Author

Boubaker Smii

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Preprint Aug 2026

Near-unit-root persistence of symmetric and asymmetric stable autoregressive sequences

For an AR($1$) sequence with coefficient $0<a<1$, the probability of staying above zero decays exponentially in the number of steps; at the unit root $a=1$ it decays polynomially, with order $n^{-1/2}$ for symmetric increments. We study this transition for AR($1$) sequences driven by symmetric and asymmetric $\alpha$-s...

José Ricardo G. Mendonça, Boubaker Smii · 0 citations

Preprint Aug 2026

Near-unit-root persistence of symmetric stable autoregressive sequences

Persistence changes character as an autoregressive coefficient approaches one: for each fixed $0<a<1$, survival above zero decays exponentially, whereas at the unit root symmetric random-walk survival is of order $n^{-1/2}$. We study this transition for AR($1$) sequences driven by symmetric $\alpha$-stable innovations...

José Ricardo G. Mendonça, B. Smii · 0 citations