| Title:
|
Robust recursive estimation of GARCH models (English) |
| Author:
|
Cipra, Tomáš |
| Author:
|
Hendrych, Radek |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
54 |
| Issue:
|
6 |
| Year:
|
2018 |
| Pages:
|
1138-1155 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
GARCH model |
| Keyword:
|
Kalman filter |
| Keyword:
|
outlier |
| Keyword:
|
robust recursive estimation |
| Keyword:
|
volatility |
| MSC:
|
62F35 |
| MSC:
|
62M10 |
| MSC:
|
91G70 |
| idZBL:
|
Zbl 07031765 |
| idMR:
|
MR3902625 |
| DOI:
|
10.14736/kyb-2018-6-1138 |
| . |
| Date available:
|
2019-02-18T14:44:45Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147601 |
| . |
| Reference:
|
[1] Aknouche, A., Guerbyenne, H.: Recursive estimation of GARCH models..Comm. Statist. Simul. Comput. 35 (2006), 925-938. MR 2291371, 10.1080/03610910600880328 |
| Reference:
|
[2] Balke, N. S., Fomby, T. B.: Large shocks, small shocks, and economic fluctuations: outliers in macroeconomics time series..J. Appl. Econometr. 31 (1994), 307-327. 10.1002/jae.3950090205 |
| Reference:
|
[3] Bernholt, T., Fried, R., Gather, U., Wegener, I.: Modified repeated median filters..Statist. Comput. 16 (2006), 177-192. MR 2227394, 10.1007/s11222-006-8449-1 |
| Reference:
|
[4] Bollerslev, T.: Generalized autoregressive conditional heteroskedasticity..J. Econometr. 31 (1986), 307-327. MR 0853051, 10.1016/0304-4076(86)90063-1 |
| Reference:
|
[5] Bose, A., Mukherjee, K.: Estimating the ARCH parameters by solving linear equations..J. Time Series Anal. 24 (2003), 127-136. MR 1965808, 10.1111/1467-9892.00296 |
| Reference:
|
[6] Calvet, L. E., Czellar, V., Ronchetti, E.: Robust filtering..J. Amer. Statist. Assoc. 110 (2015), 1591-1606. MR 3449057, 10.1080/01621459.2014.983520 |
| Reference:
|
[7] Carnero, M. A., Peña, D., Ruiz, E.: Effects of outliers on the identification and estimation of GARCH models..J. Time Series Anal. 28 (2007), 471-497. MR 2396627, 10.1111/j.1467-9892.2006.00519.x |
| Reference:
|
[8] Carnero, M. A., Peña, D., Ruiz, E.: Estimating GARCH volatility in the presence of outliers..Econom. Lett. 114 (2012), 86-90. MR 2879552, 10.1016/j.econlet.2011.09.023 |
| Reference:
|
[9] Charles, A.: Forecasting volatility with outliers in GARCH models..J. Forecast. 27 (2008), 551-565. MR 2588565, 10.1002/for.1065 |
| Reference:
|
[10] Charles, A., Darné, O.: Outliers and GARCH models in financial data..Econom. Lett. 86 (2005), 347-352. MR 2124418, 10.1016/j.econlet.2004.07.019 |
| Reference:
|
[11] Cipra, T.: Robust exponential smoothing..J. Forecast. 11 (1992), 57-69. 10.1002/for.3980110106 |
| Reference:
|
[12] Cipra, T.: Robust recursive estimation in nonlinear time-series..Comm. Statist. Theory Methods 27 (1998), 1071-1082. MR 1626293, 10.1080/03610929808832146 |
| Reference:
|
[13] Cipra, T., Hanzák, T.: Exponential smoothing for time series with outliers..Kybernetika 47 (2011), 165-178. MR 2828571 |
| Reference:
|
[14] Cipra, T., Romera, R.: Robust Kalman filter and its applications in time series analysis..Kybernetika 27 (1991), 481-494. MR 1150938 |
| Reference:
|
[15] Crevits, R., Croux, C.: Forecasting using robust exponential smoothing with damped trend and seasonal components..Working paper KBI_1714, KU Leuven, Leuven 2016 (DOI:10.13140/RG.2.2.11791.18080). 10.13140/RG.2.2.11791.18080) |
| Reference:
|
[16] Croux, C., Gelper, S.: Computational aspects of robust Holt-Winters smoothing based on M-estimation..Appl. Math. 53 (2008), 163-176. MR 2411122, 10.1007/s10492-008-0002-4 |
| Reference:
|
[17] Croux, C., Gelper, S. E. C., Mahieu, K.: Robust exponential smoothing of multivariate time series..Comput. Statist. Data Anal. 54 (2010), 2999-3006. MR 2727729, 10.1016/j.csda.2009.05.003 |
