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OLS Limit Theory for Drifting Sequences of Parameters on the Explosive Side of Unity
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 satisfyingρn → 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 ...
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Uniform Inference with General Autoregressive Processes
A unified theory of estimation and inference is developed for an autoregressive process with root in (-∞, ∞) that includes the stationary, local-to-unity, explosive and all intermediate regions. The discontinuity of the limit distribution of the t-statistic outside the stationary region and its dependence on the distribution of the innovations in the explosive regions (-∞, -1) ∪ (1, ∞) are addressed simultaneously. A novel estimation procedure, based on a data-driven combination of a near-stationary and a mildly explosive artificially constructed instrument, delivers mixed-Gaussian ...