纽约联储-广义自回归过程的统一推理（英）

Uniform Inference with General Autoregressive Processes Tassos Magdalinos | Katerina Petrova NO. 1151 APRIL 2025 Uniform Inference with General Autoregressive Processes Tassos Magdalinos and Katerina Petrova Federal Reserve Bank of New York Staff Reports, no. 1151 April 2025 https://doi.org/10.59576/sr.1151 Abstract 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 limit theory and gives rise to an asymptotically standard normal t-statistic across all autoregressive regions. The resulting hypothesis tests and confidence intervals are shown to have correct asymptotic size (uniformly over the space of autoregressive parameters and the space of innovation distribution functions) in autoregressive, predictive regression and local projection models, thereby establishing a general and unified framework for inference with autoregressive processes. Extensive Monte Carlo simulation shows that the proposed methodology exhibits very good finite sample properties over the entire autoregressive parameter space (-∞, ∞) and compares favorably to existing methods within their parametric (-1, 1] validity range. We demonstrate how our procedure can be used to construct valid confidence intervals in standard epidemiological models as well as to test in real-time for speculative bubbles in the price of the Magnificent Seven tech stocks. JEL classification: C12, C22 Key words: uniform inference, central limit theory, autoregression, predictive regression, instrumentation, mixed-Gaussianity, t-statistic, confidence intervals _________________ Petrova: Federal Reserve Bank of New York (email: katerina.petrova@ny.frb.org). Magdalinos: University of Southampton (email: a.magdalinos@soton.ac.uk). The authors thank Peter Phillips, Richard Crump, Kirill Evdokimov, Adam McCloskey, Bo Zhou, Gabriele La Spada, and Nina Boyarchenko for valuable comments and discussions. They are also grateful to Hannah O’Keefe for invaluable research assistance. This paper presents preliminary findings and is being distributed to economists and other interested readers solely to stimulate discussion and elicit comments. The views expressed in this paper are those of the author(s) and do not necessarily reflect the position of the Federal Reserve Bank of New York or the Federal Reserve System. Any errors or omissions are the responsibility of the author(s). To view the authors’ disclosure statements, visit https://www.newyorkf