| Reference:
|
[18] Dalhaus, R., Rao, S. S.: A recursive online algorithm for the estimation of time-varying ARCH parameters..Bernoulli 13 (2007), 389-422. MR 2331257, 10.3150/07-bej5009 |
| Reference:
|
[19] Engle, R. F.: Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation..Econometrica 50 (1982), 987-1007. MR 0666121, 10.2307/1912773 |
| Reference:
|
[20] Eraker, B., Johannes, M., Polson, N.: The impact of jumps in volatility and returns..J. Finance 58 (2003), 1269-1300. 10.1111/1540-6261.00566 |
| Reference:
|
[21] Fasso, A.: Recursive least squares with ARCH errors and nonparametric modelling of environmental time series..Working Paper 6, University of Bergamo 2009. |
| Reference:
|
[22] Franke, J., Härdle, W. K., Hafner, C. M.: Statistics of Financial Markets: An Introduction..Springer, Berlin 2011. MR 2722946, 10.1007/978-3-642-16521-4 |
| Reference:
|
[23] Franses, P. H., Ghijsels, H.: Additive outliers, GARCH and forecasting volatility..Int. J. Forecast. 15 (1999), 1-9. 10.1016/s0169-2070(98)00053-3 |
| Reference:
|
[24] Galeano, P., Peña, D.: Finding outliers in linear and nonlinear time series..In: Robustness and Complex Data Structures (C. Becker, R. Fried, S. Kuhnt, eds.), Springer, Berlin 2013, pp. 243-260. MR 3135884, 10.1007/978-3-642-35494-6_15 |
| Reference:
|
[25] Gelper, S., Fried, R., Croux, C.: Robust forecasting with exponential and Holt-Winters smoothing..J. Forecast. 29 (2009), 285-300. Zbl 1203.62164, MR 2752114, 10.1002/for.1125 |
| Reference:
|
[26] 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. |
| Reference:
|
[27] Grané, A., Veiga, H.: Wavelet based detection of outliers in financial time series..Comput. Statist. Data Anal. 54 (2010), 2580-2593. MR 2720462, 10.1016/j.csda.2009.12.010 |
| Reference:
|
[28] Gregory, A. V., Reeves, J. J.: Estimation and inference in ARCH model in the presence of outliers..J. Financ. Econometr. 8 (2010), 547-569. 10.1093/jjfinec/nbq028 |
| Reference:
|
[29] Grillenzoni, C.: Optimized adaptive prediction..J. Ital. Statist. Soc. 6 (1997), 37-58. 10.1007/bf03178900 |
| Reference:
|
[30] Grillenzoni, C.: Recursive generalized M-estimators of system parameters..Technometrics 39 (1997), 211-224. 10.2307/1270909 |
| Reference:
|
[31] Hendrych, R., Cipra, T.: Robustified on-line estimation of the EWMA models: Simulations and applications..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. 10.3311/ppee.9684 |
| Reference:
|
[32] Hendrych, R., Cipra, T.: Self-weighted recursive estimation of GARCH models..Comm. Statist. Simul. Comput. 47 (2018), 315-328. MR 3757688, 10.1080/03610918.2015.1053924 |
| Reference:
|
[33] Hill, J. B.: Robust estimation and inference for heavy tailed GARCH..Bernoulli 21 (2015), 1629-1669. MR 3352056, 10.3150/14-bej616 |
| Reference:
|
[34] Hotta, L. K., Tsay, R. S.: Outliers in GARCH processes..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. MR 3076022, 10.1201/b11823-20 |
| Reference:
|
[35] Hyndman, R. J., Koehler, A. B., Ord, J. K., Snyder, R. D.: Forecasting with Exponential Smoothing. The State Space Approach..Springer, Berlin 2008. 10.1111/j.1751-5823.2009.00085_17.x |
| Reference:
|
[36] Jiang, J., Zhao, Q., Hui, Y. V.: Robust modelling of ARCH models..J. Forecast. 20 (2001), 111-133. 10.1002/1099-131x(200103)20:2<111::aid-for786>3.0.co;2-n |
| Reference:
|
[37] Kierkegaard, J., Nielsen, J., Jensen, L., Madsen, H.: Estimating GARCH models using recursive methods.. |
| Reference:
|
[38] Koch, K. R., Yang, Y.: Robust Kalman filter for rank deficient observation models..J. Geodesy 72 (1998), 436-441. 10.1007/s001900050183 |
