Another Look at AR(1)

2007/10/29 by Steven R. Finch, Finch, Steven R.
Economics, Econometrics and Finance · Mathematics · #11Y60 #34D08 #37H10 #60H10 #60J05 #62M10 (Primary) #65C50 (Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Statistical Distribution Estimation and Applications #Statistical Methods and Inference #Statistics Theory (math.ST) #math.DS #math.PR #math.ST #msc:11Y60 #msc:34D08 #msc:37H10 #msc:60H10 #msc:60J05 #msc:62M10 #msc:65C50 #stat.TH

paper · pdf · doi:10.48550/arxiv.0710.5419

8 pages; introduced corrections in section 3

openalex publication_date 2007/10/29 · arxiv created 2007/12/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a stationary first-order autoregressive process X_t (with lag-one correlation rho satisfying |rho|<1), we examine the Central Limit Theorem for (1/n)*ln |X₁...X_n| and compute variances to high precision. Given a nonstationary process X_t (with |rho|>1), we examine instead (1/n)*ln|X_n| and study the distribution of ln|X_n|-n*ln|rho|.

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