Temporal Data Analysis

Temporal data analysis studies time series: sequences of observations of a variable ordered in time, usually at regular intervals. Its defining feature is that order is information: unlike independent tabular data, reordering a series destroys the signal. Observations close in time are correlated—what is called temporal dependence or autocorrelation—and that correlation is precisely what a model must exploit.

Basic concepts

A series is often decomposed into trend (its long-term direction), seasonality (periodic fluctuations of fixed, known frequency, such as day of the week or month) and an irregular component. Seasonality should be distinguished from the cycle, whose oscillations have no fixed frequency. A central concept is stationarity: a series is stationary when its statistical properties—mean, variance and autocorrelation structure—do not change over time. Many classical methods require it, and it is usually achieved by differencing, that is, subtracting the previous value from each one.

How it is evaluated: respect time

Evaluating a time-series model by shuffling the data at random is a serious mistake: it introduces data leakage, because the model would see the future during training and its metrics would look deceptively good before collapsing in production. The rule is a chronological split: the test set always comes after the training set in time. Proper validation uses windows that move forward in time—sliding, of fixed size, or expanding, accumulating the whole history—always training on the past and validating on the next period.

Models, by generation

The classical statistical methods include ARIMA, exponential smoothing (ETS) and Prophet. Deep learning contributed recurrent networks (RNN, LSTM, GRU) and probabilistic autoregressive models such as DeepAR. Specialized architectures followed: N-BEATS and N-HiTS, and the Temporal Fusion Transformer (Google, 2019), attention-based and interpretable. The most recent leap is the time-series foundation models, pre-trained at scale and able to forecast without prior retraining: TimesFM (Google), Chronos (Amazon) and Moirai (Salesforce), among others.

Limits

Real series are rarely stationary: their distribution changes—known as concept drift—abruptly, like a market shock, or gradually, like an aging sensor; and regime changes invalidate models trained on the past. Uncertainty also grows with the forecast horizon, so in critical applications a point estimate is not enough: prediction intervals with calibrated coverage are needed. Even the real reach of foundation models, still recent, is under debate.