Geodesic
Structural break detection in autoregressional conditional heteroskedasticity model: case of Student distribution
Matematičeskoe modelirovanie, Tome 35 (2023) no. 1, pp. 51-58.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider two methods of structural break detection in a piecewise generalized model of autoregressive conditional heteroscedasticity. The first method is based on Kolmogorov–Smirnov statistics and is called KS-method. The second one is based on the cumulative sums and is called KL-method. In this paper, we compare the KS- and KL-methods under the assumption of Student conditional distribution of random errors. The results of our Monte Carlo experiments were as follows: the KL-method lost to the KS-method both in terms of the average probability of first type error and in terms of the average power structural break detection.
Keywords: GARCH-t, Student distribution, volatility, change points, structural breaks, structural shifts, CUSUM.
Mots-clés : t-distribution, ICSS 
@article{MM_2023_35_1_a3,
     author = {D. A. Borzykh and A. A. Yazykov},
     title = {Structural break detection in autoregressional conditional heteroskedasticity model: case of {Student} distribution},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {51--58},
     publisher = {mathdoc},
     volume = {35},
     number = {1},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2023_35_1_a3/}
}
TY  - JOUR
AU  - D. A. Borzykh
AU  - A. A. Yazykov
TI  - Structural break detection in autoregressional conditional heteroskedasticity model: case of Student distribution
JO  - Matematičeskoe modelirovanie
PY  - 2023
SP  - 51
EP  - 58
VL  - 35
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2023_35_1_a3/
LA  - ru
ID  - MM_2023_35_1_a3
ER  - 
%0 Journal Article
%A D. A. Borzykh
%A A. A. Yazykov
%T Structural break detection in autoregressional conditional heteroskedasticity model: case of Student distribution
%J Matematičeskoe modelirovanie
%D 2023
%P 51-58
%V 35
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2023_35_1_a3/
%G ru
%F MM_2023_35_1_a3
D. A. Borzykh; A. A. Yazykov. Structural break detection in autoregressional conditional heteroskedasticity model: case of Student distribution. Matematičeskoe modelirovanie, Tome 35 (2023) no. 1, pp. 51-58. http://geodesic.mathdoc.fr/item/MM_2023_35_1_a3/

[1] D. Borzykh, A. Yazykov, “The new KS method for a structural break detection in GARCH (1,1) models”, Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), 54 (2019), 90–104

[2] P. Kokoszka, R. Leipus, “Testing for parameter changes in ARCH models”, Lithuanian Mathematical Journal, 39 (1999), 182–195 | DOI | MR

[3] T. Bollerslev, “A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return”, The Review of Economics and Statistics, 69 (1987), 542–547 | DOI

[4] R. Davis, T. Lee, G. Rodriguez-Yam, “Break detection for a class of nonlinear time series models”, Journal of Time Series Analysis, 29 (2008), 834–867 | DOI | MR

[5] K. Fukuda, “Parameter changes in GARCH model”, J. of Applied Statistics, 37 (2010), 1123–1135 | DOI | MR

[6] S. Kim, S. Cho, S. Lee, “On the CUSUM test for parameter changes in GARCH(1,1) models”, Communications in Statistics. Theory and Methods, 29 (2000), 445–462 | DOI | MR

[7] P. Kokoszka, R. Leipus, “Change-point estimation in ARCH models”, Bernoulli, 6 (2000), 513–539 | DOI | MR

[8] S. Lee, Y. Tokutsu, K. Maekawa, “The CUSUM test for parameter change in regression models with ARCH errors”, J. of the Japanese Statistical Society, 34 (2004), 173–188 | DOI | MR

[9] C. Inclán, G. Tiao, “Use of cumulative sums of squares for retrospective detection of changes of variance”, J. of the American Statis. Association, 89 (1994), 913–923 | MR

[10] H. Ombao, J. Raz, R. von Sachs, W. Guo, “The SLEX model of a non-stationary random process”, Annals of the Institute of Statistical Mathematics, 54 (2002), 171–200 | DOI | MR

[11] G. J. Ross, “Modeling financial volatility in the presence of abrupt changes”, Physica A: Statistical Mechanics and its Applications, 192:2 (2013), 350–360 | DOI

[12] A. Zhang, R. Gabrys, P. Kokoszka, “Discriminating between long memory and volatility shifts”, Austrian Journal of Statistics, 36:4 (2007), 253–275 | MR

[13] I. Berkes, E. Gombay, L. Horváth, P. Kokoszka, “Sequential change-point detection in GARCH (p, q) models”, Econometric theory, 20:6 (2004), 1140–1167 | DOI | MR