Знаковые критерии проверки гипотезы о порядке уравнения в модели скользящего среднего
ISSN 1812-3368. Вестник МГТУ им. Н.Э. Баумана. Сер. Естественные науки. 2016. № 6
13
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Горяинов Владимир Борисович
— д-р физ.-мат. наук, доцент, профессор кафедры
«Математическое моделирование» МГТУ им. Н.Э. Баумана (Российская Федерация,
105005, Москва, 2-я Бауманская ул., д. 5).
Горяинова Елена Рудольфовна
— канд. физ.-мат. наук, доцент, доцент департамента
математики на факультете экономических наук Национального исследовательского
университета «Высшая школа экономики» (НИУ ВШЭ) (Российская Федерация, 101000,
Москва, ул. Мясницкая, д. 20).
Просьба ссылаться на эту статью следующим образом:
Горяинов В.Б., Горяинова Е.Р. Знаковые критерии проверки гипотезы о порядке
уравнения в модели скользящего среднего // Вестник МГТУ им. Н.Э. Баумана.
Сер. Естественные науки. 2016. № 6. C. 4–15. DOI: 10.18698/1812-3368-2016-6-4-15
SIGN TEST FOR HYPOTHESIS ABOUT THE ORDER
OF EQUATION IN MOVING AVERAGE MODEL
V.B. Goryainov
1
vb-goryainov@bmstu.ruE.R. Goryainova
2
el-goryainova@mail.ru1
Bauman Moscow State Technical University, Moscow, Russian Federation
2
National Research University Higher School of Economics, Moscow, Russian Federation
Abstract
Keywords
The article deals with constructing the sign test for the
hypothesis about the order of equation in moving average.
We found the asymptotic distribution of the test statistics
which appeared to be the central
2
-distribution under the
null hypothesis and the noncentral
2
-distribution under
the alternative one. Knowing the asymptotic distribution
makes it possible to calculate the asymptotic relative
efficiency of the constructed sign test criterion with respect
to the known criteria. In our research we give an example
of calculating the asymptotic relative efficiency of the
constructed sign test criterion in relation to the classical
criterion, based on a sample covariance ratio. Moreover,
we determine the values of the asymptotic relative
efficiency for a normal distribution, the double exponential
distribution (Laplace distribution) and contaminated
normal distribution (Tukey distribution). It is shown that
if the innovation process in the moving average model is
contaminated with Gaussian outliers, the asymptotic
relative efficiency of this test can be arbitrarily large
compared to the traditional criterion, based on a sample
correlation coefficient
Moving
average model, hypothesis
about the order of the equation, sign
test, Tukey distribution