Lecture 5 summary · February 12, 2027

Signals, noisy measures, and information-preserving filters

Complete chapter · Laboratory ch05 · Practice · All summaries

The economic question

An indicator measures an economic quantity. A smooth retrospective graph can use observations unavailable when a real-time decision was made.

Central relation

\widetilde Y_t^{\mathrm{center}}=\frac15\sum_{j=-2}^{2}Y_{t+j},

\Delta\widetilde Y_t^{\mathrm{center}}=\frac{2\delta}{5}

Individual problem

Add 100 to each of the next two records, holding the past fixed. Compare a centered five-period estimate and a trailing three-period estimate at today.

Worked reasoning

The centered estimate increases by forty. The trailing estimate does not change. This mutation exposes future dependence without judging visual smoothness.

A consequential failure

A retrospective smoother is called a real-time signal, or changing measurement composition is called an economic regime change.

Repair

Declare filter support, release dates, and geographic composition. Run future-mutation and fixed-definition checks.