Time Series

A time series is a sequence of observations on the same unit indexed by time: $\{y_1, y_2, \ldots, y_T\}$. Examples: daily NOₓ readings, annual GDP, monthly unemployment. The defining feature is temporal ordering — past influences future — which breaks the OLS independence assumption.

When to use

Time-series tools apply whenever the data is one (or a few) unit measured repeatedly over time, as opposed to a panel of many units over time. The lecture's classical-assumption layer adds strict exogeneity (errors uncorrelated with regressors at every lead and lag), homoskedasticity over time, and no serial correlation. Three workhorse model types: static, distributed lag, and autoregressive — the choice depends on whether past $x$ or past $y$ helps predict today.