Unit Root Tests and Heavy-Tailed Innovations

Bootstrap Unit Root Tests

We consider the bootstrap unit root tests based on finite order autoregressive integrated models driven by iid innovations, with or without deterministic time trends. A general methodology is developed to approximate asymptotic distributions for the models driven by integrated time series, and used to obtain asymptotic expansions for the Dickey–Fuller unit root tests. The second-order terms in ...

Differencing and Unit Root Tests

e d In the Box-Jenkins approach to analyzing time series, a key question is whether to difference th ata, i.e., to replace the raw data {y } by the differenced series {y −y }. Experience indicates that m t t t −1 ost economic time series tend to wander and are not stationary, but that differencing often yields a e r stationary result. A key example, which often provides a fairly good descriptio...

Unit Root and Cointegration Tests

Differencing and Unit Root Tests

e d In the Box-Jenkins approach to analyzing time series, a key question is whether to difference th ata, i.e., to replace the raw data {x } by the differenced series {x −x }. Experience indicates that m t t t −1 ost economic time series tend to wander and are not stationary, but that differencing often yields a e r stationary result. A key example, which often provides a fairly good descriptio...

Recurrence Properties of Autoregressive Processes With Super-Heavy Tailed Innovations

This paper studies recurrence properties of autoregressive (AR) processes with “super-heavy tailed” innovations. Specifically, we study the case where the innovations are distributed, roughly speaking, as log-Pareto random variables (i.e., the tail decay is essentially a logarithm raised to some power). We show that these processes exhibit interesting and somewhat surprising behavior. In partic...