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存在缺失数据时的时间序列模型估计AI 解读

A method is proposed for the estimation of models for discrete time series in the presence of missing data. Some justification is given for the use of this method over alternatives; the choice of estimator is likely to be governed by the pattern of missing data, the nature of the time series model, and computational considerations. The method's performance in estimating simple models is studied by simulations, and it is applied to a time series of pollution levels containing…

预测均方误差估计中的偏差AI 解读

We examine the forecasting problem for a finite series of observations from either a nonseasonal or a seasonal autoregressive-moving average process. Four sources of bias in the usual estimator of forecast mean squared error are identified and analyzed for particular models using maximum likelihood and least squares parameter estimates. The usual estimator is found to be biased downwards, especially near the boundary of a stationary or invertible region, and the bias is…

向量自回归误差下动态联立方程模型的预测AI 解读

The asymptotic distribution of prediction is derived for the general simultaneous equation model with lagged endogenous variables and vector autoregressive errors. The results turn out to be particularly simple when no lagged endogenous variables are present. errors. It seems worthwhile to extend Schmidt's results, since the estimation of dynamic simultaneous equation models with autoregressive errors is now fairly commonplace in the literature. Also, as noted by Schmidt…

时间序列模型的拟合优度：高阶穿越的应用AI 解读

A relation between the graphical appearance of a stationary time series and its autocorrelations is discussed. The use of counts of visual features termed higher order crossings is proposed in testing goodness of fit of hypothesized models against very general alternatives. Attention is focused on a specific example of a new type of nonparametric test statistic arising from iterative feature extraction procedures called extractors. The statistic is compared with Box &…

利用秩计算变点的后验概率AI 解读

Simple approximate methods of analysis are given for change-point models using ranked observations. The models can be applied to continuous observations, providing a robust analysis in this case. For ranked observations, the models provide analyses for association. Numerical examples, involving continuous and ranked observations, are given.

多元自回归移动平均模型的预测AI 解读

A simple formula for multiperiod perdietions of mulativariate autoregressive-moving average models is derived. The formula is explicitly given as a function of suitably defined parameter matrices and an observation vectors, and includes simple models as its special cases. The asymptotic prediction mean squared error is also derived for perdictions with estimated parameters.

摘要暂缺

用于统计推断的若干傅里叶方法AI 解读

Common statistical procedures such as maximum likelihood and M-estimation admit generalized representations in the Fourier domain. The Fourier domain provides fertile ground for approaching a number of difficult problems in inference. In particular, the empirical characteristic function and its extension for stationary time series are shown to be fundamental tools which support numerically simple inference procedures having arbitrarily high asymptotic efficiency and certain…

季节调整原则及由此导出的调整方法AI 解读

The decomposition of a given time series into trend, seasonal component, and irregular component is formulated as a minimization problem. The trend is chosen such that it is as smooth as possible; the seasonal component is chosen such that it exhibits a seasonal pattern as stable as possible; and the trend and seasonal components are jointly chosen such that the given time series is explained as well as possible by these two components; that is, the irregular component is…

两个协方差平稳时间序列独立性检验的比较AI 解读

The approximate slopes of several tests of the independence of two covariance stationary time series are derived and compared. It is shown that the approximate slopes of regression tests are at least as great as those based on the residuals of univariate ARIMA models, and that there are cases in which the former are arbitrarily great while the latter are arbitrarily small. These analytical findings are supported by a Monte Carlo study that shows that in samples of size 100…

时间序列分析：理论与实践AI 解读

To Liz Alice sighed wearily.'I think you might do something better with the time,' she said, 'than waste it in asking riddles that have no answers.''If you knew Time as well as 1 do,' said the Hatter, 'you wouldn't talk about wasting it.It's him.' 'I don't know what you mean,' said Alice.'Of course you don't!' the Hatter said, tossing his head contemptuously.'I dare say you never even spoke to Time!' 'Perhaps not,' Alice cautiously replied: 'but 1 know 1 have to beat time…

平稳点过程谱参数的估计AI 解读

This paper considers the two approaches for estimating the parameters specifying the spectral density of the counting process of a stationary point process, namely the frequency domain and the time domain approaches. The relation between the two is clarified; consistency and asymptotic normality of the estimates are established. Finally the special case of a rational spectral density is considered in some detail.

