KAMA (Kaufman Adaptive Moving Average)¶

Overview¶

The Kaufman Adaptive Moving Average (KAMA) is a sophisticated adaptive moving average developed by Perry Kaufman that automatically adjusts its smoothing constant based on market efficiency and volatility. KAMA becomes faster and more responsive in trending markets while slowing down in choppy, range-bound markets to reduce whipsaws. This intelligent adaptation makes KAMA one of the most advanced trend-following indicators available.

Parameters¶

Parameter	Type	Default	Description
`input_data`	Array	Required	The price data array (typically close prices)
`period`	Integer	30	Number of periods for efficiency ratio calculation

Parameter Details¶

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

input_data - Typically uses closing prices for standard trend analysis - Can use other price types for specialized applications - Requires sufficient data points for stable efficiency ratio calculations - More historical data improves adaptation reliability

period (time_period) - Default is 30 periods for balanced adaptation - Common periods: - 10 periods: Short-term, highly adaptive - 20 periods: Standard intraday and swing trading - 30 periods: Medium-term position trading (default) - 50+ periods: Long-term trend identification - Shorter periods increase adaptation frequency - Longer periods provide smoother, less reactive trends

Usage¶

Basic Usage¶

require 'sqa/tai'

prices = [44.34, 44.09, 44.15, 43.61, 44.33, 44.83,
          45.10, 45.42, 45.84, 46.08, 46.03, 46.41,
          46.22, 45.64, 46.21, 46.25, 46.08, 46.46,
          46.82, 47.00, 47.32, 47.20, 47.57, 47.80,
          48.00, 48.15, 48.30, 48.40, 48.55, 48.70,
          48.85, 49.00, 49.15, 49.30]

# Calculate 30-period KAMA (default)
kama = SQA::TAI.kama(prices)

puts "Current KAMA: #{kama.last.round(2)}"

With Custom Parameters¶

# Calculate 10-period KAMA for shorter-term adaptation
kama_10 = SQA::TAI.kama(prices, period: 10)

# Calculate 50-period KAMA for long-term trends
kama_50 = SQA::TAI.kama(prices, period: 50)

puts "Short-term KAMA (10): #{kama_10.last.round(2)}"
puts "Standard KAMA (30): #{kama.last.round(2)}"
puts "Long-term KAMA (50): #{kama_50.last.round(2)}"

Understanding the Indicator¶

What It Measures¶

KAMA measures trend direction with intelligent adaptation:

Adaptive Trend Direction: Automatically adjusts responsiveness based on market conditions
Market Efficiency: Measures directional movement versus noise
Dynamic Smoothing: Fast in trends, slow in ranges
Whipsaw Reduction: Minimizes false signals in choppy markets

KAMA solves the fundamental problem of fixed-parameter moving averages: they cannot adapt to changing market conditions. KAMA's efficiency ratio allows it to be responsive when needed and smooth when volatility is high.

Calculation Method¶

KAMA uses the Efficiency Ratio (ER) to adapt its smoothing:

Calculate Change: Net price change over period
Calculate Volatility: Sum of absolute price changes
Calculate Efficiency Ratio: Change / Volatility
Calculate Smoothing Constant: Scale ER between fast and slow constants
Apply Adaptive Smoothing: Use SC to calculate KAMA

Formula¶

KAMA adapts its smoothing factor based on the Efficiency Ratio (ER):

Calculate Efficiency Ratio: ER = Change / Volatility
Calculate Smoothing Constant: SC = (ER * (Fast - Slow) + Slow)²
Apply: KAMA = KAMA_prev + SC * (Price - KAMA_prev)

Where Fast and Slow are the fastest and slowest smoothing constants.

Indicator Characteristics¶

Range: Unbounded (follows price range)
Type: Overlay indicator (plotted on price chart)
Lag: Adaptive (low in trends, medium in ranges)
Best Used: All market conditions, adaptive trend following

Interpretation¶

Value Ranges¶

KAMA's value adapts to market conditions:

KAMA Rising: Indicates uptrend
KAMA Falling: Indicates downtrend
KAMA Flat: Ranging market detected, reduced sensitivity

Key Levels¶

Price Above KAMA: Bullish condition
Price Below KAMA: Bearish condition
Price Crossing KAMA: Trend change (quality depends on efficiency)
KAMA Slope: Indicates trend strength and market efficiency

Signal Interpretation¶

Trend Direction
Price above rising KAMA = strong uptrend
Price below falling KAMA = strong downtrend
KAMA flat = low efficiency, avoid trend-following
Momentum Changes
KAMA steepening = increasing efficiency, strong trend
KAMA flattening = decreasing efficiency, weakening trend
KAMA adaptation = market regime change
Reversal Signals
Price crosses with high efficiency = strong signal
Price crosses with low efficiency = weak signal, likely whipsaw
Confirm with other indicators

Trading Signals¶

Buy Signals¶

Specific conditions that generate buy signals:

Primary Signal: Price crosses above KAMA while efficiency is increasing
Confirmation Signal: KAMA slope turning upward
Entry Criteria: Wait for pullback to KAMA in uptrend

Example Scenario:

When price crosses above KAMA and market efficiency is high (trending),
enter long with stop loss 2-3% below KAMA.
KAMA's adaptation means tighter stops in volatile markets.

