Renewal Regime Switching and Stable Limit Laws

摘要

The paper discusses long-memory properties and large sample behavior of partial sums in a general renewal regime switching scheme. The linear model X[subscript t] = mu[subscript t] + a[subscript t]X[subscript t - 1] + sigma[subscript t] epsilon[subscript t] with renewal switching in levels, slope or volatility and general (possibly heavy-tailed) i.i.d. noise epsilon[subscript t] is discussed in detail. Conditions on the tail behavior of interrenewal distribution and the tail index alpha element of (0,2] of epsilon[subscript t] are obtained, in order that the partial sums process of X[subscript t] is asymptotically lambda-stable with index lambda < alpha.