Understanding Lag Variables

Lag variables are essential tools in time series analysis for capturing temporal dependencies. A lag variable is a shifted version of the original time series, where each value represents the observation from a previous time step. Mathematically, if you have a time series $y_t$, the lag-1 variable is defined as $y_{\raisebox{-2pt}{$t-1$}}$, the lag-2 variable as $y_{\raisebox{-2pt}{$t-2$}}$, and so on. By including lagged values as features, you provide your model with information about past observations, allowing it to learn patterns such as trends, cycles, or seasonality. This is particularly useful in forecasting tasks, where predicting future values often depends on historical data. Without lag variables, a model may ignore valuable temporal structure, leading to poor predictions.