Sell Signals¶

Specific conditions that generate sell signals:

Primary Signal: Price crosses below KAMA while efficiency is decreasing
Confirmation Signal: KAMA slope turning downward
Exit Criteria: Exit when KAMA flattens (low efficiency detected)

Example Scenario:

When price crosses below KAMA or KAMA flattens significantly,
exit long positions. KAMA's flattening indicates ranging market ahead.

Returns¶

Returns an array of KAMA values. The first several values will be nil due to the calculation requiring sufficient data points.

Usage¶

require 'sqa/tai'

prices = [44.34, 44.09, 44.15, 43.61, 44.33, 44.83,
          45.10, 45.42, 45.84, 46.08, 46.03, 46.41,
          46.22, 45.64, 46.21, 46.25, 46.08, 46.46,
          46.82, 47.00, 47.32, 47.20, 47.57, 47.80,
          48.00, 48.15, 48.30, 48.40, 48.55, 48.70,
          48.85, 49.00, 49.15, 49.30]

# Calculate 30-period KAMA (default)
kama = SQA::TAI.kama(prices)

# Calculate 10-period KAMA for shorter-term adaptation
kama_10 = SQA::TAI.kama(prices, period: 10)

puts "Current KAMA: #{kama.last.round(2)}"

Interpretation¶

KAMA's adaptive nature makes it unique among moving averages:

Trending Markets: KAMA hugs price closely, providing timely signals
Choppy Markets: KAMA flattens out, avoiding whipsaws
Price crosses above KAMA: Potential buy signal
Price crosses below KAMA: Potential sell signal
KAMA slope: Indicates trend strength

Example: KAMA Trend Following¶

prices = load_historical_prices('AAPL')
kama = SQA::TAI.kama(prices, period: 20)

current_price = prices.last
current_kama = kama.last
previous_kama = kama[-2]

# Check KAMA direction
kama_rising = current_kama > previous_kama
kama_falling = current_kama < previous_kama

# Check price position
price_above = current_price > current_kama
price_below = current_price < current_kama

if kama_rising && price_above
  puts "STRONG UPTREND - KAMA rising, price above"
elsif kama_falling && price_below
  puts "STRONG DOWNTREND - KAMA falling, price below"
elsif kama_rising && price_below
  puts "Pullback in uptrend - potential buy opportunity"
elsif kama_falling && price_above
  puts "Rally in downtrend - potential sell opportunity"
end

Example: KAMA Crossover System¶

prices = load_historical_prices('SPY')
kama = SQA::TAI.kama(prices, period: 20)

# Check for price crossing KAMA
price_current = prices.last
price_previous = prices[-2]
kama_current = kama.last
kama_previous = kama[-2]

# Bullish crossover
if price_previous <= kama_previous && price_current > kama_current
  puts "BULLISH CROSSOVER - Price crossed above KAMA"
  puts "Entry signal: BUY"
# Bearish crossover
elsif price_previous >= kama_previous && price_current < kama_current
  puts "BEARISH CROSSOVER - Price crossed below KAMA"
  puts "Exit/Short signal: SELL"
end

Example: KAMA with Efficiency Ratio¶

prices = load_historical_prices('TSLA')
kama = SQA::TAI.kama(prices, period: 20)

# Calculate simple efficiency proxy (price range vs total movement)
period = 20
price_change = (prices.last - prices[-period]).abs
total_movement = 0
(1...period).each do |i|
  total_movement += (prices[-i] - prices[-(i+1)]).abs
end

efficiency = total_movement > 0 ? price_change / total_movement : 0

puts "Market Efficiency: #{(efficiency * 100).round(2)}%"

if efficiency > 0.5
  puts "HIGH EFFICIENCY - Strong trending market"
  puts "KAMA will be more responsive"
elsif efficiency < 0.2
  puts "LOW EFFICIENCY - Choppy market"
  puts "KAMA will be smoother, fewer signals"
else
  puts "MODERATE EFFICIENCY - Mixed market conditions"
end

Example: Multi-Timeframe KAMA¶

# Assuming different timeframe data
daily_prices = load_historical_prices('MSFT', timeframe: 'daily')
weekly_prices = load_historical_prices('MSFT', timeframe: 'weekly')

daily_kama = SQA::TAI.kama(daily_prices, period: 20)
weekly_kama = SQA::TAI.kama(weekly_prices, period: 20)

daily_price = daily_prices.last
weekly_price = weekly_prices.last

daily_trend = daily_price > daily_kama.last ? "UP" : "DOWN"
weekly_trend = weekly_price > weekly_kama.last ? "UP" : "DOWN"

puts "Daily trend: #{daily_trend}"
puts "Weekly trend: #{weekly_trend}"

if daily_trend == "UP" && weekly_trend == "UP"
  puts "ALIGNED UPTREND - Strongest bullish setup"
elsif daily_trend == "DOWN" && weekly_trend == "DOWN"
  puts "ALIGNED DOWNTREND - Strongest bearish setup"
else
  puts "CONFLICTING TRENDS - Wait for alignment"
end

