period: 21-28 for smoothest signals
Threshold: 30 (higher threshold for strongest trends only)
Focus: Major trend identification, monthly timeframe
Backtesting approach: Test ADX period and threshold on historical data for your specific asset and timeframe. Find levels where ADX > threshold corresponded with sustained profitable trends.

Practical Example¶

Complete trading example with context:

require 'sqa/tai'

# Historical price data for a stock
high_prices = [
  48.70, 48.72, 48.90, 48.87, 48.82, 49.05, 49.20, 49.35, 49.92, 50.19,
  50.12, 50.10, 50.00, 49.75, 49.80, 50.00, 50.20, 50.30, 50.50, 50.70,
  50.80, 50.90, 51.00, 51.10, 51.20, 51.30, 51.40, 51.50, 51.60, 51.70
]
low_prices = [
  47.79, 48.14, 48.39, 48.37, 48.24, 48.64, 48.94, 49.03, 49.50, 49.87,
  49.20, 49.00, 48.90, 49.00, 49.10, 49.20, 49.30, 49.40, 49.50, 49.60,
  49.70, 49.80, 49.90, 50.00, 50.10, 50.20, 50.30, 50.40, 50.50, 50.60
]
close_prices = [
  48.20, 48.61, 48.75, 48.63, 48.74, 49.03, 49.07, 49.32, 49.91, 50.13,
  49.53, 49.50, 49.25, 49.20, 49.45, 49.60, 49.80, 50.00, 50.20, 50.40,
  50.60, 50.70, 50.90, 51.00, 51.10, 51.20, 51.30, 51.40, 51.50, 51.60
]

# Calculate ADX and directional indicators
adx = SQA::TAI.adx(high_prices, low_prices, close_prices, period: 14)
plus_di = SQA::TAI.plus_di(high_prices, low_prices, close_prices, period: 14)
minus_di = SQA::TAI.minus_di(high_prices, low_prices, close_prices, period: 14)

# Current values
current_price = close_prices.last
current_adx = adx.last
previous_adx = adx[-2]
adx_5_bars_ago = adx[-5]

current_plus_di = plus_di.last
current_minus_di = minus_di.last

puts "=== ADX Trend Analysis ==="
puts "Current Price: $#{current_price.round(2)}"
puts "Current ADX: #{current_adx.round(2)}"
puts "+DI: #{current_plus_di.round(2)}, -DI: #{current_minus_di.round(2)}"
puts

# Determine trend strength
if current_adx > 50
  trend_strength = "VERY STRONG"
elsif current_adx > 25
  trend_strength = "STRONG"
elsif current_adx > 20
  trend_strength = "DEVELOPING"
else
  trend_strength = "WEAK/ABSENT"
end

# Determine trend direction
if current_plus_di > current_minus_di
  trend_direction = "UPTREND"
  directional_spread = current_plus_di - current_minus_di
else
  trend_direction = "DOWNTREND"
  directional_spread = current_minus_di - current_plus_di
end

puts "Trend Strength: #{trend_strength}"
puts "Trend Direction: #{trend_direction}"
puts "Directional Spread: #{directional_spread.round(2)}"
puts

# Trading logic
if current_adx > 25
  # Strong trend - trend-following mode
  adx_change = current_adx - adx_5_bars_ago

  if trend_direction == "UPTREND"
    puts "TRADING SIGNAL: BUY/HOLD LONG"
    puts "Strategy: Trend-following uptrend"
    puts "Entry: Look for pullbacks to support"
    puts "Stop Loss: Below recent swing low"

    if adx_change > 0
      puts "ADX rising: Trend strengthening - High confidence"
    else
      puts "ADX falling: Trend weakening - Watch for exit"
    end

  else # DOWNTREND
    puts "TRADING SIGNAL: SELL/HOLD SHORT"
    puts "Strategy: Trend-following downtrend"
    puts "Entry: Look for rallies to resistance"
    puts "Stop Loss: Above recent swing high"

    if adx_change > 0
      puts "ADX rising: Trend strengthening - High confidence"
    else
      puts "ADX falling: Trend weakening - Watch for exit"
    end
  end

elsif current_adx < 20
  # Weak trend - range-bound mode
  puts "TRADING SIGNAL: RANGE-BOUND MARKET"
  puts "Strategy: Avoid trend-following"
  puts "Consider: Oscillator-based strategies (RSI, Stochastic)"
  puts "Look for: Support/resistance bounces"
  puts "Avoid: Breakout trading until ADX rises"

else # ADX between 20-25
  # Transitional period
  if current_adx > previous_adx
    puts "TRADING SIGNAL: POTENTIAL TREND DEVELOPING"
    puts "ADX rising from #{previous_adx.round(2)} to #{current_adx.round(2)}"
    puts "Watch for ADX to cross above 25 for trend confirmation"
    puts "Prepare for #{trend_direction} if ADX continues rising"
  else
    puts "TRADING SIGNAL: TREND ENDING"
    puts "ADX falling from #{previous_adx.round(2)} to #{current_adx.round(2)}"
    puts "Trend losing strength - consider taking profits"
    puts "Prepare for range-bound market if ADX continues falling"
  end
end

