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非线性 ARCH 时间序列的非参数估计与识别：强收敛和渐近正态性AI 解读

We consider the estimation and identification of the functional structures of nonlinear econometric systems of the ARCH type. We employ nonparametric kernel estimates for the nonlinear functions characterizing the systems, and we establish strong consistency along with sharp rates of convergence under mild regularity conditions. We also prove the asymptotic normality of the estimates.

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.

非线性时间序列的非参数模型辨识：投影方法AI 解读

We study the possibility of identifying general linear and nonlinear time series models using nonparametric methods. The kernel estimators of the conditional mean and variance are used as a basis, and the properties of these quantities as model indicators are briefly discussed. Some drawbacks are pointed out, and motivated by these we introduce projections as tools of identification. The projections are especially useful for additive modeling. Expressions for the asymptotic…

非线性时间序列的非参数识别：显著滞后选择AI 解读

In this article we suggest a nonparametric procedure for selecting significant lags in the model description of a general nonlinear stationary time series. The procedure can be applied to both the conditional mean and the conditional variance and is valid for heteroscedastic series. The procedure is illustrated by simulations and sunspot data, lynx data, and blowfly data are analyzed. It is indicated that projectors can be used in conjunction with the procedure for selecting…

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…

非线性时间序列的识别：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…

NEAR(2) 与 NLAR(2) 时间序列模型的一致估计AI 解读

SUMMARY Consistent and asymptotically normal estimates for all four parameters of the NEAR(2) and NLAR(2) time series models are obtained. The estimates are given in explicit form and are easy to compute, but with simulation experiments the standard errors are large, especially for small values of the parameters, so very substantial sample sizes may be needed. Hence, from this point of view, the NEAR(2) and NLAR(2) models are of limited practical value. The simulations…

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.

自回归时间序列残差方差与阶数的估计AI 解读

SUMMARY We study the bias of Yule-Walker, least squares and Burg-type estimates of the residual variance of autoregressive processes. Both simulations and theory indicate that Yule-Walker estimates are inferior to least squares and Burg-type estimates. The effect on order determination is also studied, and we extend the results on overestimation of the AIC criterion to the general multivariate case. For strongly autocorrelated processes, Yule-Walker estimates of residual…

若干常用时间序列估计量的偏差AI 解读

We study the bias of Yule-Walker and least squares estimates for univariate and multivariate autoregressive processes. We obtain explicit formulae for the large-sample bias of YuleWalker estimates in the scalar first- and second-order cases and for least squares estimates in the general case. Both simulations and theory indicate that Yule-Walker estimates are inferior to least squares estimates. For strongly autocorrelated processes, Yule-Walker estimates can be severely…

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空间变量的一种关联度量AI 解读

A measure of association for spatial variables is proposed. The measure is based on the ranks of the observations and on the location coordinates of the measurement points. For two independent spatial variables it is shown that under optimal coordinate designs the variance of the measure is of the order l/(kn), where n is the number of data points and k is the dimension of the observation space. Conditions for asymptotic normality are stated, and asymptotic formulae for bias…