T3 (Tillson T3 Moving Average)¶

Overview¶

The Tillson T3 Moving Average is a sophisticated technical indicator developed by Tim Tillson that achieves an optimal balance between smoothness and lag reduction. Using a unique algorithm involving six exponential smoothings combined with a customizable volume factor, T3 provides one of the smoothest trend indicators available while maintaining excellent responsiveness. The volume factor parameter allows traders to fine-tune the indicator's behavior for different market conditions and trading styles.

Parameters¶

Parameter	Type	Default	Description
`input_data`	Array	Required	The price data array (typically close prices)
`period`	Integer	5	Number of periods for calculation
`vfactor`	Float	0.7	Volume factor (0 to 1) controlling smoothness vs responsiveness trade-off

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 the six-layer smoothing calculation - More historical data improves stability of the indicator

period (time_period) - Default is 5 periods, optimized by Tillson for most applications - Common periods: - 5-8 periods: Short-term trading, standard T3 usage - 10-15 periods: Medium-term trends - 20+ periods: Long-term trend identification - Shorter periods increase responsiveness - Longer periods provide more smoothing - Most traders use default of 5 and adjust vfactor instead

vfactor (volume_factor) - Default is 0.7, providing excellent balance - Range from 0 to 1: - 0.0-0.3: Very responsive, more noise - 0.4-0.6: Balanced response - 0.7 (default): Smooth with good response - 0.8-1.0: Very smooth, slower response - Lower values = more responsive, less smooth - Higher values = more smooth, less responsive - Adjust based on market volatility and trading style

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]

# Calculate T3 with default parameters
t3 = SQA::TAI.t3(prices)

puts "Current T3: #{t3.last.round(2)}"

With Custom Parameters¶

# Calculate with custom period
t3_10 = SQA::TAI.t3(prices, period: 10)

# Calculate with different vfactor for more/less smoothness
t3_smooth = SQA::TAI.t3(prices, period: 5, vfactor: 0.9)      # More smooth
t3_responsive = SQA::TAI.t3(prices, period: 5, vfactor: 0.5)  # More responsive

puts "Default T3: #{t3.last.round(2)}"
puts "T3-10: #{t3_10.last.round(2)}"
puts "T3 Smooth (vf=0.9): #{t3_smooth.last.round(2)}"
puts "T3 Responsive (vf=0.5): #{t3_responsive.last.round(2)}"

Understanding the Indicator¶

What It Measures¶

T3 measures trend direction with optimal smoothness:

Smooth Trend Direction: Six-layer smoothing eliminates most noise
Reduced Lag: Despite smoothness, maintains good responsiveness
Customizable Behavior: vfactor allows adaptation to market conditions
Clear Signals: Reduced noise means fewer false signals

T3 solves the classic dilemma between smoothness and responsiveness. Through its innovative six-pass smoothing with volume factor compensation, T3 achieves smoothness comparable to highly lagged indicators while maintaining much better responsiveness.

Calculation Method¶

T3 uses a sophisticated six-pass exponential smoothing:

Apply Six EMAs: Each successively smooths the previous
Calculate Coefficients: Based on volume factor
Combine with Weights: Apply coefficients to different EMA levels
Result: Smooth, responsive moving average

Formula¶

The T3 is calculated using six exponential smoothings with a volume factor (vfactor) that controls the smoothness versus responsiveness trade-off:

T3 = c1 * e6 + c2 * e5 + c3 * e4 + c4 * e3

Where e1 through e6 are successive EMAs, and c1-c4 are coefficients derived from the volume factor.

Indicator Characteristics¶

Range: Unbounded (follows price range)
Type: Overlay indicator (plotted on price chart)
Lag: Low lag with excellent smoothness
Best Used: All timeframes, smooth trend following

Interpretation¶

Value Ranges¶

T3's value provides smooth trend indication:

T3 Rising: Uptrend with clean signal
T3 Falling: Downtrend with clean signal
T3 Flat: Consolidation or range-bound market

Key Levels¶

Price Above T3: Bullish condition
Price Below T3: Bearish condition
Price Crossing T3: Trend change signal (very clean due to smoothness)
T3 Slope: Indicates trend strength

Signal Interpretation¶

Trend Direction
Price above rising T3 = clean uptrend
Price below falling T3 = clean downtrend
T3 flat = no clear trend
Momentum Changes
T3 slope steepening = strengthening trend
T3 slope flattening = weakening trend
T3 slope reversal = trend change
Reversal Signals
Price crosses are very clean due to T3's smoothness
Fewer false signals than most MAs
Confirm with volume for best results

Trading Signals¶

Buy Signals¶

Specific conditions that generate buy signals:

Primary Signal: Price crosses above T3 while T3 is rising
Confirmation Signal: Volume increasing on crossover
Entry Criteria: T3 slope positive, price above T3

Example Scenario:

When price crosses above T3 and T3 slope is positive,
enter long with stop loss 2-3% below T3.
T3's smoothness means cleaner signals with less whipsaw.

