{"title":"On Testing the Symmetry of Innovation Distribution in Autoregression Schemes","authors":"M. V. Boldin, A. R. Shabakaeva","doi":"10.3103/s0027132223050029","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We consider a stationary linear <span>\\(AR(p)\\)</span> model with zero mean. The autoregression parameters, as well as the distribution function (d.f.) <span>\\(G(x)\\)</span> of innovations, are unknown. We test symmetry of innovations with respect to zero in two situations. In the first case the observations are a sample from a stationary solution of <span>\\(AR(p)\\)</span>. We estimate parameters and find residuals. Based on them we construct a kind of empirical d.f. and the omega-square type test statistic. Its asymptotic d.f. under the hypothesis and the local alternatives are found. In the second situation the observations are subject to gross errors (outliers). For testing the symmetry of innovations we again construct the Pearson’s type statistic and find its asymptotic d.f. under the hypothesis and the local alternatives. We establish the asymptotic robustness of Pearson’s test as well.</p>","PeriodicalId":42963,"journal":{"name":"Moscow University Mathematics Bulletin","volume":"13 1","pages":""},"PeriodicalIF":0.2000,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Moscow University Mathematics Bulletin","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3103/s0027132223050029","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We consider a stationary linear \(AR(p)\) model with zero mean. The autoregression parameters, as well as the distribution function (d.f.) \(G(x)\) of innovations, are unknown. We test symmetry of innovations with respect to zero in two situations. In the first case the observations are a sample from a stationary solution of \(AR(p)\). We estimate parameters and find residuals. Based on them we construct a kind of empirical d.f. and the omega-square type test statistic. Its asymptotic d.f. under the hypothesis and the local alternatives are found. In the second situation the observations are subject to gross errors (outliers). For testing the symmetry of innovations we again construct the Pearson’s type statistic and find its asymptotic d.f. under the hypothesis and the local alternatives. We establish the asymptotic robustness of Pearson’s test as well.
Abstract We consider a stationary linear \(AR(p)\) model with zero mean.自回归参数以及创新值的分布函数（d.f. ）\(G(x)\)都是未知的。我们在两种情况下检验创新值相对于零的对称性。在第一种情况下，观测值是从 \(AR(p)\) 的静态解中抽取的样本。我们估计参数并找到残差。在此基础上，我们构建了一种经验 d.f.和Ω-平方类型检验统计量。在假设和局部替代条件下，找到其渐近 d.f.。在第二种情况下，观测数据会出现严重错误（异常值）。为了检验创新的对称性，我们再次构建皮尔逊类型统计量，并找出其在假设和局部替代方案下的渐近 d.f.。我们还建立了皮尔逊检验的渐近稳健性。
期刊介绍：
Moscow University Mathematics Bulletin is the journal of scientific publications reflecting the most important areas of mathematical studies at Lomonosov Moscow State University. The journal covers research in theory of functions, functional analysis, algebra, geometry, topology, ordinary and partial differential equations, probability theory, stochastic processes, mathematical statistics, optimal control, number theory, mathematical logic, theory of algorithms, discrete mathematics and computational mathematics.
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