wenmin-wu/timeseries-rolling-refit-arima-forecast

Overview

ARIMA.forecast(steps=h) compounds error and hides refit cost. A rolling one-step loop — refit on current history, predict the next point, append the true value — gives you the error distribution a nightly-retrained production model would actually see. The distinction matters: multi-step ARIMA looks much worse than it really is because errors integrate, and a static-fit model looks much better than it really is because it never sees drift. The rolling refit is the honest middle ground.

Quick Start

from statsmodels.tsa.arima.model import ARIMA
import pandas as pd

history = list(train)
predictions = []
for t in range(len(test)):
    fit = ARIMA(history, order=(5, 0, 5)).fit(method='css')  # css = faster
    yhat = float(fit.forecast(steps=1)[0])
    predictions.append(yhat)
    history.append(test.iloc[t])          # append TRUTH, not prediction

pred = pd.Series(predictions, index=test.index)
abs_err = (test - pred).abs()

Workflow

1. Split the series into train/test by a cutoff date
2. Copy train into a mutable history list
3. For each test timestamp: refit ARIMA on history, forecast one step, record it
4. Append the observed value (never the prediction) to history before the next iteration
5. Assemble predictions into a Series aligned to test.index; plot observed vs forecast and the absolute-error distribution

Key Decisions

• Append truth, not prediction: otherwise errors compound and you're back to the broken multi-step case.
• Refit every step: the whole point is to catch drift. A static fit defeats the pattern.
• method='css': conditional sum of squares is faster than full MLE and plenty accurate for walk-forward. Bump maxiter if (p,q) are large.
• Pick (p,q) once via arma_order_select_ic: BIC over a small grid on the train split, then freeze. Re-selecting each step wastes compute and rarely changes the order.
• Cost is O(len(test)): budget accordingly; for 10k+ test points, switch to state-space Kalman updates instead of full refit.

References

• A first Kaggle - Part 1 - Forecasting store #47