time series forecasting

The prediction of future values of one or more time-ordered variables from their history and from related covariates such as calendar effects, prices or weather. Forecasts may be point estimates or probabilistic (quantiles or full distributions), one step or many steps ahead, and for a single series or thousands of related ones. Classical statistical methods model trend, seasonality and autocorrelation explicitly (exponential smoothingexponential smoothing, n.: A simple forecasting method that predicts the next value as a weighted average of past values, giving the most weight to recent ones and steadily less to older ones., ARIMAARIMA, n.: A classic statistical recipe for forecasting a series of numbers over time: remove any steady trend, then predict the next value from recent values and recent prediction errors., state-space models); machine-learning approaches recast forecasting as regressionregression, n.: Predicting a number rather than a category — a house's price, tomorrow's temperature, a patient's blood pressure — by learning from past examples where the answer is known. on lagged and engineered features, typically with gradient boostinggradient boosting, n.: A method that builds a strong predictor by adding small decision trees one at a time, each trained to correct the errors that remain after all the trees before it., or train deep sequence models (recurrent networksrecurrent neural network, n.: A neural network that reads a sequence, such as a sentence or an audio clip, one piece at a time, carrying a running summary forward so that what came earlier can shape how later pieces are understood., temporal convolutions, transformerstransformer, n.: The design behind today's chatbots and much of modern AI. It handles text by letting every word look at every other word and decide which of them matter for understanding it.) across many series. Since 2023, pretrained time series foundation modelstime series foundation model, n.: A large AI model pretrained on huge numbers of time series, such as sales, traffic and sensor readings, that can forecast a new series it has never seen without being trained on it. have offered zero-shot forecasts. Evaluation must respect time order: models are backtested on rolling or expanding windows rather than shuffled cross-validationcross-validation, n.: A fair way to test a model when data are limited: split the data into several parts, train on all but one, test on the part left out, and rotate so every part takes a turn., to avoid data leakagedata leakage, n.: A mistake in building a model that lets it peek at clues it will not have in real use, such as hints about the very answer it must predict, so it shines in testing and then disappoints. from the future, and scored with error measures such as mean absolute errormean absolute error, n.: A way of scoring numerical predictions: average how far off each prediction is, ignoring direction, so the score reads as 'typically off by this much'. Lower is better. or quantilequantile regression, n.: Predicting not just a typical value but a range — say, the delivery time that 90% of orders beat — by fitting models for chosen percentiles of the outcome instead of its average. losses against naive baselinesbaseline, n.: A simple reference method that a new model must beat to show it is worth anything, such as always guessing the most common answer or reusing yesterday's value. such as 'same as last week'.

In the backtest the boosted model beat seasonal naive by 18% on MAE, but only after we added holiday features.