A Note on Bootstrapping M-estimates from Unstable AR(2) Process with Infinite Variance Innovations

Abstract

The limiting distribution for M-estimates in a non-stationary autoregressive model with heavy-tailed error is computationally intractable. To make inferences based on the M-estimates, the bootstrap procedure can be used to approximate the sampling distribution. In this paper, we show that the bootstrap scheme with $m=o(n)$ resampling sample size when $m/n \to 0$ is approximately valid in a multiple unit roots time series with innovations in the domain of attraction of a stable law with index $0<\alpha\leq2$.