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检验平稳时间序列是否为高斯过程AI 解读

A class of procedures is proposed for testing the composite hypothesis that a stationary stochastic process is Gaussian. Requiring very limited prior knowledge about the structure of the process, the tests rely on quadratic forms in deviations of certain sample statistics from their population counterparts, minimized with respect to the unknown parameters. A specific test is developed, which employs differences between components of the sample and Gaussian characteristic…

随机回归模型中最小二乘预测量的自适应预测及时间序列应用AI 解读

Herein we consider the asymptotic performance of the least squares predictors $\hat{y}_n$ of the stochastic regression model $y_n = \beta_1 x_{n1} + \cdots + \beta_p x_{np} + \varepsilon_n$. In particular, the accumulated cost function $\sum^n_{k=1} (y_k - \hat{y}_k - \varepsilon_k)^2$ is studied. The results are then applied to nonstationary autoregressive time series. A statistic is also constructed to show how many times one should difference a nonstationary time series…

自回归预测误差性质的估计AI 解读

Forecasting requires estimates of the error of prediction; however, such estimates for autoregressive forecasts depend nonlinearly on unknown parameters and distributions. Substitution estimators of mean squared error (MSE) possess bias that varies with the underlying model, and Gaussian-based prediction intervals fail if the data are not normally distributed. This article proposes methods that avoid these problems. A second-order Taylor expansion produces an estimator of…

经济时间序列的基准校准AI 解读

This article develops a statistical model-based approach to the benchmarking problem. Benchmarking is done when data from a monthly sample survey are combined with data from an annual census for the purpose of improving the survey estimates. Previous authors have used numerical analysis techniques to derive methods to perform benchmarking. This article formulates the benchmarking problem in a statistical framework and uses modern times series methods to derive a solution.…

投入产出系统的最优近似聚合AI 解读

A method of constructing aggregate input—output systems is proposed. The procedure minimizes the mean squared error of aggregate predictions. The range of data on which the aggregate model is to be applied influences the best approximate aggregate. Best approximate aggregate models maximize Ijiri's coefficient of aggregation. In a special case, Fisher's aggregated model emerges: if consistent aggregation is possible it gives the best approximate aggregate. Computations…

传染性事件过程的时间序列分析AI 解读

Between 1968 and 1972 there were 326 attempts to hijack aircraft worldwide, including 137 attempts in the United States. Those attempts were often attributed to imitation of previous hijacking incidents, and aircraft hijacking, like many other types of behavior, was described as a “contagious” phenomenon. In this article a general mathematical model is developed for serial dependence of rates at which events occur and is applied to data on the hijacking attempts in the U.S.…

非平稳时间序列的非高斯状态空间建模AI 解读

A non-Gaussian state—space approach to the modeling of nonstationary time series is shown. The model is expressed in state—space form, where the system noise and the observational noise are not necessarily Gaussian. Recursive formulas of prediction, filtering, and smoothing for the state estimation and identification of the non-Gaussian state—space model are given. Also given is a numerical method based on piecewise linear approximation to the density functions for realizing…

美国县级人口预测的准确性与偏差检验AI 解读

"This article deals with the forecast accuracy and bias of population projections for 2,971 counties in the United States. It uses three different projection techniques and data from 1950, 1960, 1970, and 1980 to make two sets of 10-year projections and one set of 20-year projections. These projections are compared with census counts to determine forecast errors. The size, direction, and distribution of forecast errors are analyzed by size of place, rate of growth, and…

插值误差方差与线性确定性指标的估计AI 解读

The autoregressive and window estimators of the inverse variance, Ri (0), say, are adopted for estimating the interpolation error variance, {Ri (0)}−1, and an index of linear determinism, A, of a stationary process {Xt}. The index A is defined as 1 −{R(0) Ri (0)}−1, where R(0) denotes the variance of Xt; A measures the proportion of total variance explained by the interpolator when interpolating Xt, say, from {Xs, S ≠ t}. Some uses of A and {Ri (0)}−1 are discussed. The…

自回归移动平均参数的稳健一致估计AI 解读

We aim at estimates of autoregressive-moving average parameters which are simultaneously consistent at the nominal Gaussian model and insensitive to outliers in the data. The estimates may be viewed as a robust version of maximum likelihood estimates of order r and, for purely autoregressive models, reduce to a special case of generalized M-estimates.

