Asymptotic properties of parameter estimation andchange-point detection procedures for a generalized autoregressive process with conditionalheteroscedasticity
Problem of change-point detection of the parameters of GARCH(p,q) process is considered.The autoregressive parameters of the process before and after the change point are supposed to beunknown. A sequential procedure for estimating the parameters based on the weighted leastsquares method is developed. The choice of the weights and the stopping rule allows one to constructan estimator with a preassigned mean square error depending on parameter H of the procedure.The asymptotic properties of the proposed estimator are studied. The asymptotic bound forthe mean square error is determined. The procedure of change-point detection is based on comparisonof the parameter estimators at different observation intervals. The upper bounds for probabilitycharacteristics of the proposed procedure: probabilities of the false alarm and the delay arefound. The results of numerical simulation demonstrating the performance of the procedure arereported.
Keywords
martingale central limit theorem, guaranteed estimation, mean square error, change-point, least squares method, GARCH(p,q), центральная предельная теорема для мартингалов, гарантированное оценивание, среднеквадратическое отклонение, метод наименьших квадратов, момент разладки, GARCH(p, q)Authors
| Name | Organization | |
| Burkatovskaya Yulia B. | National Research Tomsk Polytechnic University; National Research Tomsk State University | tracey@tpu.ru |
| Vorobeychikov Sergey E. | National Research Tomsk State University | sev@mail.tsu.ru |
| Sergeeva Ekaterina E. | National Research Tomsk Polytechnic University; National Research Tomsk State University | sergeeva_e_e@mail.ru |
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