Regular variation of order 1 nonlinear AR-ARCH models |
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Authors: | Daren BH Cline |
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Institution: | Department of Statistics, Texas A&M University, College Station, TX 77843-3143, United States |
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Abstract: | We prove both geometric ergodicity and regular variation of the stationary distribution for a class of nonlinear stochastic recursions that includes nonlinear AR-ARCH models of order 1. The Lyapounov exponent for the model, the index of regular variation and the spectral measure for the regular variation all are characterized by a simple two-state Markov chain. |
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Keywords: | primary 60G10 60J05 secondary 60G70 62M10 91B84 |
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