替代性渐近最优检验及其在动态设定中的应用AI 解读

A method is presented for generating test statistics which share the same first order asymptotic optimality properties of the classical statistics. Generalizing Neyman's (1959) work, the linearised classical statistic tests restrictions in implicit function form using a parameter estimator which is consistent and asymptotically normally distributed under the alternative hypothesis. By judicious choice of estimator and form of restrictions at which to evaluate the statistic,…

自回归过程差分阶数的确定AI 解读

One way of handling nonstationarity in time series is to compute first differences and fit a model to the differenced series unless the differenced series also looks nonstationary. In that case, second- or higher-order differencing is done. To decide if the current degree of differencing is sufficient, one can look at the autocorrelation function for slow decay. A formal statistical test for the need to difference further is available if one is willing to assume that at most…

向量自回归与现实AI 解读

This article questions the statistical significance of variance decompositions and impulse response functions for unrestricted vector auto regressions. It suggests that previous authors have failed to provide confidence intervals for variance decompositions and impulse response functions. Two methods of computing such confidence intervals are developed: first, using a normal approximation; second, using bootstrapped resampling. An example from Sims's work is used to…

摘要暂缺

欧洲经济共同体生产调查预期的形成与预测表现：时间序列研究AI 解读

This article provides an empirical analysis of manufacturers' survey responses on short-term production expectations. If such surveys provide valid anticipations of production activity in customer industries, they should be valuable information to management in supplier industries. Two major questions are considered: (a) Are survey expectations valid predictors of future production activity as reported later by the manufacturers and/or as measured by official statistics? (b)…

单变量时间序列二阶差分的对称检验AI 解读

A test for the null hypothesis that a time series has characteristic equations with two unit roots is presented. The test, based on a standard regression computation, is shown to have good power properties when compared to previously existing tests.

英国经济的存量—流量一致宏观计量模型：第二部分AI 解读

Abstract This paper is the second of a series of two which describe the estimation and simulation of a stock‐flow consistent macro‐economic model of the UK economy. The first part (Davis, 1987) surveyed the theoretical literature on stock‐adjustment dynamics, criticized existing UK forecasting models for omitting many potential stock‐flow interactions and gave an outline of the model which is constructed here. The estimation and simulation results suggest that variables…

SUMMARY The parameter density is the polynomial matrices of vector autoregressive moving average (VARMA) time series models is generally very low. Thus, estimation of fully parameterized high order models or of models with many variables is an ineffective, if not impractical, way of utilizing computing power. In the article we present methods for identifying the nonzero elements in VARMA(1,1) models, and show how these procedures can be used to construct models of higher…

独立随机变量序列中变点极大似然估计量的分布近似AI 解读

The problem of estimating the change-point in a sequence of independent random variables is considered. As the sample sizes before and after the change-point tend to infinity, Hinkley (1970) showed that the maximum likelihood estimate of the change-point converges in distribution to that of the change-point based on an infinite sample. Letting the amount of change in distribution approach 0, it is shown that the distribution, suitably normalized, of the maximum likelihood…

随机过程的定性稳健性AI 解读

In this paper we generalize Hampel's concept of qualitative robustness of a sequence of estimators to the case of stochastic processes with non-i.i.d. observations, defining appropriate metrics between samples. We also present a different approach to qualitative robustness which formalizes the notion of resistance. We give two definitions based on this approach: strong and weak resistance. We show that for estimating a finite dimensional real parameter, $\pi$-robustness is…

一阶平稳自回归过程均值的序贯估计AI 解读

This paper considers the problem of sequential point and fixed-width confidence interval estimation of the location parameter when the errors form an autoregressive process with unknown scale and autoregressive parameters. The sequential point estimator considered here is based on sample mean and is shown to be asymptotically risk efficient as the cost per observation tends to zero. The sequential interval estimator is shown to be asymptotically consistent and the…

无模型一步向前预测区间：渐近理论与小样本模拟AI 解读

We show that the empirical quantile process from an ARMA$(1, q)$ process which is strongly mixing $\Delta_s$, and is either Gaussian or double exponential, converges to a Gaussian process. This result is used to derive model-free one-step-ahead prediction intervals for such processes. Simulations demonstrate where the asymptotic theory can and cannot be applied to small samples.

近非平稳一阶自回归过程的渐近推断AI 解读

A first-order autoregressive process, $Y_t = \beta Y_{t - 1} + \epsilon_t$, is said to be nearly nonstationary when $\beta$ is close to one. The limiting distribution of the least-squares estimate $b_n$ for $\beta$ is studied when $Y_t$ is nearly nonstationary. By reparameterizing $\beta$ to be $1 - \gamma/n, \gamma$ being a fixed constant, it is shown that the limiting distribution of $\tau_n = (\sum^n_{t = 1}Y^2_{t - 1})^{1/2}(b_n - \beta)$ converges to $\mathscr{L}(\gamma)$…

识别时间序列中的简化结构AI 解读

This article studies how to identify hidden factors in multivariate time series process. This problem is important because, when the series are driven by a set of common factors, (a) a large number of parameters may be needed to obtain an adequate representation of the system and (b) the estimated parameters will be highly correlated. Therefore, a complex and badly defined relationship can appear when, in fact, a simpler and parsimonious model in terms of a few common…