Directional Movement Index (DX)¶

The Directional Movement Index (DX) measures the strength of directional movement in a price trend, regardless of direction. Developed by J. Welles Wilder as part of the Directional Movement System, DX is the raw calculation used to derive the Average Directional Index (ADX). It quantifies how strongly price is moving in a particular direction by comparing the Plus Directional Indicator (+DI) and Minus Directional Indicator (-DI).

Formula¶

DX is calculated using the directional indicators: 1. Calculate +DM (Plus Directional Movement) = Current High - Previous High (if positive and greater than downward movement) 2. Calculate -DM (Minus Directional Movement) = Previous Low - Current Low (if positive and greater than upward movement) 3. Calculate True Range (TR) = max(High-Low, |High-PrevClose|, |Low-PrevClose|) 4. Calculate +DI = (Smoothed +DM / Smoothed TR) * 100 5. Calculate -DI = (Smoothed -DM / Smoothed TR) * 100 6. DX = |(+DI - -DI)| / (+DI + -DI) * 100

Parameters¶

Parameter	Type	Required	Default	Description
`high`	Array	Yes	-	Array of high prices
`low`	Array	Yes	-	Array of low prices
`close`	Array	Yes	-	Array of close prices
`period`	Integer	No	14	Number of periods for smoothing

Returns¶

Returns an array of DX values ranging from 0 to 100.

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]
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]
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]

dx = SQA::TAI.dx(high, low, close, period: 14)

puts "Current DX: #{dx.last.round(2)}"

Interpretation¶

DX Value	Directional Strength
0-25	Weak or absent directional movement (ranging market)
25-50	Moderate directional movement (developing trend)
50-75	Strong directional movement (established trend)
75-100	Very strong directional movement (powerful trend)

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

Key Points: - DX measures the strength of directional movement, not direction - Higher DX = stronger trend (either up or down) - Lower DX = weaker trend or ranging market - DX > 25 typically indicates meaningful directional movement - DX is volatile; ADX smooths DX for easier interpretation

Example: Basic DX Analysis¶

high, low, close = load_historical_ohlc('AAPL')
dx = SQA::TAI.dx(high, low, close, period: 14)

current_dx = dx.last

case current_dx
when 0...25
  puts "WEAK DIRECTIONAL MOVEMENT (DX: #{current_dx.round(2)})"
  puts "Market is ranging or consolidating"
  puts "Trend-following strategies not recommended"
when 25...50
  puts "MODERATE DIRECTIONAL MOVEMENT (DX: #{current_dx.round(2)})"
  puts "Developing trend - monitor for confirmation"
when 50...75
  puts "STRONG DIRECTIONAL MOVEMENT (DX: #{current_dx.round(2)})"
  puts "Established trend - good for trend following"
else
  puts "VERY STRONG DIRECTIONAL MOVEMENT (DX: #{current_dx.round(2)})"
  puts "Powerful trend - potential exhaustion watch"
end

Example: DX with Directional Indicators¶

high, low, close = load_historical_ohlc('SPY')

dx = SQA::TAI.dx(high, low, close, period: 14)
plus_di = SQA::TAI.plus_di(high, low, close, period: 14)
minus_di = SQA::TAI.minus_di(high, low, close, period: 14)

current_dx = dx.last
current_plus = plus_di.last
current_minus = minus_di.last

# Calculate directional movement spread
di_spread = (current_plus - current_minus).abs

puts "DX: #{current_dx.round(2)}"
puts "+DI: #{current_plus.round(2)}"
puts "-DI: #{current_minus.round(2)}"
puts "DI Spread: #{di_spread.round(2)}"

# Identify trend direction and strength
if current_dx > 25
  if current_plus > current_minus
    puts "STRONG UPWARD DIRECTIONAL MOVEMENT"
    puts "Bullish trend with #{current_dx.round(2)} strength"
  else
    puts "STRONG DOWNWARD DIRECTIONAL MOVEMENT"
    puts "Bearish trend with #{current_dx.round(2)} strength"
  end
else
  puts "WEAK DIRECTIONAL MOVEMENT"
  puts "No clear trend - market consolidating"
  puts "+DI and -DI relatively balanced"
end

# High DX indicates one DI dominates
if current_dx > 50
  puts "Very high DI divergence - one direction dominates"
end

Example: DX Spike Detection¶

high, low, close = load_historical_ohlc('TSLA')
dx = SQA::TAI.dx(high, low, close, period: 14)

current_dx = dx.last
prev_dx = dx[-2]
dx_5_ago = dx[-6]

dx_change = current_dx - prev_dx
dx_5_change = current_dx - dx_5_ago

puts "Current DX: #{current_dx.round(2)}"
puts "Previous DX: #{prev_dx.round(2)}"
puts "Change: #{dx_change.round(2)}"

