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Time-Series
Econometrics
Ian Helfrich PhD ↗

Lecture 1 summary · January 15, 2027

The decision and its information set

Complete chapter · Laboratory ch01 · Practice · All summaries

The economic question

Define an economic target and decision deadline before choosing a model. A low error cannot rescue information unavailable at the origin.

Central relation

E[(Y−a)2∣I]=Var⁡(Y∣I)+(E[Y∣I]−a)2\mathbb E[(Y-a)^2\mid\mathcal I]=\operatorname{Var}(Y\mid\mathcal I)+(\mathbb E[Y\mid\mathcal I]-a)^2

Individual problem

Equally weighted temperatures are 40 and 80. Heating exposure is the positive part of 65 minus temperature. Compare transformation before and after averaging.

Worked reasoning

Average temperature is 60, so its heating exposure is 5. Average heating exposure is one half of 25, or 12.5. Nonlinear transformation does not commute with averaging.

A consequential failure

Observed target-month weather is quietly included in an earlier forecast.

Repair

Retain observation, release, vintage, origin, and target dates. Forecast an unavailable predictor or declare a scenario.