Authors: Tassos Magdalinos and Katerina Petrova
-
-
The New York Innovation Center bridges the worlds of finance, technology, and innovation and generates insights into high-value central bank-related opportunities.
Do you have a request for information and records? Learn how to submit it.
Learn about the history of the New York Fed and central banking in the United States through articles, speeches, photos and video.
-
-
-
The Governance & Culture Reform hub is designed to foster discussion about corporate governance and the reform of culture and behavior in the financial services industry.
Need to file a report with the New York Fed? Here are all of the forms, instructions and other information related to regulatory and statistical reporting in one spot.
The New York Fed works to protect consumers as well as provides information and resources on how to avoid and report specific scams.
-
-
-
The New York Innovation Center bridges the worlds of finance, technology, and innovation and generates insights into high-value central bank-related opportunities.
The growing role of nonbank financial institutions, or NBFIs, in U.S. financial markets is a transformational trend with implications for monetary policy and financial stability.
The New York Fed offers the Central Banking Seminar and several specialized courses for central bankers and financial supervisors.
-
-
-
The Economic Inequality & Equitable Growth hub is a collection of research, analysis and convenings to help better understand economic inequality.
The Governance & Culture Reform hub is designed to foster discussion about corporate governance and the reform of culture and behavior in the financial services industry.
-
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
By continuing to use our site, you agree to our Terms of Use and Privacy Statement. You can learn more about how we use cookies by reviewing our Privacy Statement. 