| Reference:
|
[39] Lanius, V., Gather, U.: Robust online signal extraction from multivariate time series..Comput. Statist. Data Anal. 54 (2010), 966-975. MR 2580931, 10.1016/j.csda.2009.10.009 |
| Reference:
|
[40] Ling, S.: Self-weighted and local quasi-maximum likelihood estimators for ARMA-GARCH/ IGARCH models..J. Econometr. 140 (2007), 849-873. MR 2408929, 10.1016/j.jeconom.2006.07.016 |
| Reference:
|
[41] Ljung, L.: System Identification: Theory for the User..Prentice Hall PTR, Upper Saddle River 1999. |
| Reference:
|
[42] Ljung, L., Söderström, T. S.: Theory and Practice of Recursive Identification..MIT Press, Cambridge 1983. MR 0719192 |
| Reference:
|
[43] Michálek, J.: Robust methods in exponential smoothing..Kybernetika 32 (1996), 289-306. MR 1438221 |
| Reference:
|
[44] Muler, N., Yohai, V.: Robust estimates for GARCH models..J. Statist. Planning Inference 138 (2008), 2918-2940. MR 2442223, 10.1016/j.jspi.2007.11.003 |
| Reference:
|
[45] Park, B.-J.: An outlier robust GARCH model and forecasting volatility of exchange rate returns..J. Forecast. 21 (2002), 381-393. 10.1002/for.827 |
| Reference:
|
[46] Peng, L., Yao, Q.: Least absolute deviations estimation for ARCH and GARCH models..Biometrika 90 (2003), 967-975. MR 2024770, 10.1093/biomet/90.4.967 |
| Reference:
|
[47] Romera, R., Cipra, T.: On practical implementation of robust Kalman filtering..Comm. Statist. Simul. Comput. 24 (1995), 461-488. Zbl 0850.62688, MR 1333047, 10.1080/03610919508813252 |
| Reference:
|
[48] Ruckdeschel, P., Spangl, B., Pupashenko, D.: Robust Kalman tracking and smoothing with propagating and non propagating outliers..Statist. Papers 55 (2014), 93-123. MR 3152769, 10.1007/s00362-012-0496-4 |
| Reference:
|
[49] Sakata, S., White, H.: High breakdown point conditional dispersion estimation with application to S&P 500 daily returns volatility..Econometrica 66 (1998), 529-567. 10.2307/2998574 |
| Reference:
|
[50] Shaolin, H. U., Meinke, K., Ouyang, H., Guoji, S.: Outlier-tolerant Kalman filter of state vectors in linear stochastic system..Int. J. Advanced Computer Sci. Appl. 2 (2011), 37-41. 10.14569/ijacsa.2011.021206 |
| Reference:
|
[51] Söderström, T. S., Stoica, P.: System Identification..Prentice Hall, New York 1989. |
| Reference:
|
[52] Tsay, R. S.: Analysis of Financial Time Series..Wiley, Hoboken 2013. MR 2778591 |
| Reference:
|
[53] Yang, Y.: Adaptively robust Kalman filters with applications in navigation..In: Sciences of Geodesy (G. Xu, ed.), Springer, Berlin 2010, pp. 49-82. 10.14569/ijacsa.2011.021206 |
| Reference:
|
[54] Yang, Y., Gao, W., Zhang, X.: Robust Kalman filtering with constraints: a case study for integrated navigation..J. Geodesy 84 (2010), 373-381. 10.1007/s00190-010-0374-6 |
| Reference:
|
[55] Zhang, R., Ling, S.: Asymptotic inference for AR models with heavy-tailed G-GARCH noises..Econometr. Theory 31 (2015), 880-890. MR 3377272, 10.1017/s0266466614000632 |
| Reference:
|
[56] Zhu, K., Li, W. K.: A new Pearson-type QMLE for conditionally heteroskedastic models..J. Business Econom. Statist. 33 (2015), 552-565. MR 3416600, 10.1080/07350015.2014.977446 |
| Reference:
|
[57] Zhu, K., Ling, S.: Global self-weighted and local quasi-maximum exponential likelihood estimators for ARMA-GARCH/IGARCH models..Ann. Statist. 39 (2011), 2131-2163. MR 2893864, 10.1214/11-aos895 |
| Reference:
|
[58] Zhu, K., Ling, S.: LADE-based inference for ARMA models with unspecified and heavy-tailed heteroscedastic noises..J. Amer. Statist. Assoc. 110 (2015), 784-794. MR 3367264, 10.1080/01621459.2014.977386 |
| . |
