OLS Limit Theory for Drifting Sequences of Parameters on the Explosive Side of Unity

Tassos Magdalinos () and Katerina Petrova
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Tassos Magdalinos: https://www.southampton.ac.uk/people/5x7sz7/professor-anastasios-magdalinos

No 1113, Staff Reports from Federal Reserve Bank of New York

Abstract: 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.

Keywords: triangular array; explosive autoregression; linear process; conditional heteroskedasticity; mixingale; Cauchy distribution (search for similar items in EconPapers)
JEL-codes: C12 C18 C22 (search for similar items in EconPapers)
Pages: 48
Date: 2024-08-01
New Economics Papers: this item is included in nep-ecm and nep-ets
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DOI: 10.59576/sr.1113

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