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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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