Mildly Explosive Autoregression with Anti‐persistent Errors*

2020/08/30 by Yiu Lim Lui, Weilin Xiao, Jun Yu
Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #Financial Risk and Volatility Modeling #Statistical Distribution Estimation and Applications

paper · doi:10.1111/obes.12395

openalex publication_date 2020/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/22

Abstract

Abstract An asymptotic distribution is derived for the least squares (LS) estimate of a first‐order autoregression with a mildly explosive root and anti‐persistent errors. While the sample moments depend on the Hurst parameter asymptotically, the Cauchy limiting distribution theory remains valid for the LS estimates in the model without intercept and a model with an asymptotically negligible intercept. Monte Carlo studies are designed to check the precision of the Cauchy distribution in finite samples. An empirical study based on the monthly NASDAQ index highlights the usefulness of the model and the new limiting distribution.

Citations

• EXPLOSIVE BEHAVIOR IN THE 1990s NASDAQ: WHEN DID EXUBERANCE ESCALATE ASSET VALUES?*
• TESTING FOR MULTIPLE BUBBLES: LIMIT THEORY OF REAL‐TIME DETECTORS
• Testing for Multiple Bubbles: Historical Episodes of Exuberance and Collapse in the S&P 500

Related

• Asymptotic distributions related to mildly-explosive second order autoregressive models
• Testing for a Moderately Explosive Process with Structural Change in Drift*
• Asymptotic Inference for AR(1) Penal Data
• The nonexplosive solution of explosive autoregressions
• Confidence distributions for the parameters in an autoregressive process