How does exponential smoothing work for forecasting and how is it different from a moving average?

Exponential smoothing is a forecasting technique that assigns exponentially declining weights to past observations, giving the most importance to recent data. Unlike a simple moving average (SMA) which weights all observations in the window equally, exponential smoothing lets you control how quickly old data fades out.

Simple Exponential Smoothing Formula

F_{t+1} = alpha Y_t + (1 − alpha) F_t

Where:

• F_{t+1} = forecast for next period
• Y_t = actual observation this period
• F_t = previous forecast
• alpha = smoothing parameter (0 < alpha < 1)

The Alpha Parameter

Worked Example

Brookfield Risk Analytics is forecasting daily portfolio returns for VaR calculation using alpha = 0.3:

Exponential Smoothing vs. Simple Moving Average

• SMA with a 20-day window weights days 1 through 20 equally at 5% each, then drops day 1 entirely on day 21.
• Exponential smoothing never fully drops old data — it just decays. The effective weight on an observation k periods ago is alpha * (1−alpha)^k.
• This makes exponential smoothing more responsive to regime changes (e.g., a sudden volatility spike) while avoiding the 'cliff effect' of the SMA.

Connection to EWMA Volatility

The RiskMetrics EWMA model for variance is essentially exponential smoothing applied to squared returns:

sigma^2_{t+1} = lambda sigma^2_t + (1 − lambda) r^2_t

Here, lambda = 1 − alpha. RiskMetrics uses lambda = 0.94 for daily data, meaning alpha = 0.06 — a slow decay that produces stable volatility estimates.

Exam Tip: If asked to choose alpha, minimize the mean squared forecast error over a holdout sample. The FRM exam may give you a table of observations and ask you to compute the exponential smoothing forecast step by step.

Check out our FRM quantitative analysis practice for more forecasting problems.