Moving Average Calculator

Understanding Moving Averages in Data & Financial Analysis

A moving average is a statistical calculation used to analyze data points by creating a series of averages of different subsets of the full data set. In financial and time-series analysis, moving averages smooth out short-term fluctuations and highlight longer-term trends or cycles.

Types of Moving Averages

1. Simple Moving Average (SMA)

The Simple Moving Average takes the unweighted arithmetic mean of $k$ values in a sliding window:

$$\text{SMA}_t = \frac{1}{k} \sum_{i=0}^{k-1} X_{t-i}$$

2. Weighted Moving Average (WMA)

The Weighted Moving Average assigns linearly increasing weights to more recent data points in the window:

$$\text{WMA}_t = \frac{\sum_{i=1}^{k} i \cdot X_{t-k+i}}{\frac{k(k+1)}{2}}$$

3. Exponential Moving Average (EMA)

The Exponential Moving Average applies exponentially decreasing weights to older data points, making it highly responsive to recent changes:

$$\text{EMA}_t = \alpha \cdot X_t + (1 - \alpha) \cdot \text{EMA}_{t-1}$$

where the smoothing factor $\alpha = \frac{2}{k + 1}$.