Authors: Tassos Magdalinos and Katerina Petrova
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Staff Reports
OLS Limit Theory for Drifting Sequences of Parameters on the Explosive Side of Unity
Number 1113
August 2024
August 2024
JEL classification: C12, C18, C22
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.
Author Disclosure Statement(s)
Tassos Magdalinos and Katerina Petrova
Both authors declare that they have no relevant or material financial interests that relate to the research described in this paper. Prior to circulation, this paper was reviewed in accordance with the Federal Reserve Bank of New York review policy, available at: https://www.newyorkfed.org/research/staff_reports/index.html.
Both authors declare that they have no relevant or material financial interests that relate to the research described in this paper. Prior to circulation, this paper was reviewed in accordance with the Federal Reserve Bank of New York review policy, available at: https://www.newyorkfed.org/research/staff_reports/index.html.
Suggested Citation:
Magdalinos, Tassos, and Katerina Petrova. 2024. “OLS Limit Theory for Drifting Sequences of Parameters on the Explosive Side of Unity.” Federal Reserve Bank of New York Staff Reports, no. 1113, August. https://doi.org/10.59576/sr.1113
Magdalinos, Tassos, and Katerina Petrova. 2024. “OLS Limit Theory for Drifting Sequences of Parameters on the Explosive Side of Unity.” Federal Reserve Bank of New York Staff Reports, no. 1113, August. https://doi.org/10.59576/sr.1113
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