The oscillator is plotted as a single line from 0 to 100 and uses weighted sums of 3 oscillators (typically 7, 14 and 28 period time frames) to smooth out the variations that occur in indicators which only use one time period. These time periods overlap, i.e. the 28-period time frame includes the 14-period time frame and the 7-period time frame. This means that the action of the shortest time frame is included in the calculation  will be magnified 3 times in terms of impact on the results.

Formula & Calculation

1. True Low : TL(t) = min(low(t), close(t-1)) 

2. Buy Pressure :   BP(t) = close(t) - TL(t) 

3. True Range TR(t) = max(high(t) - low(t), high(t) - close(t-1), close(t-1) - low(t))

4. Buy Pressure Sums over 1st period (resp. 2nd and 3rd) : BPSum(p1) = BP(t) + ... + BP(t-p1) 

5. True Range Sums over 1st period (resp. 2nd and 3rd) : TRSum(p1) = TR(t) + ... + TR(t-p1)

   6. Raw Ultimate Oscillator : RawUO = 4 * (BPSum(p1) / TRSum(p1)) + 2 * (BPSum(p2) / TRSum(p2)) + (BPSum(p3) / TRSum(p3)) 

   7.Final Ultimate Oscillator : UO = 100 * (RawUO / (4 + 2 + 1))

How to Generate Trading Signals

The Ultimate Oscillator has 3 parameters for the 3 periods over which the buy pressures and true ranges are calculated.

A buy signal is generated when:

• There is a bullish divergence (the price reaches a lower low but the Ultimate Oscillator does not)

• The Ultimate Oscillator moves below 30 (oversold territory) and then rises above the highest point reached during the bullish divergence

A sell signal is generated when:

• There is a bearish divergence (the price reaches a higher high but the Ultimate Oscillator does not)

• The Ultimate Oscillator moves above 50 and then falls below the lowest point reached during the bearish divergence

A long position should be closed and profit taken when:

• A sell signal (described above) occurs

  OR

• The Ultimate Oscillator moves above 50 and then falls below 45, or it rises above 70

A short position should be closed and profit taken when:

• A buy signal (described above) occurs

  OR

• The Ultimate Oscillator rises above 65, or falls below 30

Note: 

The Ultimate Oscillator combines short-term, intermediate-term, and long-term price action into one oscillator that gives overbought and oversold readings, buy and sell signals, and in addition, confirms price action as well as divergences.

Larry Williams, describes the need for different time periods because:

Short-term

The short-term oscillator peaks earlier than price action peaks

Long-term

The long-term oscillator is late in responding to price action reversals and lags them.