Robust recursive estimation of GARCH models
Kybernetika (2018)
- Volume: 54, Issue: 6, page 1138-1155
- ISSN: 0023-5954
Access Full Article
topAbstract
topHow to cite
topCipra, Tomáš, and Hendrych, Radek. "Robust recursive estimation of GARCH models." Kybernetika 54.6 (2018): 1138-1155. <http://eudml.org/doc/294821>.
@article{Cipra2018,
abstract = {The robust recursive algorithm for the parameter estimation and the volatility prediction in GARCH models is suggested. It seems to be useful for various financial time series, in particular for (high-frequency) log returns contaminated by additive outliers. The proposed procedure can be effective in the risk control and regulation when the prediction of volatility is the main concern since it is capable to distinguish and correct outlaid bursts of volatility. This conclusion is demonstrated by simulations and real data examples presented in the paper.},
author = {Cipra, Tomáš, Hendrych, Radek},
journal = {Kybernetika},
keywords = {GARCH model; Kalman filter; outlier; robust recursive estimation; volatility},
language = {eng},
number = {6},
pages = {1138-1155},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Robust recursive estimation of GARCH models},
url = {http://eudml.org/doc/294821},
volume = {54},
year = {2018},
}
TY - JOUR
AU - Cipra, Tomáš
AU - Hendrych, Radek
TI - Robust recursive estimation of GARCH models
JO - Kybernetika
PY - 2018
PB - Institute of Information Theory and Automation AS CR
VL - 54
IS - 6
SP - 1138
EP - 1155
AB - The robust recursive algorithm for the parameter estimation and the volatility prediction in GARCH models is suggested. It seems to be useful for various financial time series, in particular for (high-frequency) log returns contaminated by additive outliers. The proposed procedure can be effective in the risk control and regulation when the prediction of volatility is the main concern since it is capable to distinguish and correct outlaid bursts of volatility. This conclusion is demonstrated by simulations and real data examples presented in the paper.
LA - eng
KW - GARCH model; Kalman filter; outlier; robust recursive estimation; volatility
UR - http://eudml.org/doc/294821
ER -
References
top- Aknouche, A., Guerbyenne, H., 10.1080/03610910600880328, Comm. Statist. Simul. Comput. 35 (2006), 925-938. MR2291371DOI10.1080/03610910600880328
- Balke, N. S., Fomby, T. B., 10.1002/jae.3950090205, J. Appl. Econometr. 31 (1994), 307-327. DOI10.1002/jae.3950090205
- Bernholt, T., Fried, R., Gather, U., Wegener, I., 10.1007/s11222-006-8449-1, Statist. Comput. 16 (2006), 177-192. MR2227394DOI10.1007/s11222-006-8449-1
- Bollerslev, T., 10.1016/0304-4076(86)90063-1, J. Econometr. 31 (1986), 307-327. MR0853051DOI10.1016/0304-4076(86)90063-1
- Bose, A., Mukherjee, K., 10.1111/1467-9892.00296, J. Time Series Anal. 24 (2003), 127-136. MR1965808DOI10.1111/1467-9892.00296
- Calvet, L. E., Czellar, V., Ronchetti, E., 10.1080/01621459.2014.983520, J. Amer. Statist. Assoc. 110 (2015), 1591-1606. MR3449057DOI10.1080/01621459.2014.983520
- Carnero, M. A., Peña, D., Ruiz, E., 10.1111/j.1467-9892.2006.00519.x, J. Time Series Anal. 28 (2007), 471-497. MR2396627DOI10.1111/j.1467-9892.2006.00519.x
- Carnero, M. A., Peña, D., Ruiz, E., 10.1016/j.econlet.2011.09.023, Econom. Lett. 114 (2012), 86-90. MR2879552DOI10.1016/j.econlet.2011.09.023
- Charles, A., 10.1002/for.1065, J. Forecast. 27 (2008), 551-565. MR2588565DOI10.1002/for.1065
- Charles, A., Darné, O., 10.1016/j.econlet.2004.07.019, Econom. Lett. 86 (2005), 347-352. MR2124418DOI10.1016/j.econlet.2004.07.019
- Cipra, T., 10.1002/for.3980110106, J. Forecast. 11 (1992), 57-69. DOI10.1002/for.3980110106
