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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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Bustos O., Fraiman R., Yohai V.J.

Asymptotic behaviour of the estimates based on residual

autocovariances for ARMA models // Lecture Notes in Statist. 1984. Vol. 26. P. 26–49.

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Mukantseva L.A.

Testing normality in one-dimensional and multi-dimensional linear

regression // Theory of Probability and its Applications. 1978. Vol. 22. P. 591–602.

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.ru

E.R. Goryainova

2

el-goryainova@mail.ru

1

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