Lecture 2 summary · January 22, 2027

Persistence, recursion, and aggregation

Complete chapter · Laboratory ch02 · Practice · All summaries

The economic question

Persistence carries an earlier deviation forward. The intercept is an increment in the recursion; it is not generally the long-run mean.

Central relation

\mu=\frac{c}{1-\phi},

\gamma(0)=\frac{\sigma^2}{1-\phi^2},

V_h=\sigma^2\sum_{j=0}^{h-1}\phi^{2j}

Individual problem

Intercept is 3, persistence 0.5, innovation standard deviation 2, and current level 10. Find the mean, two-period forecast, and error variance.

Worked reasoning

The stationary mean is six. The forecast is seven. Error variance is five and standard deviation is the square root of five. These are known-parameter results.

A consequential failure

A quarterly average is treated as a sampled endpoint with persistence equal to cubed monthly persistence.

Repair

Expand all nine cross-quarter covariances under the actual averaging rule. Compare aggregate correlation with endpoint sampling.