Forecasting Foundations

Modified

March 29, 2026

1 A tidy forecasting workflow

1.0.1 Foundations

Forecasting requires methodological discipline:

  • Split the data (train/test)
  • Establish benchmark models
  • Forecast
  • Measure accuracy
  • Select a baseline
  • Refit and produce the final forecast

1.0.2 Example dataset

We use a built-in dataset from fpp3: aus_production.

  • It is already a tsibble
  • It contains multiple economic production series
  • We focus on Gas

1.0.3 Visualize

1.0.4 Train/test split

  • Split the series into training and test sets.
  • The test set length should match the forecast horizon.

For this example, we use the last 8 quarters as test data.

n_train  n_test 
    212       6

In time series, the training set must contain earlier observations and the test set later observations.
We mimic the real-world scenario: use past data to forecast the future.

1.0.5 Benchmark models

Before fitting complex models, we establish benchmarks.

Common benchmark methods in tidyverts:

  • Mean method: MEAN()
  • Naïve method: NAIVE()
  • Seasonal naïve method: SNAIVE()
  • Drift method: RW(... drift())
Code
bench_fit <- gas_train |> 
  model(
    mean   = MEAN(Gas),
    naive  = NAIVE(Gas),
    snaive = SNAIVE(Gas),
    drift  = RW(Gas ~ drift())
  )

1.0.6 Forecast

Generate forecasts with a horizon equal to the test set length.

Code
bench_fcst <- bench_fit |> 
  forecast(h = nrow(gas_test))

(Optional) Plot forecasts:

Code
bench_fcst |> 
  autoplot(gas_train, level = 95) |> 
  autolayer(gas_test, Gas, alpha = 0.7)

1.0.7 Forecast accuracy

We measure forecast accuracy using forecast errors:

e_{T+h} = y_{T+h} - \hat{y}_{T+h|T}

Compute accuracy metrics:

Code
bench_acc <- bench_fcst |> 
  accuracy(gas_test) |> 
  arrange(MASE)

bench_acc

Selection rule:

  • Prefer models that perform well on MASE (scale-independent).
  • For seasonal data, snaive is often a strong benchmark.

1.0.8 Error metrics

Using forecast errors, we can compute summary metrics:

Common error metrics
Scale Metric Description Formula
Scale-dependent
  • RMSE
  • MAE
  • Root Mean Squared Error
  • Mean Absolute Error
  • \sqrt{\text{mean}(e_{t}^{2})}
  • \text{mean}(|e_{t}|)
Scale-independent
  • MAPE
  • MASE
  • RMMSE
  • Mean Absolute Percentage Error
  • Mean Absolute Scaled Error
  • Root Mean Squared Scaled Error
  • \text{mean}(|p_{t}|)
  • \text{mean}(|q_{t}|)
  • \sqrt{\text{mean}(q_{t}^{2})}

1.0.9 Refit and forecast

Once a benchmark is selected based on the test set, refit it using all available data, then forecast the desired future horizon.

Example: refit snaive and forecast the next 8 quarters.

Code
final_fit <- aus_production |> 
  model(
    final_model = SNAIVE(Gas)
  )

final_fcst <- final_fit |> 
  forecast(h = "8 quarters")

1.0.10 Communicate

Forecasting is not finished when numbers are produced.
Results must be communicated clearly and honestly.

Minimum communication checklist:

  • Plot: history + forecast + prediction intervals
  • Horizon: what the forecast period represents
  • Baseline: state the benchmark model used
  • Uncertainty: prediction intervals are essential
  • Limitations: structural breaks, short samples, changing conditions
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