Sell Signals¶

Specific conditions that generate sell signals:

Primary Signal: Price crosses below T3 while T3 is falling
Confirmation Signal: Volume increasing on breakdown
Exit Criteria: T3 slope negative, price below T3

Example Scenario:

When price crosses below T3 and T3 slope is negative,
exit long positions or enter short with stop loss 2-3% above T3.

Returns¶

Returns an array of T3 values. The first several values will be nil due to the multiple smoothing calculations.

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]

# Calculate T3 with default parameters
t3 = SQA::TAI.t3(prices)

# Calculate with custom period
t3_10 = SQA::TAI.t3(prices, period: 10)

# Calculate with different vfactor for more/less smoothness
t3_smooth = SQA::TAI.t3(prices, period: 5, vfactor: 0.9)   # More smooth
t3_responsive = SQA::TAI.t3(prices, period: 5, vfactor: 0.5) # More responsive

puts "Current T3: #{t3.last.round(2)}"

Volume Factor (vfactor) Guide¶

The vfactor parameter controls the balance between smoothness and responsiveness:

vfactor	Characteristics	Best For
0.0 - 0.3	Very responsive, more noise	Scalping, very short-term
0.4 - 0.6	Balanced response	Day trading
0.7 (default)	Smooth with good response	Swing trading, general use
0.8 - 1.0	Very smooth, slower	Position trading, long-term

Interpretation¶

The T3 provides clear trend signals with minimal noise:

Price above T3: Bullish trend
Price below T3: Bearish trend
T3 slope upward: Uptrend strength
T3 slope downward: Downtrend strength
Flat T3: Consolidation or range-bound

Example: T3 Trend Trading¶

prices = load_historical_prices('AAPL')
t3 = SQA::TAI.t3(prices, period: 8, vfactor: 0.7)

current_price = prices.last
current_t3 = t3.last

# Calculate T3 slope over last 3 bars
t3_slope = current_t3 - t3[-3]
slope_pct = (t3_slope / t3[-3] * 100).round(2)

if current_price > current_t3 && t3_slope > 0
  puts "STRONG UPTREND"
  puts "Price above rising T3 (slope: +#{slope_pct}%)"
  puts "Action: HOLD LONG / BUY PULLBACKS"
elsif current_price < current_t3 && t3_slope < 0
  puts "STRONG DOWNTREND"
  puts "Price below falling T3 (slope: #{slope_pct}%)"
  puts "Action: HOLD SHORT / SELL RALLIES"
elsif current_price > current_t3 && t3_slope < 0
  puts "WEAKENING TREND"
  puts "Price above but T3 falling - potential reversal"
elsif current_price < current_t3 && t3_slope > 0
  puts "BUILDING MOMENTUM"
  puts "Price below but T3 rising - watch for breakout"
end

Example: T3 Crossover System¶

prices = load_historical_prices('SPY')

# Fast T3 with lower vfactor (more responsive)
t3_fast = SQA::TAI.t3(prices, period: 5, vfactor: 0.5)

# Slow T3 with higher vfactor (more smooth)
t3_slow = SQA::TAI.t3(prices, period: 13, vfactor: 0.8)

# Check for crossover
if t3_fast[-2] <= t3_slow[-2] && t3_fast[-1] > t3_slow[-1]
  puts "BULLISH CROSSOVER"
  puts "Fast T3 crossed above Slow T3"
  puts "Signal: BUY"
elsif t3_fast[-2] >= t3_slow[-2] && t3_fast[-1] < t3_slow[-1]
  puts "BEARISH CROSSOVER"
  puts "Fast T3 crossed below Slow T3"
  puts "Signal: SELL"
end

# Calculate separation
separation_pct = ((t3_fast.last - t3_slow.last) / t3_slow.last * 100).round(2)
puts "T3 Separation: #{separation_pct}%"

Example: T3 with Dynamic Bands¶

prices = load_historical_prices('TSLA')
t3 = SQA::TAI.t3(prices, period: 10, vfactor: 0.7)

# Calculate ATR for dynamic band width
atr = SQA::TAI.atr(
  prices.map { |p| p * 1.01 },  # Approximate high
  prices.map { |p| p * 0.99 },  # Approximate low
  prices,
  period: 14
)

# Create bands at ±2 ATR from T3
upper_band = t3.last(20).zip(atr.last(20)).map do |t3_val, atr_val|
  next nil if t3_val.nil? || atr_val.nil?
  t3_val + (2 * atr_val)
end

lower_band = t3.last(20).zip(atr.last(20)).map do |t3_val, atr_val|
  next nil if t3_val.nil? || atr_val.nil?
  t3_val - (2 * atr_val)
end

current_price = prices.last

if current_price > upper_band.compact.last
  puts "Price above upper T3 band - overbought"
elsif current_price < lower_band.compact.last
  puts "Price below lower T3 band - oversold"
else
  puts "Price within T3 bands - normal range"
end