# Detect rapid DX increases (trend development)
if dx_change > 10 && current_dx > 25
  puts "SHARP DX INCREASE - New trend forming!"
  puts "Directional movement accelerating"
elsif dx_change < -10 && current_dx < 25
  puts "SHARP DX DECREASE - Trend weakening"
  puts "Entering range-bound conditions"
end

# Sustained DX increase over multiple periods
if dx_5_change > 20
  puts "DX rising strongly over 5 periods"
  puts "Trend gaining momentum consistently"
end

# DX spikes and reversal
if current_dx > 60 && prev_dx > 60 && dx_change < 0
  puts "DX declining from very high levels"
  puts "Possible trend exhaustion - watch for reversal"
end

Example: DX Divergence Analysis¶

high, low, close = load_historical_ohlc('NVDA')

dx = SQA::TAI.dx(high, low, close, period: 14)
plus_di = SQA::TAI.plus_di(high, low, close, period: 14)
minus_di = SQA::TAI.minus_di(high, low, close, period: 14)

# Find price and DX peaks
price_high_1 = close[-20..-10].max
price_high_2 = close[-9..-1].max

dx_high_1 = dx[-20..-10].compact.max
dx_high_2 = dx[-9..-1].compact.max

# Bearish divergence: price higher high, DX lower high
if price_high_2 > price_high_1 && dx_high_2 < dx_high_1
  puts "BEARISH DIVERGENCE DETECTED"
  puts "Price higher high: #{price_high_1.round(2)} -> #{price_high_2.round(2)}"
  puts "DX lower high: #{dx_high_1.round(2)} -> #{dx_high_2.round(2)}"
  puts "Directional strength weakening despite higher prices"
  puts "Warning: Trend may be losing momentum"
end

# Bullish divergence: price lower low, DX higher low
price_low_1 = close[-20..-10].min
price_low_2 = close[-9..-1].min

dx_low_1 = dx[-20..-10].compact.min
dx_low_2 = dx[-9..-1].compact.min

if price_low_2 < price_low_1 && dx_low_2 > dx_low_1
  puts "BULLISH DIVERGENCE DETECTED"
  puts "Price lower low: #{price_low_1.round(2)} -> #{price_low_2.round(2)}"
  puts "DX higher low: #{dx_low_1.round(2)} -> #{dx_low_2.round(2)}"
  puts "Directional strength building despite lower prices"
  puts "Potential trend reversal forming"
end

Example: DX Breakout Confirmation¶

high, low, close = load_historical_ohlc('MSFT')

dx = SQA::TAI.dx(high, low, close, period: 14)
plus_di = SQA::TAI.plus_di(high, low, close, period: 14)

# Identify resistance breakout
resistance = 250.00
current_price = close.last
prev_price = close[-2]

current_dx = dx.last
prev_dx = dx[-2]

# Price breaks resistance
if current_price > resistance && prev_price <= resistance
  puts "PRICE BREAKOUT at #{current_price.round(2)}"

  # Check DX confirmation
  if current_dx > 25 && current_dx > prev_dx
    puts "DX CONFIRMS BREAKOUT (#{current_dx.round(2)})"
    puts "Strong directional movement supporting breakout"
    puts "High probability of sustained move"
  elsif current_dx < 20
    puts "WARNING: DX LOW (#{current_dx.round(2)})"
    puts "Weak directional strength - false breakout risk"
    puts "Wait for DX to rise above 25 for confirmation"
  else
    puts "DX moderate (#{current_dx.round(2)})"
    puts "Monitor for DX increase to confirm trend"
  end

  # Check directional indicator alignment
  if plus_di.last > minus_di.last
    puts "+DI > -DI: Directional indicators support upside"
  end
end

Example: DX vs ADX Comparison¶

high, low, close = load_historical_ohlc('GOOGL')

dx = SQA::TAI.dx(high, low, close, period: 14)
adx = SQA::TAI.adx(high, low, close, period: 14)

current_dx = dx.last
current_adx = adx.last

puts "DX (raw): #{current_dx.round(2)}"
puts "ADX (smoothed): #{current_adx.round(2)}"
puts "Difference: #{(current_dx - current_adx).round(2)}"

# DX is more volatile, ADX is smoother
if current_dx > current_adx + 20
  puts "DX SPIKE above ADX"
  puts "Recent surge in directional strength"
  puts "New trend developing - ADX will follow"
elsif current_dx < current_adx - 10
  puts "DX BELOW ADX"
  puts "Recent directional weakness"
  puts "Trend may be losing steam"
else
  puts "DX and ADX aligned"
  puts "Consistent directional movement"
end