检测小幅变化的非参数控制图AI 解读

We consider sequential observation of independent random variables $X_1,\cdots, X_N$ whose distribution changes from $F$ to $G$ after the first $\lbrack N\theta \rbrack$ variables. The object is to detect the unknown change-point quickly without too many false alarms. A nonparametric control chart based on partial weighted sums of sequential ranks is proposed. It is shown that if the change from $F$ to $G$ is small, then as $N \rightarrow \infty$, the appropriately scaled…

随机差分方程的参数估计AI 解读

Let $Y_t$ satisfy the stochastic difference equation $Y_t = \sum^q_{i=1} \psi_{ti} \alpha_i + \sum^p_{j=1} \gamma_j Y_{t-j} + e_t,$ where the $\{\psi_{ti}\}$ are fixed sequences and (or) weakly stationary time series and the $e_t$ are independent random variables, each with mean zero and variance $\sigma^2$. The form of the limiting distributions of the least squares estimators of $\alpha_i$ and $\gamma_j$ depend upon the absolute value of the largest root of the…

某些时间序列模型中最优设计的唯一性与最终唯一性AI 解读

Using the results of Barrow, et al., and Chow on the optimal placement of knots in the approximation of functions by piecewise polynomials, we show the uniqueness or "eventual uniqueness" of optimal designs for certain time series models considered by Sacks and Ylvisaker, and Wahba. In addition, the limiting behavior (as the sample size increases) of the variance of the BLUE of the regression coefficient is characterized in terms of the density defining the design, and the…

摘要暂缺

不恰当去趋势造成的时间序列虚假周期性AI 解读

Econometric analysis of time series data is frequently preceded by regression on time to remove a trent component in the date. The resulting residuals are then treated as a stationary series to which procedures requiring stationarity, such as spectral analysis, can be applied. The objective is often to investigate the dynamics of transitory movements in the systems, for example, in econometric models of the business cycle. When the data does consist of a deterministic…

自回归移动平均模型马尔可夫表示的参数估计AI 解读

Tuan (1978) discussed the approximate maximum likelihood estimation of the parameters of the Markovian representation of the autoregressive-moving average model. He considered an indirect method, using the equivalent quasiautoregressive moving average form, the parameters of which are in one to one correspondence with those of the Markovian representation. A method of finding exact joint maximum likelihood estimates of the parameters and the initial state of the process is…

利用振幅依赖自回归时间序列模型刻画非线性随机振动AI 解读

The behaviour of nonlinear deterministic vibrations has been studied by many authors, and may typically include such features as jump phenomena and limit cycles. Nonlinear random vibrations in continuous time have also been studied and these may commonly give rise to the phenomenon of amplitude-dependent frequency. A discrete time series model is introduced, which may be demonstrated to have properties similar to those of nonlinear random vibrations. This model is of…

一种时间序列递推的二阶性质AI 解读

In this work we prove the asymptotic efficiency of a certain time series recursion for the parameters of an ARMAX time series model.

最优自回归谱估计AI 解读

An asymptotic lower bound is obtained for the integrated relative squared error of autoregressive spectral estimate when the order of autoregression is selected. The bound is attained in the limit by the same selection as has been proposed for prediction.

非对称时间序列AI 解读

Asymmetric time series respond to innovations with one of two different rules according to whether the innovation is positive or negative. Quoted industrial prices are apparently such a series. It has been observed that when market conditions change, quoted prices are not revised immediately. This delay operates more strongly against reductions in price quotations than against increases. A statistical model for such asymmetric times series is developed and analyzed. An…

多参数稳态演化模型AI 解读

SUMMARY This paper generalizes and extends the idea of a steady evolution of a time series to multiparameter processes with any observational distribution. Particular examples of such processes are given. These include the multivariate steady process, univariate normal processes where the observational variance is unknown and series of multinomial observations with a steady model on the cell probabilities.

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…