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针对平滑随机趋势的检验AI 解读

Abstract A trend estimated from an unobserved components model tends to be smoother when it is modelled as an integrated random walk rather than a random walk with drift. This article derives a test of the null hypothesis that the trend is deterministic against the alternative that it is an integrated random walk. It is assumed that the other component in the model is normally distributed white noise. Critical values are tabulated, the asymptotic distribution is derived and…

共同随机趋势检验AI 解读

This paper is concerned with tests in multivariate time series models made up of random walk (with drift) and stationary components. When the stationary component is white noise, a Lagrange multiplier test of the hypothesis that the covariance matrix of the disturbances driving the multivariate random walk is null is shown to be locally best invariant, something that does not automatically follow in the multivariate case. The asymptotic distribution of the test statistic is…

仿射不变的多元单样本符号检验AI 解读

SUMMARY Brown and Hettmansperger introduced an affine invariant bivariate analogue of the sign test based on the generalized median of Oja. In this paper its general multivariate extension is presented. The proposed multivariate permutation or sign change test is affine invariant with an easily computable covariance matrix. For elliptic distributions the proposed test and Randles's test are asymptotically equivalent. Formulae for calculating asymptotic relative efficiencies…

二元符号检验AI 解读

In this article the bivariate location problem is treated. New appealing bivariate analogs of the univariate sign tests are proposed for testing the null hypothesis concerning the unknown symmetry center. These tests remain unaltered under any nonsingular linear transformation. From these promising findings a whole family of locally most powerful invariant sign tests is introduced. The tests proposed earlier (Blumen 1958; Hodges 1955) are specific members of this family. For…

检验参数是否随时间保持不变AI 解读

Tests are proposed for detecting possible changes in parameters when the observations are obtained sequentially in time. While deriving the tests the alternative one has in mind specifies the parameter process as a martingale. The distribution theory of these tests relies on the large-sample results; that is, only the limiting null distributions are known (except in very special cases). The main tool in establishing these limiting distributions is weak convergence of…

时间序列确定性线性趋势的检验AI 解读

Most powerful tests are derived for the hypothesis that deterministic linear trend occurs in time series against the alternative that trend consists of random walk subject to drift. Comparisons of these tests and of the tests suggested by LaMotte and McWhorter (1978) are made in terms of exact powers and Pitman asymptotic relative efficiencies.

简单线性模型中随机游走系数检验的比较AI 解读

The locally most powerful test is derived for the hypothesis that the regression coefficients are constant over time against the alternative that they vary according to the random walk process. When the regression equation contains the constant term only, comparisons are made with the tests suggested by LaMotte and McWhorter (1978). These are based on exact powers and on three different types of asymptotic efficiencies including the classical Pitman and Bahadur approaches…