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Stationary distribution of absolute autoregression. (English) Zbl 1249.60067
Summary: A procedure for the computation of the stationary density of the absolute autoregression (AAR) model driven by white noise with symmetrical density is described. This method is used for deriving explicit formulas for the stationary distribution and further characteristics of AAR models with given distribution of white noise. The cases of Gaussian, Cauchy, Laplace and discrete rectangular distribution are investigated in detail.

60G10 Stationary stochastic processes
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[1] Anděl J.: Dependent random variables with a given marginal distribution. Acta Univ. Carolin. - Math. Phys. 24 (1983), 3-12 · Zbl 0527.62084
[2] Anděl J.: Marginal distributions of autoregressive processes. Trans. 9th Prague Conference Inform. Theory, Statist. Dec. Functions, Random Processes. Academia, Praha 1983 · Zbl 0537.60027
[3] Anděl J., Bartoň T.: A note on the threshold AR(1) model with Cauchy innovations. J. Time Ser. Anal. 7 (1986), 1-5 · Zbl 0587.60033 · doi:10.1111/j.1467-9892.1986.tb00481.x
[4] Anděl J., Netuka, I., Zvára K.: On threshold autoregressive processes. Kybernetika 20 (1984), 89-106 · Zbl 0547.62058 · eudml:27648
[5] Chan K. S., Tong H.: A note on certain integral equations associated with non-linear time series analysis. Probab. Theory Related Fields 73 (1986), 153-159 · Zbl 0579.45006 · doi:10.1007/BF01845999
[6] Loges W.: The stationary marginal distribution of a threshold AR(1) process. J. Time Ser. Anal. 25 (2004), 103-125 · Zbl 1051.62080 · doi:10.1111/j.1467-9892.2004.00339.x
[7] Tong H.: Non-Linear Time Series. Clarendon Press, Oxford 1990 · Zbl 0835.62076
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