On geometric ergodicity and prediction in nonnegative non-linear autoregressive processes

Petr Zvára

Kybernetika (2004)

  • Volume: 40, Issue: 6, page [691]-702
  • ISSN: 0023-5954

Abstract

top
A non-linear AR(1) process is investigated when the associated white noise is positive. A criterion is derived for the geometric ergodicity of the process. Some explicit formulas are derived for one and two steps ahead extrapolation. Influence of parameter estimation on extrapolation is studied.

How to cite

top

Zvára, Petr. "On geometric ergodicity and prediction in nonnegative non-linear autoregressive processes." Kybernetika 40.6 (2004): [691]-702. <http://eudml.org/doc/33729>.

@article{Zvára2004,
abstract = {A non-linear AR(1) process is investigated when the associated white noise is positive. A criterion is derived for the geometric ergodicity of the process. Some explicit formulas are derived for one and two steps ahead extrapolation. Influence of parameter estimation on extrapolation is studied.},
author = {Zvára, Petr},
journal = {Kybernetika},
keywords = {geometric ergodicity; non-linear autoregression; least squares extrapolation; least squares extrapolation},
language = {eng},
number = {6},
pages = {[691]-702},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On geometric ergodicity and prediction in nonnegative non-linear autoregressive processes},
url = {http://eudml.org/doc/33729},
volume = {40},
year = {2004},
}

TY - JOUR
AU - Zvára, Petr
TI - On geometric ergodicity and prediction in nonnegative non-linear autoregressive processes
JO - Kybernetika
PY - 2004
PB - Institute of Information Theory and Automation AS CR
VL - 40
IS - 6
SP - [691]
EP - 702
AB - A non-linear AR(1) process is investigated when the associated white noise is positive. A criterion is derived for the geometric ergodicity of the process. Some explicit formulas are derived for one and two steps ahead extrapolation. Influence of parameter estimation on extrapolation is studied.
LA - eng
KW - geometric ergodicity; non-linear autoregression; least squares extrapolation; least squares extrapolation
UR - http://eudml.org/doc/33729
ER -

References

top
  1. Anděl J., 10.1111/j.1467-9892.1989.tb00011.x, J. Time Ser. Anal. 10 (1989), 1–11 (1989) DOI10.1111/j.1467-9892.1989.tb00011.x
  2. Anděl J., 10.1007/BF02564427, Test 6 (1997), 91–100 (1997) MR1466434DOI10.1007/BF02564427
  3. Anděl J., Dupač V., Extrapolations in non-linear autoregressive processes, Kybernetika 35 (1999), 383–389 (1999) MR1704673
  4. Bhansali R. J., Effects of not knowing the order of an autoregressive process on the mean squared error of prediction – I, J. Amer. Statist. Assoc. 76 (1981), 588–597 (1981) Zbl0472.62093MR0629746
  5. Bhattacharya R., Lee, Ch., 10.1016/0167-7152(94)00082-J, Statist. Probab. Lett. 22 (1995), 311–315 (1995) MR1333189DOI10.1016/0167-7152(94)00082-J
  6. Cline D. B. H., Pu H., 10.1016/S0167-7152(98)00081-9, Statist. Probab. Lett. 40 (1998), 139–148 (1998) MR1650873DOI10.1016/S0167-7152(98)00081-9
  7. Datta S., Mathew, G., McCormick W. P., 10.1111/1467-842X.00026, Austral. & New Zealand J. Statist. 40 (1998), 229–239 (1998) Zbl0923.62092MR1631108DOI10.1111/1467-842X.00026
  8. Fuller W. A., Hasza D. P., 10.1016/0304-4076(80)90012-3, J. Econometrics 13 (1980), 139–157 (1980) Zbl0521.62078MR0575084DOI10.1016/0304-4076(80)90012-3
  9. Lee O., 10.1016/S0167-7152(99)00096-6, Statist. Probab. Lett. 46 (2000), 121–131 MR1748866DOI10.1016/S0167-7152(99)00096-6
  10. Moeanaddin R., Tong H., 10.1111/j.1467-9892.1990.tb00040.x, J. Time Ser. Anal. 11 (1990), 33–48 (1990) MR1046979DOI10.1111/j.1467-9892.1990.tb00040.x
  11. Tjøstheim D., 10.2307/1427459, Adv. in Appl. Probab. 22 (1990), 587–611 (1990) DOI10.2307/1427459
  12. Tong H., Non-linear Time Series, Clarendon Press, Oxford 1990 Zbl0835.62076

NotesEmbed ?

top

You must be logged in to post comments.