Article
Keywords:
absolute autoregression; stationary distribution; marginal distribution
Summary:
A procedure for computation of 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 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.
References:
[1] Anděl J.:
Dependent random variables with a given marginal distribution. Acta Univ. Carolin. – Math. Phys. 24 (1983), 3–12
MR 0733140
[2] Anděl J.:
Marginal distributions of autoregressive processes. In: Trans. 9th Prague Conference Inform. Theory, Statist. Dec. Functions, Random Processes. Academia, Praha 1983
MR 0757732 |
Zbl 0537.60027
[4] Anděl J., Netuka, I., Zvára K.:
On threshold autoregressive processes. Kybernetika 20 (1984), 89–106
MR 0747062 |
Zbl 0547.62058
[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
DOI 10.1007/BF01845999 |
MR 0849071
[7] Tong H.:
Non-Linear Time Series. Clarendon Press, Oxford 1990
Zbl 0835.62076