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Unit root — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Unit_root
License (as archived): CC-BY-SA-4.0
Archived: 2026-11-07T18:20:45.538Z
SHA-256 of the archived text: 0897a7c13838e0ebb0765b7ce1999243e0fb6cf0709ade807505d7fc6ad83030
Stable URL of this page: https://metraipolis.com/documento/dc_a95752cdf201

How to cite

Unit root — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Unit_root (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_a95752cdf201 (Metraipolis archive dc_a95752cdf201, sha256 0897a7c13838e0ebb0765b7ce1999243e0fb6cf0709ade807505d7fc6ad83030)

BibTeX

@misc{dca95752cdf201,
  title = {Unit root — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Unit_root},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_a95752cdf201; sha256 0897a7c13838e0ebb0765b7ce1999243e0fb6cf0709ade807505d7fc6ad83030},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Unit_root. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In probability theory and statistics, a unit root is a property of certain stochastic processes (such as a random walk) that can create challenges for statistical inference in time series models. A linear stochastic process contains a unit root if 1 is a solution to its characteristic equation. Processes with a unit root are non-stationary, because they do not necessarily exhibit a deterministic trend. If the other roots of the characteristic equation lie inside the unit circle—that is, have a modulus (absolute value) less than one—then the first difference of the process will be stationary; otherwise, the process will need to be differenced multiple times to become stationary. If there are d unit roots, the process will have to be differenced d times in order to make it stationary. Due to this characteristic, unit root processes are also called difference stationary. Unit root processes may sometimes be confused with trend-stationary processes; while they share many properties, they are different in many aspects. It is possible for a time series to be non-stationary, yet have no unit root and be trend-stationary. In both unit root and trend-stationary processes, the mean can be growing or decreasing over time; however, in the presence of a shock, trend-stationary processes are mean-reverting (i.e. transitory, the time series will converge again towards the growing mean, which was not affected by the shock) while unit-root processes have a permanent impact on the mean (i.e. no convergence over time). If a root of the process's characteristic equation is larger than 1, then it is called an explosive process, even though such processes are sometimes inaccurately called unit roots processes. The presence of a unit root can be tested using a unit root test.

Tema degli esploratori: statistica e scienza dei dati (deposito sistematico; ricerca «statistical inference»).
Fonte: Wikipedia in inglese, voce «Unit root» — https://en.wikipedia.org/wiki/Unit_root
Wikidata Q1307899: «feature of some stochastic processes» (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q1307899
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Unit_root?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1374374982, consultata il 2026-11-07T18:12:53.864Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 41a8f16f345c391ba4c286a1014a9a80c9c7f3569e226677dd1cc4a3b2e6263d