- Cipra, T., 10.1080/03610929808832146, Comm. Statist. Theory Methods 27 (1998), 1071-1082. MR1626293DOI10.1080/03610929808832146
- Cipra, T., Hanzák, T., Exponential smoothing for time series with outliers., Kybernetika 47 (2011), 165-178. MR2828571
- Cipra, T., Romera, R., Robust Kalman filter and its applications in time series analysis., Kybernetika 27 (1991), 481-494. MR1150938
- Crevits, R., Croux, C., 10.13140/RG.2.2.11791.18080), Working paper KBI_1714, KU Leuven, Leuven 2016 (DOI:10.13140/RG.2.2.11791.18080). DOI10.13140/RG.2.2.11791.18080)
- Croux, C., Gelper, S., 10.1007/s10492-008-0002-4, Appl. Math. 53 (2008), 163-176. MR2411122DOI10.1007/s10492-008-0002-4
- Croux, C., Gelper, S. E. C., Mahieu, K., 10.1016/j.csda.2009.05.003, Comput. Statist. Data Anal. 54 (2010), 2999-3006. MR2727729DOI10.1016/j.csda.2009.05.003
- Dalhaus, R., Rao, S. S., 10.3150/07-bej5009, Bernoulli 13 (2007), 389-422. MR2331257DOI10.3150/07-bej5009
- Engle, R. F., 10.2307/1912773, Econometrica 50 (1982), 987-1007. MR0666121DOI10.2307/1912773
- Eraker, B., Johannes, M., Polson, N., 10.1111/1540-6261.00566, J. Finance 58 (2003), 1269-1300. DOI10.1111/1540-6261.00566
- Fasso, A., Recursive least squares with ARCH errors and nonparametric modelling of environmental time series., Working Paper 6, University of Bergamo 2009.
- Franke, J., Härdle, W. K., Hafner, C. M., 10.1007/978-3-642-16521-4, Springer, Berlin 2011. MR2722946DOI10.1007/978-3-642-16521-4
- Franses, P. H., Ghijsels, H., 10.1016/s0169-2070(98)00053-3, Int. J. Forecast. 15 (1999), 1-9. DOI10.1016/s0169-2070(98)00053-3
- Galeano, P., Peña, D., 10.1007/978-3-642-35494-6_15, In: Robustness and Complex Data Structures (C. Becker, R. Fried, S. Kuhnt, eds.), Springer, Berlin 2013, pp. 243-260. MR3135884DOI10.1007/978-3-642-35494-6_15
- Gelper, S., Fried, R., Croux, C., 10.1002/for.1125, J. Forecast. 29 (2009), 285-300. Zbl1203.62164MR2752114DOI10.1002/for.1125
- Gerencsér, L., Orlovits, Z., Torma, B., Recursive estimation of GARCH processes., In: Proc. 19th International Symposium on Mathematical Theory and Systems - MTNS (A. Edelmayer, ed.), Eötvös Loránd University, Budapest 2010, pp. 2415-2422.
- Grané, A., Veiga, H., 10.1016/j.csda.2009.12.010, Comput. Statist. Data Anal. 54 (2010), 2580-2593. MR2720462DOI10.1016/j.csda.2009.12.010
- Gregory, A. V., Reeves, J. J., 10.1093/jjfinec/nbq028, J. Financ. Econometr. 8 (2010), 547-569. DOI10.1093/jjfinec/nbq028
- Grillenzoni, C., 10.1007/bf03178900, J. Ital. Statist. Soc. 6 (1997), 37-58. DOI10.1007/bf03178900
- Grillenzoni, C., 10.2307/1270909, Technometrics 39 (1997), 211-224. DOI10.2307/1270909
- Hendrych, R., Cipra, T., 10.3311/ppee.9684, In: Proc. 33rd International Conference Mathematical Methods in Economics (D. Martinčák, J. Ircingová, and P. Janeček, eds.). University of West Bohemia, Pilsen 2014, pp. 237-242. DOI10.3311/ppee.9684
- Hendrych, R., Cipra, T., 10.1080/03610918.2015.1053924, Comm. Statist. Simul. Comput. 47 (2018), 315-328. MR3757688DOI10.1080/03610918.2015.1053924
- Hill, J. B., 10.3150/14-bej616, Bernoulli 21 (2015), 1629-1669. MR3352056DOI10.3150/14-bej616
- Hotta, L. K., Tsay, R. S., 10.1201/b11823-20, In: Economic time series: Modeling and seasonality (W. R. Bell, S. H. Holan, and T. S. McElroy, eds.). CRC Press, Boca Raton 2012, pp. 337-358. MR3076022DOI10.1201/b11823-20
- Hyndman, R. J., Koehler, A. B., Ord, J. K., Snyder, R. D., 10.1111/j.1751-5823.2009.00085_17.x, Springer, Berlin 2008. DOI10.1111/j.1751-5823.2009.00085_17.x
- Jiang, J., Zhao, Q., Hui, Y. V., 10.1002/1099-131x(200103)20:2<111::aid-for786>3.0.co;2-n, J. Forecast. 20 (2001), 111-133. DOI10.1002/1099-131x(200103)20:2<111::aid-for786>3.0.co;2-n
- Kierkegaard, J., Nielsen, J., Jensen, L., Madsen, H., Estimating GARCH models using recursive methods.
