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Time-Series
Econometrics
Ian Helfrich PhD ↗

Lecture 11 summary · April 2, 2027

A stable relation between moving levels

Complete chapter · Laboratory ch11 · Practice · All summaries

The economic question

Moving levels can share a stationary spread. The long-run relation and short-run adjustment are distinct, and a change forecast must be returned to the current level.

Central relation

et=Yt−βXt−a,e_t=Y_t-\beta X_t-a,
ΔYt=αet−1+γΔXt+ut\Delta Y_t=\alpha e_{t-1}+\gamma\Delta X_t+u_t

Individual problem

The relation is Y = 2.5X + 4. Current X is twenty and Y sixty-four. Adjustment is negative 0.3; short-run coefficient 1.2; expected change in X is two. Forecast change and level.

Worked reasoning

The equilibrium error is ten. Expected change is negative three plus 2.4, or negative 0.6. The level forecast is 63.4.

A consequential failure

Cointegration is declared from level R squared, ordinary DF references are used on estimated residuals, or a change is reported as a level.

Repair

Establish integration and deterministic terms, use a cointegration-appropriate reference, and add predicted changes to the current observed level.