Simple & Exponential Moving Averages

Simple & Exponential Moving Averages

Moving averages smooth out price data to identify trends. They are the foundation of most technical indicators.

Simple Moving Average (SMA)

The SMA over a window of size w at time t is the arithmetic mean of the last w prices:

SMA[t] = (prices[t] + prices[t-1] + ... + prices[t-w+1]) / w

The first w - 1 values are None because there is not enough data yet.

Exponential Moving Average (EMA)

The EMA applies an exponentially decaying weight to past prices using a smoothing factor alpha:

EMA[0] = prices[0]
EMA[t] = alpha * prices[t] + (1 - alpha) * EMA[t-1]

Higher alpha gives more weight to recent prices.

Task

Implement:

• sma(prices, window) — returns a list where the first window - 1 elements are None and subsequent elements are the rolling mean.
• ema(prices, alpha) — returns the exponential moving average starting from prices[0].