- Koch, K. R., Yang, Y., 10.1007/s001900050183, J. Geodesy 72 (1998), 436-441. DOI10.1007/s001900050183
- Lanius, V., Gather, U., 10.1016/j.csda.2009.10.009, Comput. Statist. Data Anal. 54 (2010), 966-975. MR2580931DOI10.1016/j.csda.2009.10.009
- Ling, S., 10.1016/j.jeconom.2006.07.016, J. Econometr. 140 (2007), 849-873. MR2408929DOI10.1016/j.jeconom.2006.07.016
- Ljung, L., System Identification: Theory for the User., Prentice Hall PTR, Upper Saddle River 1999.
- Ljung, L., Söderström, T. S., Theory and Practice of Recursive Identification., MIT Press, Cambridge 1983. MR0719192
- Michálek, J., Robust methods in exponential smoothing., Kybernetika 32 (1996), 289-306. MR1438221
- Muler, N., Yohai, V., 10.1016/j.jspi.2007.11.003, J. Statist. Planning Inference 138 (2008), 2918-2940. MR2442223DOI10.1016/j.jspi.2007.11.003
- Park, B.-J., 10.1002/for.827, J. Forecast. 21 (2002), 381-393. DOI10.1002/for.827
- Peng, L., Yao, Q., 10.1093/biomet/90.4.967, Biometrika 90 (2003), 967-975. MR2024770DOI10.1093/biomet/90.4.967
- Romera, R., Cipra, T., 10.1080/03610919508813252, Comm. Statist. Simul. Comput. 24 (1995), 461-488. Zbl0850.62688MR1333047DOI10.1080/03610919508813252
- Ruckdeschel, P., Spangl, B., Pupashenko, D., 10.1007/s00362-012-0496-4, Statist. Papers 55 (2014), 93-123. MR3152769DOI10.1007/s00362-012-0496-4
- Sakata, S., White, H., 10.2307/2998574, Econometrica 66 (1998), 529-567. DOI10.2307/2998574
- Shaolin, H. U., Meinke, K., Ouyang, H., Guoji, S., 10.14569/ijacsa.2011.021206, Int. J. Advanced Computer Sci. Appl. 2 (2011), 37-41. DOI10.14569/ijacsa.2011.021206
- Söderström, T. S., Stoica, P., System Identification., Prentice Hall, New York 1989.
- Tsay, R. S., Analysis of Financial Time Series., Wiley, Hoboken 2013. MR2778591
- Yang, Y., 10.14569/ijacsa.2011.021206, In: Sciences of Geodesy (G. Xu, ed.), Springer, Berlin 2010, pp. 49-82. DOI10.14569/ijacsa.2011.021206
- Yang, Y., Gao, W., Zhang, X., 10.1007/s00190-010-0374-6, J. Geodesy 84 (2010), 373-381. DOI10.1007/s00190-010-0374-6
- Zhang, R., Ling, S., 10.1017/s0266466614000632, Econometr. Theory 31 (2015), 880-890. MR3377272DOI10.1017/s0266466614000632
- Zhu, K., Li, W. K., 10.1080/07350015.2014.977446, J. Business Econom. Statist. 33 (2015), 552-565. MR3416600DOI10.1080/07350015.2014.977446
- Zhu, K., Ling, S., 10.1214/11-aos895, Ann. Statist. 39 (2011), 2131-2163. MR2893864DOI10.1214/11-aos895
- Zhu, K., Ling, S., 10.1080/01621459.2014.977386, J. Amer. Statist. Assoc. 110 (2015), 784-794. MR3367264DOI10.1080/01621459.2014.977386
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.