Forecasting Foundations

A tidy forecasting workflow

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

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

Visualize

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 

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())

bench_fit <- gas_train |> 
  model(
    mean   = MEAN(Gas),
    naive  = NAIVE(Gas),
    snaive = SNAIVE(Gas),
    drift  = RW(Gas ~ drift())
  )

Forecast

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

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

(Optional) Plot forecasts:

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

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.

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})}

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.

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

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

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