`UltimateOscillator`#

Description#

UltimateOscillator (Larry Williams, 1976) combines three timeframes of "buying pressure to true range" ratios into a single weighted oscillator. The three timeframes are intended to capture short, medium, and long momentum simultaneously.

\[\begin{split} \begin{aligned} \text{BP}[t] &= \text{close} - \min(\text{low},\ \text{close}_{t-1}) \\ \text{TR}[t] &= \max(\text{high},\ \text{close}_{t-1}) - \min(\text{low},\ \text{close}_{t-1}) \\ \text{avg}_k &= \frac{\sum \text{BP} \text{ over } \text{period}_k}{\sum \text{TR} \text{ over } \text{period}_k} \\ \text{UO}[t] &= 100 \cdot \frac{4 \cdot \text{avg}_1 + 2 \cdot \text{avg}_2 + \text{avg}_3}{7} \end{aligned} \end{split}\]

The 4 / 2 / 1 weighting puts the heaviest emphasis on the shortest period.

3-input, 1-output (FunctorBase<_, 3, 1>) on (high, low, close).

Parameters:

period1 (default 7): shortest timeframe.
period2 (default 14): medium timeframe.
period3 (default 28): longest timeframe.

Warmup: NaN until sample index max(period1, period2, period3) (TA-Lib's convention; gates on the longest window).

Output range: [0, 100].

NaN handling#

Policy: ignore. A NaN in any input at index t causes the function to skip that step: output at t is NaN and internal state is unchanged. Subsequent finite samples are processed as if step t had not occurred.

Examples#

Usage example#

import numpy as np
import plotly.graph_objects as go
from plotly.subplots import make_subplots
from screamer import UltimateOscillator

np.random.seed(0)
close = 100*np.exp(np.cumsum(np.random.normal(0, 0.01, size=300)))
open_ = np.concatenate([[close[0]], close[:-1]])
wick = np.abs(np.random.normal(0, 0.4, size=300))
high = np.maximum(open_, close) + wick
low  = np.minimum(open_, close) - wick
out = UltimateOscillator()(high, low, close)

fig = make_subplots(rows=2, cols=1, shared_xaxes=True,
                    row_heights=[0.55, 0.45], vertical_spacing=0.08)
fig.add_trace(go.Scatter(y=high, name="high", line=dict(color="#888")), row=1, col=1)
fig.add_trace(go.Scatter(y=low, name="low", line=dict(color="#bbb")), row=1, col=1)
fig.add_trace(go.Scatter(y=close, name="close", line=dict(color="royalblue")), row=1, col=1)
fig.add_trace(go.Scatter(y=out, name="UO(7,14,28)", line=dict(color="red")), row=2, col=1)
fig.update_layout(title="Ultimate oscillator (UltimateOscillator)",
                  margin=dict(l=20, r=20, t=60, b=20),
                  legend=dict(orientation="h", yanchor="bottom", y=1.02, xanchor="right", x=1))
fig.update_yaxes(title_text="price", row=1, col=1)
fig.update_yaxes(title_text="UO (0-100)", row=2, col=1)
fig.show()

Implementation Details#

Composition: tracks prev_close as a single scalar plus six detail::RollingSum buffers -- one for BP and one for TR at each of the three periods. Each RollingSum is O(1) per step, so the total per-step cost is O(1).

Reference#

Bit-exact match to talib.ULTOSC(high, low, close, timeperiod1, timeperiod2, timeperiod3) post-warmup (verified to ~1e-14 in tests/test_third_party_alignment.py).

UltimateOscillator#