Forecasting Methods: Moving Average vs Exponential Smoothing

Forecasting predicts future values from historical data. This guide compares the four most common time-series methods, shows worked calculations, and explains how to measure which forecast is most accurate.

Try each method on your own data with the free Forecasting Calculator.

1. Simple Moving Average (SMA)

The forecast is the average of the last n actual values. It smooths out noise but lags behind trends.

📐 Formula

Forecast(t) = (Aₜ₋₁ + Aₜ₋₂ + … + Aₜ₋ₙ) / n

For data 10, 12, 14, 16 with n = 3, the next forecast = (12 + 14 + 16) / 3 = 14.

2. Weighted Moving Average (WMA)

Like SMA, but recent periods get more weight, so it reacts faster to change.

📐 Formula

Forecast(t) = (w₁·Aₜ₋₁ + w₂·Aₜ₋₂ + … ) / Σw

3. Exponential Smoothing

Every past value contributes, with weights decaying geometrically. The smoothing constant α (0–1) controls responsiveness:

📐 Formula

F(t) = F(t−1) + α · (A(t−1) − F(t−1))

A high α reacts quickly to recent changes; a low α produces a smoother, more stable forecast.

4. Linear Trend (Regression)

When data rises or falls steadily, fit a least-squares line ŷ = a + b·t and project it forward. For perfectly linear data like 10, 12, 14, 16, 18, the next value is 20.

Measuring Forecast Accuracy

Compare methods using the forecast errors (actual − forecast):

📐 Formula

MAD = mean of |error| (mean absolute deviation) MSE = mean of error² (mean squared error) MAPE = mean of |error / actual| × 100 (mean absolute percentage error)

Lower values mean a better fit. MAD is easy to interpret; MSE punishes large errors; MAPE gives a scale-free percentage.

Choosing a Method

Stable, noisy data: moving average or exponential smoothing with a low α.
Data with recent shifts: weighted moving average or a higher α.
Clear upward/downward trend: linear trend regression.

Always test more than one method and pick the one with the lowest error on your data.

Common Mistakes

Overreacting to noise — too small a moving-average window or too high an α chases randomness.
Ignoring trend — smoothing methods lag behind a strong trend; use regression instead.
Comparing on one metric only — check MAD, MSE, and MAPE together.

Try It Yourself

Paste your historical series into the Forecasting Calculator, choose a method, and get the forecast plus MAD, MSE, and MAPE side by side. To fit a trend line explicitly, use the Linear Regression Calculator.

Key Takeaways

Moving averages smooth noise; exponential smoothing weights recent data; regression captures trend.
The smoothing constant α trades responsiveness against stability.
Compare methods with MAD, MSE, and MAPE and pick the lowest error.