Time series forecasting

1 · What it is

Time series forecasting predicts future values of something recorded over time. Planning depends on it: staffing a call centre next week, stocking a warehouse, or deciding whether to build a power plant. Past data usually mixes a few patterns. A trend is a long-term rise or fall. A seasonal pattern repeats on a fixed calendar period, such as every December. A cycle rises and falls without a fixed period, usually with the economy. Some series, like daily changes in a stock price, are mostly random fluctuations with little to predict.

Every forecast should be compared with simple baselines. The naive method repeats the last value; seasonal naive repeats the value from the same month last year; the mean method uses the average of all history. A new method that cannot beat these is not worth using. Exponential smoothing and ARIMA are the two most widely used classical approaches. Exponential smoothing takes a weighted average of past values, with recent ones counting more. ARIMA describes autocorrelation: how each value relates to earlier ones. Python’s statsmodels library implements both, and Google BigQuery can fit an ARIMA_PLUS model in SQL or use its built-in TimesFM model. Machine learning turns past values into lag features: scikit-learn’s example feeds recent bike rentals into a gradient boosting model to predict the next hour. DeepAR, a 2017 method, trains a recurrent network on many related series and outputs probabilistic forecasts; its paper reported about 15 per cent better accuracy on its datasets. Newer is not automatically better, though: a 2018 study of 1,045 monthly series found popular machine learning methods less accurate than eight traditional statistical ones at every horizon tested.

The testing rule is strict: judge a model only on data it never saw, and keep time in order. Hold out the latest stretch as a test set, ideally at least as long as the furthest forecast you need. Rolling-origin evaluation repeats this with the cut moved forward, and each training set holds only earlier values. A random shuffle breaks the rule by training on the future, which is a form of data leakage; in scikit-learn’s bike example, the shuffled score was too optimistic. Errors are summed up as MAE (the average size of the misses), RMSE (the square root of the average squared miss) or MAPE (the average percentage miss), which fails when an actual value is zero. A prediction interval adds a range that should contain the real value with a stated probability, often 80 or 95 per cent.

Forecasting assumes the way things are changing will carry on. Errors grow the further ahead you look. A financial or political crisis can make the future unlike the past, and some forecasts, such as exchange rates, change the very thing they predict.