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时间序列线性的非参数检验AI 解读

We introduce tests of linearity for time series based on nonparametric estimates of the conditional mean and the conditional variance. The tests are compared to a number of parametric tests and to nonparametric tests based on the bispectrum. Asymptotic expressions give bad approximations, and the null distribution under linearity is constructed using resampling of the best linear approximation. The new tests perform well on the examples tested.

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基于经验分布函数的序列独立性非参数检验AI 解读

The Blum, Kiefer & Rosenblatt (1961) statistic for testing independence is considered in a time series setting. This test is, under mild conditions, shown to be consistent against lag one dependent alternatives. The null distribution of the test statistic is established, both when the marginal distribution is continuous and when it is discrete. Simulation results giving information on the size and the power of the test are provided, and comparisons are made with other tests…

非线性时间序列识别：一阶刻画与阶数确定AI 解读

We study the possibility of identifying nonlinear time series using nonparametric estimates of the conditional mean and conditional variance. It is shown that most nonlinear models satisfy the assumptions needed to apply nonparametric asymptotic theory. Sampling variations of the conditional quantities are studied by simulation and explained by asymptotic arguments for a number of first-order nonlinear autoregressive processes. The conditional mean and variance can be used…

自回归谱估计中的谱峰丢失AI 解读

Autoregressive spectral analysis depends on the method used for estimating the autoregressive parameters. It is shown by an asymptotic analysis involving second-order terms that least-squares estimates should be preferred to Yule-Walker estimates, since Yule-Walker estimates may result in loss of spectral peaks and strong bias. The results are confirmed by simulations which include also Burg-type estimates.

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