# Warn of potential exhaustion
if current_adx > 50
  puts "\n⚠️  WARNING: ADX Very High"
  puts "Trend may be overextended"
  puts "Watch for ADX peak and reversal"
  puts "Consider tightening stops or taking partial profits"
end

Similar Indicators¶

ADXR (ADX Rating): Smoothed version of ADX that averages current ADX with ADX from N periods ago. ADXR is less volatile and provides more stable trend strength readings. Use ADXR when you want fewer false signals and smoother trend identification.
DX (Directional Movement Index): The raw directional movement calculation before smoothing into ADX. DX is more volatile but more responsive. ADX is the preferred indicator as it smooths out DX noise.

Complementary Indicators¶

PLUS_DI (+DI): Measures positive directional movement (uptrend strength). Essential companion to ADX. Use +DI > -DI to identify uptrend direction when ADX shows strength.
MINUS_DI (-DI): Measures negative directional movement (downtrend strength). Essential companion to ADX. Use -DI > +DI to identify downtrend direction when ADX shows strength.
ATR (Average True Range): Measures volatility and is part of the same Wilder system. Use ATR for position sizing and stop loss placement when ADX identifies trend.

Indicator Family¶

ADX belongs to the Directional Movement System family developed by Wilder: - DX: Raw directional movement calculation - ADX: Smoothed DX showing trend strength - ADXR: Further smoothed ADX - +DI/-DI: Directional indicators showing trend direction

When to prefer ADX: For determining whether to use trend-following or range-bound strategies. ADX is the gold standard for trend strength identification and market regime filtering. Always combine with directional indicators (+DI/-DI) for complete analysis.

Advanced Topics¶

Multi-Timeframe Analysis¶

Use ADX across multiple timeframes for robust trend identification:

Higher timeframe ADX (daily/weekly) identifies major trend strength and overall market regime
Lower timeframe ADX (4H/1H) identifies short-term trend strength for precise entry timing
Strongest trends when all timeframes show ADX > 25 (e.g., weekly ADX 35, daily ADX 30, 4H ADX 28)

Example: If weekly ADX is 40 (very strong trend) and daily ADX is 28 (strong trend), focus on daily pullbacks as entry opportunities in the direction of the weekly trend.

Market Regime Adaptation¶

ADX behavior and optimal thresholds vary by market type:

Low Volatility Markets (utilities, bonds): ADX rarely exceeds 30. Use threshold of 20 for trend confirmation. ADX > 25 indicates exceptionally strong trend.
Medium Volatility Markets (large-cap stocks, major forex pairs): Standard ADX thresholds work well. Use 25 for trend confirmation, 40+ indicates very strong trend.
High Volatility Markets (crypto, small-caps, emerging markets): ADX can frequently spike above 40. Consider using 30-35 as trend threshold to avoid false signals.
Trending Periods: In sustained bull/bear markets, ADX stays elevated. Use ADX falling below 30 (instead of 25) as trend-end signal.

Statistical Validation¶

ADX reliability metrics and considerations:

Lag Period: ADX typically lags price by 2× the period setting. With 14-period ADX, expect signals about 28 bars after trend begins.
False Positive Rate: ADX crossing above 25 fails to produce sustained trend approximately 30-40% of time. Always use with directional confirmation.
Optimal Threshold: Studies show ADX threshold of 25 is optimal for most markets, but varies by asset. Backtest your specific market to find optimal level.
Trend Persistence: When ADX crosses above 25, average trend duration is 1.5-2× the ADX period. With 14-period ADX, expect trend to last 21-28 bars on average.
Risk/Reward: Trading only when ADX > 25 increases win rate by approximately 15-20% compared to taking all signals, while reducing trade frequency by 40-50%.

References¶

Wilder, J. Welles Jr. "New Concepts in Technical Trading Systems" (1978) - Original ADX publication and Directional Movement System
Murphy, John J. "Technical Analysis of the Financial Markets" (1999) - Comprehensive ADX interpretation and application
Kaufman, Perry J. "Trading Systems and Methods" (2013) - Statistical analysis of ADX performance
TradingView: ADX Educational Guide
StockCharts: ADX Technical Analysis