# Ultimate Oscillator

## Overview

The Ultimate Oscillator 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. The oscillator is plotted as a single line from 0 to 100.

The ultimate oscillator was developed by Larry Williams.

## Formula

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))

## Parameters

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

## Interpretation

• There is a bullish divergence (the price reaches a lower low but the Ultimate Oscillator does not)
• The Ultimate Oscillator falls below 30 (oversold territory) and then rises above the highest point reached during the bullish divergence

A sell signal appears when:

• There is a bearish divergence (the price reaches a higher high but the Ultimate Oscillator does not)
• The Ultimate Oscillator rises above 50 and then falls below the lowest point reached during the bearish divergence

A long position should be closed when:

• A sell signal (described above) occurs OR
• The Ultimate Oscillator rises above 50 and then falls below 45, or it rises above 70

A short position should be closed when:

• A buy signal (described above) occurs OR
• The Ultimate Oscillator rises above 65, or falls below 30