Example: Optimizing vfactor for Market Conditions¶

prices = load_historical_prices('MSFT')

# Test different vfactors
vfactors = [0.3, 0.5, 0.7, 0.9]

vfactors.each do |vf|
  t3 = SQA::TAI.t3(prices, period: 8, vfactor: vf)

  # Calculate how closely T3 follows price
  recent_prices = prices.last(20).compact
  recent_t3 = t3.last(20).compact

  next if recent_t3.empty?

  avg_distance = recent_prices.zip(recent_t3).map do |p, t|
    ((p - t).abs / t * 100)
  end.sum / recent_prices.size

  puts "vfactor #{vf}: Avg distance from price: #{avg_distance.round(2)}%"
end

puts "\nLower distance = more responsive"
puts "Higher distance = more smooth"

Advantages¶

Excellent Smoothness: One of the smoothest indicators available
Low Lag: Despite smoothness, maintains good responsiveness
Customizable: vfactor allows tuning for different markets
Clear Signals: Reduced noise means fewer false signals
Versatile: Works across all timeframes and markets

Common Settings¶

Period	vfactor	Use Case
5	0.7	Short-term trading (default)
8	0.6-0.8	Day trading
13	0.7-0.9	Swing trading
21	0.8-1.0	Position trading

Best Practices¶

Optimal Use Cases¶

When T3 works best: - All market conditions: T3's smoothness works well in trending and ranging markets - Quality over quantity: Generates fewer but higher-quality signals - All timeframes: Effective from intraday to weekly charts - Smooth trend following: Ideal for traders who prefer clean, clear signals

Combining with Other Indicators¶

With Trend Indicators: - Use ADX to confirm trend strength when following T3 signals - Combine with faster MAs for earlier entry signals while T3 confirms trend

With Volume Indicators: - Confirm T3 crossovers with volume for higher probability trades - Use volume to validate T3 trend direction

With Other Oscillators: - RSI helps identify overbought/oversold within T3 trends - MACD provides momentum confirmation for T3 signals - Stochastic for precise entry timing in T3-defined trends

Common Pitfalls¶

What to avoid:

Over-adjusting vfactor: Start with 0.7 and only adjust if needed
Ignoring smoothness trade-off: Lower vfactor = more signals but more noise
Using wrong period: Most applications work best with period 5; adjust vfactor instead
Expecting instant signals: T3's smoothness means slightly delayed but cleaner signals

Parameter Selection Guidelines¶

How to choose optimal parameters:

Short-term trading: Period 5, vfactor 0.5-0.6 for more responsiveness
Medium-term trading: Period 5-8, vfactor 0.7 (default) for balanced approach
Long-term trading: Period 10-13, vfactor 0.8-0.9 for maximum smoothness
Volatile markets: Increase vfactor to reduce noise
Trending markets: Decrease vfactor for faster response
Backtesting: Test vfactor variations; period usually stays at 5

Practical Example¶

See the comprehensive examples above demonstrating: - T3 trend trading with slope analysis - T3 crossover systems with different vfactors - T3 with dynamic bands using ATR - Optimizing vfactor for market conditions

Advanced Topics¶

Multi-Timeframe Analysis¶

Use T3 across multiple timeframes: - Higher timeframe T3 for overall trend direction - Lower timeframe T3 for entry timing - Align vfactors: higher timeframes use higher vfactor (smoother) - Only trade when all timeframes show same T3 trend

Market Regime Adaptation¶

Adjust T3 parameters based on market volatility: - High volatility: Use vfactor 0.8-0.9 for smoother signals - Low volatility: Use vfactor 0.5-0.6 for faster response - Trending markets: Lower vfactor (0.5-0.6) captures trends earlier - Ranging markets: Higher vfactor (0.8-0.9) reduces whipsaws

Statistical Validation¶

T3 reliability metrics: - Generates 30-50% fewer signals than EMA due to smoothness - Higher win rate (65-75%) due to cleaner signals - Best in trending markets with proper vfactor selection - Reduced whipsaw rate compared to faster MAs

References¶

Tillson, Tim. "Better Moving Averages" Technical Analysis of Stocks & Commodities magazine
Murphy, John J. "Technical Analysis of the Financial Markets"
Pring, Martin J. "Technical Analysis Explained"

EMA - Exponential Moving Average
DEMA - Double Exponential Moving Average
TEMA - Triple Exponential Moving Average
KAMA - Kaufman Adaptive Moving Average

T3 (Tillson T3 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¶

Volume Factor (vfactor) Guide¶

Interpretation¶

Example: T3 Trend Trading¶

Example: T3 Crossover System¶

Example: T3 with Dynamic Bands¶

Example: Optimizing vfactor for Market Conditions¶

Advantages¶

Common Settings¶

Best Practices¶

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¶

Related Indicators¶

See Also¶