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OLS limit theory for drifting sequences of parameters on the explosive side of unity

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Bibliographic Details
Authors and Corporations: Magdalinos, Tassos (Author), Petrova, Katerina (Author)
Other Authors: Petrova, Katerina [Author]
Type of Resource: E-Book
Language: English
published:
Series: Federal Reserve Bank of New York: Staff reports ; no. 1113 (August 2024)
Subjects:
triangular array
explosive autoregression
linear process
conditional heteroskedasticity
mixingale
Cauchy distribution
Graue Literatur
Source: Verbunddaten SWB
Lizenzfreie Online-Ressourcen
Description
Summary: A limit theory is developed for the least squares estimator for mildly and purely explosive autoregressions under drifting sequences of parameters with autoregressive roots ρn satisfying ρn → ρ ∈ (-∞, -1] ∪ [1, ∞) and n (|ρn| -1) → ∞. Drifting sequences of innovations and initial conditions are also considered. A standard specification of a short memory linear process for the autoregressive innovations is extended to a triangular array formulation both for the deterministic weights and for the primitive innovations of the linear process, which are allowed to be heteroskedastic L1-mixingales. The paper provides conditions that guarantee the validity of Cauchy limit distribution for the OLS estimator and standard Gaussian limit distribution for the t-statistic under this extended explosive and mildly explosive framework.
Physical Description: 1 Online-Ressource (circa 48 Seiten)
DOI: 10.59576/sr.1113