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MENTAL MODEL · M8078

Unit Root Process

Unit Root Process
BusinessHigh supportEconomics
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Updated 2026-08-10

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INTRODUCTION

English translation pending.

CORE DEFINITION

A time series with a characteristic root of one, meaning it is non-stationary and that shocks have permanent effects. Because the effect of each shock accumulates without decaying, the variance grows over time. Regressing one unit root process on another can produce a spurious regression, and the distinction between temporary fluctuation and permanent change matters for analysis.

SCAFFOLDING EFFECT

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- Stationarity test: run ADF or PP tests before trusting any regression on the series. - Differencing step: difference the series or move to a cointegration setup when a root is found. - Shock reading: treat a shock as permanent rather than expecting the level to come back.

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A characteristic root of one turns the series into a random walk, so the effect of each shock accumulates permanently instead of decaying and the variance diverges over time. Regressing such non-stationary series directly tends to produce spurious results.

MINIMUM ACTION

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Source support: Explicit

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    en.wikipedia.orghttps://en.wikipedia.org/wiki/Unit_rootZH · Explicit
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