Forecast a seasonal series with STL plus seasonal-naive drift

A lightweight, dependency-free forecaster for a single seasonal series. The series is decomposed with stats::stl() into trend, seasonal and remainder. The trend is extrapolated linearly from its last frequency fitted values (the recent local slope), the seasonal pattern is carried forward by repeating the last full cycle of the seasonal component (a seasonal-naive forecast), and the point forecast is their sum.

Usage

ts_forecast(x, h = 12, frequency = NULL, level = 0.95)

Arguments

x: A ts object, or a numeric vector (then frequency is required).
h: Forecast horizon: the number of future steps (a positive integer).
frequency: Number of observations per period; taken from x when it is a ts.
level: Prediction-interval coverage (a single number strictly between 0 and 1).

Value

A data frame with one row per forecast step and columns time (the future times, on the same scale as stats::time()), fit, lwr and upr.

Details

Prediction intervals are a random-walk-style normal band: the one-step standard deviation is estimated from the STL remainder and the interval at horizon h is fit +/- z * sigma * sqrt(h), so the band necessarily widens with the horizon. This mirrors how seasonal-naive forecast variance accumulates over time and gives an honest, monotonically growing uncertainty band without pulling in a heavy modelling dependency. For a fully specified statistical model use, for example, forecast::forecast() and pass the resulting fit/interval columns to timeseries_plot() directly.

Examples

fc <- ts_forecast(AirPassengers, h = 12)
head(fc)
#>       time      fit      lwr      upr
#> 1 1961.000 477.4164 437.8107 517.0222
#> 2 1961.083 471.7217 415.7107 527.7326
#> 3 1961.167 507.9436 439.3444 576.5427
#> 4 1961.250 506.7005 427.4890 585.9119
#> 5 1961.333 513.2907 424.7296 601.8518
#> 6 1961.417 555.3931 458.3792 652.4069
# Interval width grows with the horizon
diff(fc$upr - fc$lwr) >= 0
#>  [1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE