Simple exponential smoothing

\(\ell_t = \alpha y_t + (1-\alpha)\ell_{t-1}\), with alpha chosen by grid search on the in-sample SSE when not supplied.

Usage

morie_joseph_simple_exponential_smoothing(y, alpha = NULL, horizon = 1)

Arguments

y

series.

alpha

smoothing parameter in (0, 1]; fitted when NULL.

horizon

steps ahead.

Value

list with forecast, level, fitted, residuals, alpha, sse, effective_window.

Details

The forecast is FLAT at every horizon, because the model has a level and nothing else. On a trending series that is not a mild approximation – the forecast is wrong by an amount that grows with the horizon, and Holt's method is the fix. The reported effective_window is \(2/\alpha - 1\), the number of past observations the smoother is effectively averaging.

References

Hyndman, R. J. et al. (2008). Forecasting with Exponential Smoothing. Springer.

Examples

round(morie_joseph_simple_exponential_smoothing(c(3, 5, 4, 6, 5))$alpha, 2)
#> [1] 0.62