OLS limit theory for drifting sequences of parameters on the explosive side of unity - Tassos Magdalinos; Katerina Petrova (Federal Reserve Bank of New York, 2024)
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 (|ρn| -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.
Keywords: C12; C18; C22; 330; triangular array; explosive autoregression; linear process; conditional heteroskedasticity; mixingale; Cauchy distribution