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Time-Series
Econometrics
Ian Helfrich PhD ↗

Lecture 7 summary · February 26, 2027

Weather, seasonality, and dynamic regression

Complete chapter · Laboratory ch07 · Practice · All summaries

The economic question

Economic predictors can explain demand while the residual remains dynamic. A feasible forecast must specify the future predictor path.

Central relation

Yt−ϕYt−1=(Xt−ϕXt−1)′β+εtY_t-\phi Y_{t-1}=(X_t-\phi X_{t-1})\prime\beta+\varepsilon_t

Individual problem

Transform a regression with AR(1) errors. Which regressors must change? Can observed next-month weather enter the current forecast?

Worked reasoning

Transform the outcome and every design column, including the intercept. Observed future weather is unavailable now; use a forecast or scenario. Monthly-temperature transforms are exposure proxies.

A consequential failure

Only the outcome is transformed, or realized future weather is substituted for a feasible predictor.

Repair

Transform the full design consistently, declare initial-observation treatment, and distinguish predictor uncertainty from a fixed scenario.