A Weighted Least Squares Method for Guaranteed Estimation of Parameters of ARCH(1) Process.
A sequential procedure for estimating of parameters of ARCH(1) process is proposed. The process is described by equations2 21l l l l l x x −= Ґт Ґе ; Ґт = Ґм - Ґл .Here {Ґеl}lЎГ1 is a sequence of independent identically distributed random variables with zeromean and unit variance. Parameters Ґм and Ґл are supposed to be unknown. The procedure for estimatingof unknown parameters uses the weighted least squares method. The choice of coefficientsand stopping rule guarantees the quality of obtained estimators. The results are illustrated by numericalexamples.
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Authors
| Name | Organization | |
| Burkatovskaya Yulia B. | Tomsk Polytechnic University | burkatovskaya@sibmail.com |
| Vorobeychikov Sergey É. | Tomsk StateUniversity | sev@mail.tsu.ru |
References
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Воробейчиков С.Э., Медер Н.А. On guaranteed estimation of parameter of random processes by the weighted least square method // Preprints of the 15th Triennial World Congress of the International Federation of Automatic Control. Barcelona. Spain, 21 - 26 July 2002. Nо. 1200.
Дмитриенко А.А., Конев В.В. О последовательной классификации процессов авторегрессии с неизвестной дисперсией помех // Проблемы передачи информации. 1995. Т. 31. Вып. 4. С. 51 - 62.