Advantages Over Traditional Moving Averages¶

Adaptive: Automatically adjusts to market conditions
Reduced Whipsaws: Slows down in choppy markets
Timely in Trends: Responds quickly in trending markets
Self-Optimizing: No need to constantly adjust parameters

Common Settings¶

Period	Use Case
10	Short-term, highly adaptive
20	Standard intraday and swing trading
30	Medium-term position trading (default)
50+	Long-term trend identification

Optimal Use Cases¶

When KAMA works best: - All market conditions: KAMA adapts to both trending and ranging markets - Volatile markets: Automatically adjusts to volatility changes - All timeframes: Effective on all timeframes due to adaptive nature - Smart trend following: Best for traders who want automatic adaptation

Combining with Other Indicators¶

With Trend Indicators: - Use ADX to measure trend strength alongside KAMA efficiency - Combine with fixed MA to compare adaptive vs non-adaptive signals

With Volume Indicators: - Confirm KAMA signals with volume for higher probability - Use volume to validate efficiency ratio readings

With Other Oscillators: - RSI helps identify overbought/oversold within KAMA trends - MACD provides momentum confirmation for KAMA signals

Common Pitfalls¶

What to avoid:

Ignoring Efficiency: Don't trade KAMA signals in low-efficiency markets
Over-optimization: Period affects efficiency calculation; don't over-optimize
Expecting Constant Response: KAMA changes speed; accept this variability
Using Alone: While adaptive, KAMA still benefits from confirmation

Parameter Selection Guidelines¶

How to choose optimal parameters:

Short-term trading: 10-20 period KAMA for frequent adaptation
Medium-term trading: 20-30 period KAMA for balanced adaptation
Long-term trading: 30-50 period KAMA for major trend identification
Backtesting: Test period selection but remember KAMA auto-adapts

Practical Example¶

See the comprehensive examples above demonstrating: - KAMA trend following with efficiency analysis - KAMA crossover systems - Multi-timeframe KAMA alignment - Efficiency ratio interpretation

Advanced Topics¶

Multi-Timeframe Analysis¶

Use KAMA across multiple timeframes: - Higher timeframe KAMA for overall market direction - Lower timeframe KAMA for entry timing - Compare efficiency ratios across timeframes - Only trade when efficiency is high on multiple timeframes

Market Regime Adaptation¶

KAMA automatically adapts but understanding helps: - High efficiency (>0.5): Strong trending, KAMA responsive - Medium efficiency (0.2-0.5): Mixed conditions, KAMA balanced - Low efficiency (<0.2): Ranging market, KAMA slow - Monitor efficiency to understand KAMA behavior

Statistical Validation¶

KAMA reliability metrics: - Most reliable when efficiency ratio is high (>0.5) - Reduces whipsaws by 30-50% vs fixed MAs in ranging markets - Maintains trend-following effectiveness in trending markets - Best combined with efficiency ratio analysis for signal quality

References¶

Kaufman, Perry J. "Trading Systems and Methods"
Kaufman, Perry J. "New Trading Systems and Methods"
Murphy, John J. "Technical Analysis of the Financial Markets"

Best Practices¶

Combine with Volume: Confirm KAMA signals with volume
Use Multiple Timeframes: Check alignment across timeframes
Wait for Confirmed Breaks: Avoid false signals at KAMA touches
Consider Market Regime: KAMA works best in markets with clear trend/range cycles
Monitor Efficiency: Track efficiency ratio to understand KAMA's current mode

EMA - Exponential Moving Average
DEMA - Double Exponential Moving Average
TEMA - Triple Exponential Moving Average
T3 - Tillson T3 Moving Average
MAMA - MESA Adaptive Moving Average

KAMA (Kaufman Adaptive Moving Average)¶

Overview¶

Parameters¶

Parameter Details¶

Usage¶

Basic Usage¶

With Custom Parameters¶

Understanding the Indicator¶

What It Measures¶

Calculation Method¶

Formula¶

Indicator Characteristics¶

Interpretation¶

Value Ranges¶

Key Levels¶

Signal Interpretation¶

Trading Signals¶

Buy Signals¶

Sell Signals¶

Returns¶

Usage¶

Interpretation¶

Example: KAMA Trend Following¶

Example: KAMA Crossover System¶

Example: KAMA with Efficiency Ratio¶

Example: Multi-Timeframe KAMA¶

Advantages Over Traditional Moving Averages¶

Common Settings¶

Optimal Use Cases¶

Combining with Other Indicators¶

Common Pitfalls¶

Parameter Selection Guidelines¶

Practical Example¶

Advanced Topics¶

Multi-Timeframe Analysis¶

Market Regime Adaptation¶

Statistical Validation¶

References¶

Best Practices¶

Related Indicators¶

See Also¶