What Is a Worked Example of the Ultimate Oscillator?

Direct answer: what a worked example means here

A worked example of the Ultimate Oscillator is a fully transparent numerical calculation that starts from assumed price inputs (high, low, close for several bars), then applies the indicator’s formulas step by step, and finally states the output value and assumptions.

Ultimate Oscillator is a momentum indicator built from three “lookback” horizons (commonly 7, 14, and 28 periods). It estimates buying pressure relative to the overall trading range using three intermediate ratios, then blends them into one oscillator.

Because no real-time market data is assumed here, the example uses invented but internally consistent numbers so you can independently verify every arithmetic step.

Mechanism or definition: the moving parts

For each bar t, define:

• Buying Pressure (BP): (BP_t = Close_t - Low_t) if (Close_t \ge Low_t). (In most practical cases, close is above or equal to low.)
• True Range (TR): a measure of how wide price moved, computed as (TR_t = max(High_t - Low_t, |High_t - Close_{t-1}|, |Low_t - Close_{t-1}|)).
• A ratio per horizon: (AvgBP/TR = \frac{\sum BP}{\sum TR}) over the horizon’s bars.

Ultimate Oscillator blends three horizon ratios. A common weighted form is:

(UO = 100 \times \frac{4\cdot S_7 + 2\cdot S_14 + 1\cdot S_28}{4 + 2 + 1})

where (S_7), (S_14), and (S_28) are the summed BP/TR ratios across 7, 14, and 28 periods respectively.

Important: the oscillator’s value depends on your exact period lengths and on accurate high/low/close series.

Evidence or example: one complete numerical scenario

Assumptions (explicit):

1. We use horizon lengths 7, 14, and 28 periods (as commonly used).
2. To keep the arithmetic manageable, we demonstrate the calculation using shortened “effective horizons” that mirror the same formula structure. Specifically, we compute the weighted blend from three horizons of 2, 3, and 4 bars, using the same weights 4, 2, and 1.
3. We set previous closes needed for TR using the bar-to-bar relationships provided below.
4. All values are in the same price units.

We create four bars for the underlying sequence (Bar 1 to Bar 4). Let each bar have (High), (Low), (Close), and Bar 0 has (Close_0) to support TR on Bar 1.

Base series:

• Close_0 = 100
• Bar 1: High=101, Low=99.5, Close=100.5
• Bar 2: High=102, Low=100, Close=101
• Bar 3: High=102.5, Low=100.5, Close=100.8
• Bar 4: High=103, Low=101, Close=102

Step A: compute BP for each bar ((BP_t = Close_t - Low_t)).

• BP1 = 100.5 − 99.5 = 1.0
• BP2 = 101 − 100 = 1.0
• BP3 = 100.8 − 100.5 = 0.3
• BP4 = 102 − 101 = 1.0

Step B: compute TR for each bar (needs (Close_{t-1})). Use (TR_t = max(High_t - Low_t, |High_t - Close_{t-1}|, |Low_t - Close_{t-1}|)).

• TR1:
  • High1−Low1 = 101 − 99.5 = 1.5
  • |High1−Close0| = |101 − 100| = 1
  • |Low1−Close0| = |99.5 − 100| = 0.5
  • TR1 = 1.5
• TR2:
  • High2−Low2 = 102 − 100 = 2
  • |High2−Close1| = |102 − 100.5| = 1.5
  • |Low2−Close1| = |100 − 100.5| = 0.5
  • TR2 = 2
• TR3:
  • High3−Low3 = 102.5 − 100.5 = 2
  • |High3−Close2| = |102.5 − 101| = 1.5
  • |Low3−Close2| = |100.5 − 101| = 0.5
  • TR3 = 2
• TR4:
  • High4−Low4 = 103 − 101 = 2
  • |High4−Close3| = |103 − 100.8| = 2.2
  • |Low4−Close3| = |101 − 100.8| = 0.2
  • TR4 = 2.2

Step C: compute three horizon “averages” as summed BP divided by summed TR. We use effective horizons matching the demonstration:

• S(2): use Bars 3-4 (2 bars)
  • Sum BP = BP3 + BP4 = 0.3 + 1.0 = 1.3
  • Sum TR = TR3 + TR4 = 2 + 2.2 = 4.2
  • S2 = 1.3 / 4.2 ≈ 0.3095238
• S(3): use Bars 2-4 (3 bars)
  • Sum BP = BP2 + BP3 + BP4 = 1.0 + 0.3 + 1.0 = 2.3
  • Sum TR = TR2 + TR3 + TR4 = 2 + 2 + 2.2 = 6.2
  • S3 = 2.3 / 6.2 ≈ 0.3709677
• S(4): use Bars 1-4 (4 bars)
  • Sum BP = BP1 + BP2 + BP3 + BP4 = 1.0 + 1.0 + 0.3 + 1.0 = 3.3
  • Sum TR = TR1 + TR2 + TR3 + TR4 = 1.5 + 2 + 2 + 2.2 = 7.7
  • S4 = 3.3 / 7.7 ≈ 0.4285714

Step D: apply the weighted blend using weights 4, 2, 1 (same structure as common Ultimate Oscillator):