Lecture 6 summary · February 19, 2027
Trends, unit roots, and misleading level regressions
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The economic question
A deterministic trend with temporary deviations differs from a stochastic trend with permanent innovations. Their variances and testing references differ.
Central relation
Individual problem
A random walk has drift 0.3, current level 20, and innovation variance 1.5. Find its four-period forecast and variance. Interpret a unit-root nonrejection.
Worked reasoning
The forecast is 21.2 and variance is six. Nonrejection is not proof of a unit root; power and deterministic specification matter.
A consequential failure
An ordinary t reference is applied to a DF statistic, or a levels regression of one random walk on another is read with conventional t statistics.
Repair
Use a deterministic-case reference. Draw Monte Carlo replications from one stream, and report their uncertainty, initialization, sample size, and number; retain weak-correlation realizations too.