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A generalization of stationary AR(1) schemes. (English) Zbl 1156.60304
Summary: Here we develop a first order autoregressive model $$\{X_n\}$$ that is marginally stationary where $$X_n$$ is the sum/ extreme of $$k$$ i.i.d observations. We prove that stationary solutions to these models are also either semi-selfdecomposable/ extreme-semiself decomposable or, sum/ extreme stable with respect to Harris distribution.

##### MSC:
 60E07 Infinitely divisible distributions; stable distributions 60E10 Characteristic functions; other transforms 60G10 Stationary stochastic processes 60G18 Self-similar stochastic processes 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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