Geodesic
Linear approximations to some non-linear AR(1) processes
Kybernetika, Tome 36 (2000) no. 4, pp. 389-399 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Some methods for approximating non-linear AR(1) processes by classical linear AR(1) models are proposed. The quality of approximation is studied in special non-linear AR(1) models by means of comparisons of quality of extrapolation and interpolation in the original models and in their approximations. It is assumed that the white noise has either rectangular or exponential distribution.
Some methods for approximating non-linear AR(1) processes by classical linear AR(1) models are proposed. The quality of approximation is studied in special non-linear AR(1) models by means of comparisons of quality of extrapolation and interpolation in the original models and in their approximations. It is assumed that the white noise has either rectangular or exponential distribution.
Classification : 60G10, 62M10, 62M15 
@article{KYB_2000_36_4_a0,
     author = {And\v{e}l, Ji\v{r}{\'\i}},
     title = {Linear approximations to some non-linear {AR(1)} processes},
     journal = {Kybernetika},
     pages = {389--399},
     year = {2000},
     volume = {36},
     number = {4},
     mrnumber = {1830645},
     zbl = {1248.62140},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2000_36_4_a0/}
}
TY  - JOUR
AU  - Anděl, Jiří
TI  - Linear approximations to some non-linear AR(1) processes
JO  - Kybernetika
PY  - 2000
SP  - 389
EP  - 399
VL  - 36
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/KYB_2000_36_4_a0/
LA  - en
ID  - KYB_2000_36_4_a0
ER  - 
%0 Journal Article
%A Anděl, Jiří
%T Linear approximations to some non-linear AR(1) processes
%J Kybernetika
%D 2000
%P 389-399
%V 36
%N 4
%U http://geodesic.mathdoc.fr/item/KYB_2000_36_4_a0/
%G en
%F KYB_2000_36_4_a0
Anděl, Jiří. Linear approximations to some non-linear AR(1) processes. Kybernetika, Tome 36 (2000) no. 4, pp. 389-399. http://geodesic.mathdoc.fr/item/KYB_2000_36_4_a0/

[1] Anděl J.: On extrapolation in some non-linear AR(1) processes. Comm. Statist. – Theory Methods 26 (1997), 581–587 | DOI | MR

[2] Anděl J., Dupač V.: Extrapolations in non-linear autoregressive processes. Kybernetika 35 (1999), 383–389 | MR

[3] Pemberton J.: Piecewise Constant Models for Univariate Time Series. Technical Report MCS-90-04, Department of Mathematics, University of Salford, Salford 1990

[4] Pemberton J.: Measuring nonlinearity in time series. In: Developments in Time Series Analysis (T. Subba Rao, ed.), Chapman and Hall, London 1993, pp. 230–240 | MR | Zbl

[5] Tong H.: Non-linear Time Series. Clarendon Press, Oxford 1990 | Zbl

[6] Young P.: Time variable and state dependent modelling of non-stationary and nonlinear time series. In: Developments in Time Series Analysis (T. Subba Rao, ed.), Chapman and Hall, London 1993, pp. 374–413 | Zbl