A bootstrap approximation to a unit root test statistic for heavy-tailed observations

✍ Scribed by Lajos Horváth; Piotr Kokoszka

• Book ID: 104302072
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 167 KB
• Volume: 62
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(03)00007-5

✦ Synopsis

In the context of the AR(1) model with innovations in the domain of attraction of an -stable law, we develop a residual bootstrap approximation to the distribution of a least-squares estimator of the autoregressive parameter when this parameter is equal to unity. Our procedure requires drawing bootstrap samples of size m ¡ n, n being the size of the original sample. We establish the convergence in probability of the bootstrap distribution function assuming that m → ∞ and m=n → 0. An analogous result is established for the partial sum process of the bootstrap noise sequence.