Exponentially Weighted Moving Average (EWMA)

• Definition: An EWMA is a type of moving average that applies exponentially decreasing weights to older observations. This means more recent data points contribute more strongly to the average than older data points.
• Alpha (α): The smoothing factor (sometimes denoted alpha) determines how quickly the influence of older observations decreases.
  • If α is close to 1 (e.g., 0.9), the EWMA reacts quickly to recent changes and discounts older data more heavily.
  • If α is smaller (e.g., 0.1), the EWMA reacts more slowly, retaining more memory of older observations.
• Using EWMA in Pandas:
  • Import pandas and load your time series data into a DataFrame or Series.
  • Use the ewm() method to specify the alpha or span, com, halflife, etc.
  • Then chain the mean() function to compute the EWMA.

Example Code in Pandas

import pandas as pd

# Suppose 'df' is your pandas DataFrame with a 'close' column for prices
# Set alpha to 0.3 as an example
alpha_value = 0.3

df['ewma'] = df['close'].ewm(alpha=alpha_value, adjust=False).mean()

print(df.head())

In this example, each new EWMA value is computed using a fraction α=0.3 of the current observation and 1 - α of the previous EWMA value.