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双线性时间序列模型理论AI 解读

SUMMARY The theory of bilinear time series models is considered in this paper. The sufficient conditions for asymptotic stationarity of the bilinear time series models are derived, and the expressions for the variance and covariance are obtained. The conditions for the invertibility of the model are also included. The estimation of the parameters of the scalar bilinear time series model is considered. The bilinear models are fitted to sunspot numbers and also to a P-wave of…

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传递函数时间依赖性的若干检验AI 解读

In studies of linear open loop systems, the assumption of time invariance is often tacitly made. In this paper we exploit a convenient frequency-domain approach to furnish tests for the time dependence of a transfer function, which is the most crucial notion in the case of linear systems. An extension of Tukey's test for nonadditivity is given in § 4. The proposed tests are illustrated numerically with both simulated and real data.

线性开环系统时变性的检验AI 解读

Summary We consider the problem of testing a given open-loop system for time-dependence. The test is based on just a single realization of the input and a single realization of the output. It makes use of the concept of the “evolutionary cross-spectra” of a non-stationary vector process and rests essentially on testing the “uniformity” of a set of vectors, whose components consist of the “evolutionary gain-spectra” and “evolutionary phase-spectra”. Using a logarithmic…

含时变参数的非平稳时间序列模型拟合AI 解读

Summary We use the method of weighted least squares to estimate the time-dependent parameters of non-stationary time-series models. Approximate expressions for the bias and variance of the estimates, which could be used to assess the merits of various weight functions on the basis of “mean square error” criterion, are obtained. In Section 5, it is shown that the estimates obtained by weighted least-squares method are the same as estimates obtained by weighted…

时间序列非平稳性的检验AI 解读

Summary We consider the problem of testing a given time-series for stationarity. The approach is based on evolutionary spectral analysis, and the proposed method consists essentially in testing the “homogeneity” of a set of evolutionary spectra evaluated at different instants of time. Using a logarithmic transformation, we show that the mechanics of the test are formally equivalent to a two-factor analysis of variance procedure when the residual variance is known, a priori.…

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p 依赖时间序列离散程度趋势检验中 Cox–Stuart 检验的渐近相对效率AI 解读

Cox and Stuart's tests (Cox & Stuart, 1955) are applied to test for trend in dispersion of a p-dependent time series. For a particular trend model the asymptotic relative efficiencies are obtained for the S1 and S2 tests relative to the teat based on the maximum likelihood estimate.