| Title:
|
On calculation of stationary density of autoregressive processes (English) |
| Author:
|
Anděl, Jiří |
| Author:
|
Hrach, Karel |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
36 |
| Issue:
|
3 |
| Year:
|
2000 |
| Pages:
|
[311]-319 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
An iterative procedure for computation of stationary density of autoregressive processes is proposed. On an example with exponentially distributed white noise it is demonstrated that the procedure converges geometrically fast. The AR(1) and AR(2) models are analyzed in detail. (English) |
| Keyword:
|
AR(1) model |
| Keyword:
|
AR(2) model |
| MSC:
|
60G10 |
| MSC:
|
62M10 |
| MSC:
|
65C60 |
| idZBL:
|
Zbl 1248.62141 |
| idMR:
|
MR1773506 |
| . |
| Date available:
|
2009-09-24T19:33:04Z |
| Last updated:
|
2015-03-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135352 |
| . |
| Reference:
|
[1] Anděl J.: Dependent random variables with a given marginal distribution.Acta Univ. Carolin. – Math. Phys. 24 (1983), 3–11 MR 0733140 |
| Reference:
|
[2] Anděl J.: Marginal distributions of autoregressive processes.In: Trans. 9th Prague Conf. Inform. Theory, Statist. Decision Functions, Random Processes, Academia, Prague 1983, pp. 127–135 MR 0757732 |
| Reference:
|
[3] Anděl J.: On linear processes with given moments.J. Time Ser. Anal. 8 (1987), 373–378 MR 0917790, 10.1111/j.1467-9892.1987.tb00001.x |
| Reference:
|
[4] Anděl J.: AR(1) processes with given moments of marginal distribution.Kybernetika 22 (1989), 337–347 Zbl 0701.62087, MR 1024709 |
| Reference:
|
[5] 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, MR 0832348, 10.1111/j.1467-9892.1986.tb00481.x |
| Reference:
|
[6] Anděl J., Garrido M.: On stationary distributions of some time series models.In: Trans. 10th Prague Conf. Inform. Theory, Statist. Decision Functions, Random Processes, Academia, Prague 1988, pp. 193–202 MR 1136274 |
| Reference:
|
[7] Anděl J., Gómez M., Vega C.: Stationary distribution of some nonlinear AR(1) processes.Kybernetika 25 (1989), 453–460 Zbl 0701.60029, MR 1035151 |
| Reference:
|
[8] Anděl J., Netuka I., Zvára K.: On threshold autoregressive processes.Kybernetika 20 (1984), 89–106 Zbl 0547.62058, MR 0747062 |
| Reference:
|
[9] Bernier J.: Inventaire des modèles et processus stochastique applicables de la description des déluts journaliers des riviers.Rev. Inst. Internat. Statist. 38 (1970), 50–71 10.2307/1402324 |
| Reference:
|
[10] Davis R. A., Rosenblatt M.: Parameter estimation for some time series models without contiguity.Statist. Probab. Lett. 11 (1991), 515–521 Zbl 0725.62079, MR 1116746, 10.1016/0167-7152(91)90117-A |
| Reference:
|
[11] Feller W.: An Introduction to Probability Theory and its Applications II.Wiley, New York 1966 MR 0210154 |
| Reference:
|
[12] Gaver D. P., Lewis P. A. W.: First–order autoregressive gamma sequences and point processes.Adv. in Appl. Probab. 12 (1980), 727–745 Zbl 0453.60048, MR 0578846, 10.2307/1426429 |
| Reference:
|
[13] Haiman G.: Upper and lower bounds for the tail of the invariant distribution of some AR(1) processes.In: Asymptotic Methods in Probability and Statistics (B. Szyszkowicz, ed.), North–Holland/Elsevier, Amsterdam 1998, pp. 723–730 Zbl 0926.62080, MR 1661513 |
| Reference:
|
[14] Hamilton J. D.: Time Series Analysis.Princeton University Press, Princeton 1994 Zbl 0831.62061, MR 1278033 |
| Reference:
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| Reference:
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[16] Rényi A.: Probability Theory.Akadémiai Kiadó, Budapest 1970 |
| Reference:
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[17] Sondhi M. M.: Random processes with specified spectral density and first–order probability density.Bell System Technical J. 62 (1983), 679–701 10.1002/j.1538-7305.1983.tb04411.x |
| Reference:
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[18] Štěpán J.: Teorie pravděpodobnosti.Academia, Praha 1987 |
| Reference:
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