How to Calculate Moving Averages (SMA, EMA, and WMA)

SMA = Sum of values over N periods / N Equal weight given to all periods in the window. Data: daily temperatures: 15, 17, 14, 18, 20, 19, 22 (°C) 5-day SMA (day 5): (15+17+14+18+20) / 5 = 84/5 = 16.8°C 5-day SMA (day 6): (17+14+18+20+19) / 5 = 88/5 = 17.6°C 5-day SMA (day 7): (14+18+20+19+22) / 5 = 93/5 = 18.6°C SMA lag: always responds slowly to recent changes. A 200-day SMA on stock prices moves very slowly. Advantage: removes noise and short-term volatility. Disadvantage: slow to signal real trend changes.

EMA gives more weight to recent data. Smoothing factor: k = 2 / (N + 1) EMA_today = Price_today x k + EMA_yesterday x (1 - k) For a 5-period EMA: k = 2/(5+1) = 0.333 Using same data: 15, 17, 14, 18, 20, 19, 22 Start: EMA at period 1 = 15 (first value) Period 2: 17 x 0.333 + 15 x 0.667 = 5.66 + 10.00 = 15.66 Period 3: 14 x 0.333 + 15.66 x 0.667 = 4.66 + 10.44 = 15.10 Period 4: 18 x 0.333 + 15.10 x 0.667 = 5.99 + 10.07 = 16.06 Period 5: 20 x 0.333 + 16.06 x 0.667 = 6.66 + 10.71 = 17.37 Period 6: 19 x 0.333 + 17.37 x 0.667 = 6.33 + 11.58 = 17.91 Period 7: 22 x 0.333 + 17.91 x 0.667 = 7.33 + 11.95 = 19.27

WMA assigns linearly increasing weights to more recent data. For N periods, weights are: 1, 2, 3, ... N (most recent gets weight N) Sum of weights = N x (N+1) / 2 5-period WMA for days 3-7: 14, 18, 20, 19, 22 Weights: 1, 2, 3, 4, 5 (5 is most recent) Sum of weights: 5 x 6 / 2 = 15 WMA = (14x1 + 18x2 + 20x3 + 19x4 + 22x5) / 15 = (14 + 36 + 60 + 76 + 110) / 15 = 296 / 15 = 19.73