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Python: March 2025
In “Removing Moving Average Lag” in this issue, John Ehlers introduces his projected moving average (PMA), designed to remove the lag inherent in moving averages. His approach involves adding the slope times half the length of the average to the average itself to accomplish the projected moving average. The code listings given in Ehlers’ article cover the projected moving average as a function; the projected moving average indicator (and its prediction) to plot on a chart; and slope and its prediction, which in this case is an output from the PMA function code and is used to create an oscillator.
Following is an implementation of Ehlers’ coding in Python:
Code: Select all
#
# import required python libraries
#
import pandas as pd
import numpy as np
import datetime as dt
import matplotlib.pyplot as plt
import yfinance as yf
#
# Retrieve S&P 500 daily price data from Yahoo Finance
#
symbol = '^GSPC'
ohlcv = yf.download(symbol, start="2015-01-15", end="2025-01-22")
ohlcv
#
# Introducing the Projected Moving Average PMA
#
def linear_regression_slope(samples):
# Use numpy's polyfit to calculate the slope (1st degree polynomial)
m, b = np.polyfit(np.arange(len(samples)), np.array(samples), 1)
return m
def calc_linear_regression_slope(in_series, length):
slope = in_series.rolling(length).apply(linear_regression_slope)
return slope
def calc_sma(in_series, length):
return in_series.rolling(length).mean()
def calc_pma(in_series, length):
sma = calc_sma(in_series, length)
slope = calc_linear_regression_slope(in_series, length)
pma = (sma + slope * length / 2)
return pma
#
# S&P500 applying SMA and PMA indicators using 30 trading days
#
length = 30
df = ohlcv.copy()
df['SMA'] = calc_sma(df['Close'], length)
df['PMA'] = calc_pma(df['Close'], length)
simple_plot1(df['2023-09':'2024-09-04'], length)
#
# S&P500 applying SMA and PMA indicators using 200 trading days
#
length = 200
df = ohlcv.copy()
df['SMA'] = calc_sma(df['Close'], length)
df['PMA'] = calc_pma(df['Close'], length)
simple_plot1(df['2023-09':'2024-09-04'], length)
#
# Prediction to Further Reduce Lag
#
def calc_pma_prediction(pma, slope, length):
# Predict = PMA + 0.5*(Slope - Slope[2])*Length
predict = pma + (slope - slope.shift(2)) * length / 2
return predict
#
# S&P500 applying PMA and PMA Prediction indicators
#
length = 30
df = ohlcv.copy()
df['SMA'] = calc_sma(df['Close'], length)
df['PMA'] = calc_pma(df['Close'], length)
#df['LRC'] = df['Close'].rolling(length).apply(linear_regression_curve)
df['Slope'] = df['Close'].rolling(length).apply(linear_regression_slope)
df['Predict'] = calc_pma_prediction(df['PMA'], df['Slope'], length)
df['Signal'] = np.where(df['Predict'] > df['PMA'], 1, 0)
simple_plot2(df['2023-09':'2024-09-04'], length, signal_ena=True)
#
# Introducing Generalized Prediction of an Indicator
#
def calc_general_prediction(smooth):
predict = 1.5*smooth - 0.5*smooth.shift(4)
return predict
#
# S&P 500 appling Slope and Slope Prediction indicators
#
length = 30
df = ohlcv.copy()
df['SMA'] = calc_sma(df['Close'], length)
df['PMA'] = calc_pma(df['Close'], length)
#df['LRC'] = df['Close'].rolling(length).apply(linear_regression_curve)
df['Slope'] = df['Close'].rolling(length).apply(linear_regression_slope)
df['Predict'] = calc_pma_prediction(df['PMA'], df['Slope'], length)
df['Slope Predict'] = calc_general_prediction(df['Slope'])
