Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/302211 
Year of Publication: 
2024
Series/Report no.: 
Staff Reports No. 1113
Publisher: 
Federal Reserve Bank of New York, New York, NY
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 Ç ρ ∈ (-É, -1] ∪ [1, É) and n (#x03c1;n-1) Ç É. 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.
Subjects: 
triangular array
explosive autoregression
linear process
conditional heteroskedasticity
mixingale
Cauchy distribution
JEL: 
C12
C18
C22
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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