Guaranteed estimation of parameters and faultdetection in GARCH(1,1)-process
Problem of fault detection of parameters of GARCH(1,1) process is considered. Parameters ofthe process before and after the change point are assumed to be unknown. An efficient algorithmfor detecting change point, which uses estimators of unknown parameters, is proposed. A sequentialprocedure for estimating the GARCH parameters based on the weighted least squares methodwith special weights is proposed. The choice of weights and the stopping rule guarantees the preassignedaccuracy of the estimation, which depends on parameter of procedure. Asymptotic propertiesof proposed estimators are studied. The asymptotic boundary for mean squares error is obtained.The procedure of change point detection is based on a comparison of parameters estimatorson different observation intervals. The upper bound for probabilities of false alarm and thedelay was found. Results of numerical simulation are given.
Keywords
mean square error,
GARCH model,
fault detection,
least squares method,
модифицированный МНК,
момент разладки,
GARCH(1, 1)Authors
| Sergeeva Ekaterina E. | National Research Tomsk State University | sergeeva_e_e@mail.ru |
| Vorobeychikov Sergey E. | National Research Tomsk State University | sev@mail.tsu.ru |
Всего: 2
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