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Python: September 2026
In his article in this issue, “Adaptive SuperSmoother,” John Ehlers introduces his adaptive SuperSmoother indicator based on his original SuperSmoother indicator. Presented here is Python code to construct and display the indicator.
"""
Python code to implement concepts in Technical Analysis of Stocks & Commodiities magazine
article "Adaptive SuperSmoother" by John F Ehlers. This python code is provided for the
TraderTips section of the magazine.
Written By:
Rajeev Jain, July 2026
jainraje@yahoo,com
All code available in GitHub:
https://github.com/jainraje/TraderTipArticles/
"""
Code: Select all
# import required python modules
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import yfinance as yf
import math
print(yf.__version__)
# retrive OHLCV using YFinance
symbol = 'QQQ'
ohlcv = yf.download(
symbol,
start="2000-01-01",
end="2026-07-11",
group_by="Ticker",
auto_adjust=False,
)
ohlcv = ohlcv[symbol]
ohlcv
# functions to implement indicators calculations
def rms(series, length):
series = np.asarray(series, dtype=float)
out = np.full(len(series), np.nan)
for i in range(length - 1, len(series)):
window = series[i - length + 1:i + 1]
out[i] = np.sqrt(np.mean(window ** 2))
return out
def supersmoother(price, period):
price = np.asarray(price, dtype=float)
out = np.full(len(price), np.nan)
if len(price) < 3:
return price.copy()
Q = np.exp(-1.414 * np.pi / period)
c1 = 2 * Q * np.cos(1.414 * np.pi / period)
c2 = Q * Q
a0 = (1 - c1 + c2) / 2
# initialization
out[0] = price[0]
out[1] = price[1]
for i in range(2, len(price)):
out[i] = (
a0 * (price[i] + price[i - 1])
+ c1 * out[i - 1]
- c2 * out[i - 2]
)
return out
def adaptive_supersmoother(close, period0=20, rms_length=81):
close = np.asarray(close, dtype=float)
n = len(close)
# outputs
ss_adaptive = np.full(n, np.nan)
ss_fixed = np.full(n, np.nan)
period_series = np.full(n, np.nan)
# initial pass (we update recursively)
ss_temp = supersmoother(close, period0)
roc1 = np.full(n, np.nan)
roc = np.full(n, np.nan)
for i in range(1, n):
roc1[i] = ss_temp[i] - ss_temp[i - 1]
# RMS normalization
start = max(0, i - rms_length + 1)
window = roc1[start:i + 1]
rocrms = np.sqrt(np.mean(window ** 2)) if len(window) > 0 else 0
if rocrms != 0:
roc[i] = abs(roc1[i] / rocrms)
else:
roc[i] = 0
roc[i] = min(roc[i], 2)
period = period0 * (1 - 0.5 * roc[i]) ** 2
period = max(period, 2)
period_series[i] = period
# Recompute adaptive SS properly (true recursive adaptive filter)
ss_adaptive[0] = close[0]
ss_adaptive[1] = close[1]
for i in range(2, n):
p = period_series[i - 1] if not np.isnan(period_series[i - 1]) else period0
Q = np.exp(-1.414 * np.pi / p)
c1 = 2 * Q * np.cos(1.414 * np.pi / p)
c2 = Q * Q
a0 = (1 - c1 + c2) / 2
ss_adaptive[i] = (
a0 * (close[i] + close[i - 1])
+ c1 * ss_adaptive[i - 1]
- c2 * ss_adaptive[i - 2]
)
return {
"adaptive_ss": ss_adaptive,
"fixed_ss": supersmoother(close, period0),
"roc": roc,
"period": period_series
}
def adaptive_supersmoother_series(close, period0=20, rms_length=81):
return pd.Series(
adaptive_supersmoother(close, period0, rms_length)["adaptive_ss"],
index=close.index
)
# function which encapsultes indicator call and signal generationr
def run_calcs(ohlcv):
df = ohlcv[['Close']].copy()
df['SS'] = supersmoother(df['Close'], period=20)
df['ASS'] = adaptive_supersmoother_series(df['Close'])
df['ASS OSC'] = df['ASS'] - df['SS']
df['ASS OSC NORM'] = (df['ASS'] - df['SS']) / df['Close'].rolling(20).std()
#df['Signal'] = np.where(df['ASS OSC'] > 0, 1,0)
df['Signal'] = np.where(df['ASS OSC'] > 0.1, 1,
np.where(df['ASS OSC'] < -0.1, 0, np.nan))
df['Signal'] = df['Signal'].ffill()
return df
df = run_calcs(ohlcv)
df
def simple_plot(df):
import matplotlib.pyplot as plt
fig, (ax1, ax2) = plt.subplots(
2, 1,
figsize=(9, 6),
sharex=True,
gridspec_kw={"height_ratios": [3, 1]}
)
# -------------------
# TOP: Price + filters + signal
# -------------------
ax1.plot(df.index, df['Close'], label='Close', color='black', linewidth=1.5)
ax1.plot(df.index, df['SS'], label='SuperSmoother (SS)', linewidth=1.2)
ax1.plot(df.index, df['ASS'], label='Adaptive SS (ASS)', linewidth=1.2)
ax1.set_ylabel('Price')
ax1.grid(True)
# Signal on secondary axis (TOP)
ax1b = ax1.twinx()
ax1b.step(df.index, df['Signal'], where='post',
label='Signal (ASS OSC > 0)', color='green', alpha=0.5)
ax1b.set_ylabel('Signal (0/1)')
ax1b.set_ylim(-0.1, 1.1)
# combine legends (top)
l1, lab1 = ax1.get_legend_handles_labels()
l2, lab2 = ax1b.get_legend_handles_labels()
ax1.legend(l1 + l2, lab1 + lab2, loc='upper left')
ax1.set_title('Price + SuperSmoother + Adaptive SS with Signal')
# -------------------
# BOTTOM: Oscillator
# -------------------
ax2.plot(df.index, df['ASS OSC'], label='ASS - SS Oscillator', color='purple', alpha=0.8)
ax2.plot(df.index, df['ASS OSC NORM'], label='ASS NORM- SS Oscillator', color='orange', alpha=0.8)
ax2.axhline(0, color='black', linewidth=1)
ax2.set_ylabel('Osc')
ax2.set_xlabel('Date')
ax2.grid(True)
ax2.legend()
plt.tight_layout()
plt.show()
simple_plot(df['2026':])
Sample Chart FIGURE 8: PYTHON. The original SuperSmoother indicator (cyan plotline) and the adaptive version of the SuperSmoother indicator (orange) are plotted in the price pane; the SuperSmoother oscillator is shown in the lower pane. The perpendicular green lines show example signals.