# Track DX volatility
dx_volatility = dx[-10..-1].compact.map { |v| (v - current_adx).abs }.sum / 10
puts "DX volatility around ADX: #{dx_volatility.round(2)}"

if dx_volatility > 15
  puts "High DX volatility - choppy directional changes"
elsif dx_volatility < 5
  puts "Low DX volatility - stable directional trend"
end

Example: Multi-Period DX Analysis¶

high, low, close = load_historical_ohlc('AMZN')

# Calculate multiple periods
dx_7 = SQA::TAI.dx(high, low, close, period: 7)
dx_14 = SQA::TAI.dx(high, low, close, period: 14)
dx_21 = SQA::TAI.dx(high, low, close, period: 21)

puts "Short-term DX (7): #{dx_7.last.round(2)}"
puts "Standard DX (14): #{dx_14.last.round(2)}"
puts "Long-term DX (21): #{dx_21.last.round(2)}"

# All periods strong = very strong trend
if dx_7.last > 40 && dx_14.last > 40 && dx_21.last > 40
  puts "ALL TIMEFRAMES SHOW STRONG DIRECTIONAL MOVEMENT"
  puts "Established, powerful trend across all periods"
elsif dx_7.last < 20 && dx_14.last < 20 && dx_21.last < 20
  puts "ALL TIMEFRAMES SHOW WEAK DIRECTIONAL MOVEMENT"
  puts "Strong range-bound market - avoid trend strategies"
end

# Divergence between timeframes
if dx_7.last > 50 && dx_21.last < 30
  puts "Short-term DX strong, long-term weak"
  puts "Recent surge in directional movement"
  puts "New trend potentially forming"
elsif dx_7.last < 25 && dx_21.last > 40
  puts "Short-term DX weak, long-term strong"
  puts "Recent consolidation in established trend"
  puts "Potential continuation after pause"
end

# Calculate DX slope across periods
dx_trend = (dx_7.last + dx_14.last + dx_21.last) / 3
puts "Average DX across periods: #{dx_trend.round(2)}"

Common Settings¶

Period	Use Case
7	Short-term, sensitive to recent changes
14	Standard (Wilder's original)
21	Longer-term, smoother trends
28	Very smooth, major trends only

Trading Strategies¶

1. Trend Filter¶

Enter trend trades only when DX > 25
Use range strategies when DX < 25
Higher DX = stronger trend signal

2. Breakout Confirmation¶

Price breakout + DX > 30 = confirmed breakout
Price breakout + DX < 20 = potential false breakout
Wait for DX to rise above 25 after breakout

3. DX Divergence¶

Price higher highs + DX lower highs = bearish divergence
Price lower lows + DX higher lows = bullish divergence
Indicates weakening/strengthening directional momentum

4. DX Extremes¶

DX > 60: Very strong trend, watch for exhaustion
DX < 15: Very weak trend, consolidation likely
DX spike from low to high: New trend emerging

Key Differences: DX vs ADX¶

Feature	DX	ADX
Calculation	Raw directional strength	Smoothed average of DX
Volatility	More volatile, reactive	Smoother, stable
Signal Speed	Faster signals	Lagging signals
Best For	Detecting trend changes	Confirming trend strength
Reading	More choppy	Easier to read

Understanding DX Components¶

DX is calculated from the directional indicators:

When +DI >> -DI: - Large difference creates high DX - Strong upward directional movement - Bullish trend strength

When -DI >> +DI: - Large difference creates high DX - Strong downward directional movement - Bearish trend strength

When +DI ≈ -DI: - Small difference creates low DX - Weak directional movement - Range-bound market

Advanced Techniques¶

1. DX Rate of Change¶

Track how quickly DX changes to identify trend acceleration:

dx_roc = ((dx.last - dx[-5]) / dx[-5] * 100).round(2)
puts "DX Rate of Change: #{dx_roc}%"

2. DX Zones¶

Customize thresholds based on asset volatility: - High volatility stocks: Use 30/20 instead of 25 - Low volatility stocks: Use 20/15 - Cryptocurrencies: Use 35/25

3. DX Histogram¶

Visualize DX changes period-to-period:

dx_change = dx.last - dx[-2]
puts "DX Change: #{dx_change > 0 ? '+' : ''}#{dx_change.round(2)}"

4. Combine with Volume¶

Strong DX + High Volume = High conviction trend Strong DX + Low Volume = Weak trend, caution

ADX - Average Directional Index (smoothed DX)
ADXR - ADX Rating
PLUS_DI - Plus Directional Indicator
MINUS_DI - Minus Directional Indicator