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ARMA 模型新息方差的稳健区间估计AI 解读

For the autoregressive-moving average time series model, the normal theory procedure for setting confidence intervals for the error variance is not robust against nonnormality. This paper proposes three asymptotically robust techniques: they are a "standard-error" procedure, an analog of Box's simple data splitting technique, and the jackknife procedure. The large sample distribution of each of these techniques is derived.

依赖误差回归模型中稳健估计量的行为AI 解读

This paper proves the asymptotic linearity in the regression parameter of a class of linear rank statistics when errors in the regression model are strictly stationary and strongly mixing. Besides this, several other weak convergence results are proved which yield the asymptotic normality of $L$ and $M$ estimators of the regression parameter under the above dependent structure. All these results are useful in studying the effect of the above dependence on the asymptotic…

用修正 Almon 滞后逼近任意分布滞后结构AI 解读

A uniform approximation of any arbitrary lag structure can be achieved from a distributed lag formulation which is a combination of the Almon and geometric lag formulations.

估计多条平稳时间序列均值函数的经验贝叶斯方法AI 解读

An empirical Bayes procedure is considered for estimating a mean value function imbedded within a collection of N stationary time series. Two cases are considered: a mean value function that is a fixed function of time and one that is a stationary normal process. Estimators for the spectral densities are derived from prior data using an extension to time series of the usual one-way analysis of variance. These estimators are inserted into approximations for the classical…

用于出生人数预测的自回归单整移动平均模型AI 解读

Autoregressive integrated moving average (ARIMA) models are developed for birth time series, and their relationship with classical models for population growth is investigated. Parsimonious versions for the ARIMA models are obtained which retain the most important pieces of information including the length of generation of the population. The technique is applied to birth time series data for Norway.

用修正 Almon 滞后逼近任意分布滞后结构AI 解读

A uniform approximation of any arbitrary lag structure can be achieved from a distributed lag formulation which is a combination of the Almon and geometric lag formulations.

无限方差自回归过程最小二乘估计的渐近行为AI 解读

Let $y_t$ be an order $p$ autoregressive process of the form $y_t + \sum^p_{s=1} \beta_s y_{t-s} = u_t$, where the $u_t$'s are i.i.d. variables with a symmetric distribution $F$ such that $E \log^+ |u_t| < \infty$. For the Yule-Walker version $\beta_T^\ast$ of the least-squares estimate of $\beta = (\beta_1,\cdots, \beta_p)$, it is shown that $T^\frac{1}{2}(\beta_T^\ast - \beta)$ is bounded in probability.

平稳时间序列谱密度的一种估计量AI 解读

An estimator for the spectral density of a stationary time sequence is introduced. The form of the estimator is motivated by the analogy with the summability theory of Fourier series. A theorem relating to rate of consistency is proved. The effect of a mean correction is considered.

谱估计中的若干贝叶斯考虑AI 解读

This paper considers the problem of incorporating prior information about the shape and smoothness of a specrtal density into the formation of a spectral estimate. Two types of finite dimensional parameters are considered, the spectral ordinates at a specified collection of frequencies and the amount of power in each of a set of frequency bands. A method which is conditional on the .asymptotic distribution of periodogram averages is proposed. A formal procedure applies…

趋势去除方法札记：多项式回归与差分法的比较AI 解读

This paper deals with the theoretical development of some aspects of the trend removal problem. The objective is to show the difference between the two most popular trend removal methods: first differences and linear least squares regression. On the one hand, we show that if first differences are used to eliminate a linear trend, the series of residuals would be stationary but would not be white noises as they contain a first lag autocorrelation of -0.50. Furthermore, the…

多元数据的序列相关检验AI 解读

Consider a sample from a multiple time series that is stationary and Gaussian. A test is presented for independence among the multivariate observations that comprise this sample. The test is a generalization of the Kolmogorov-Smirnov test for serial correlation in a single time series. In the test, pairs of spectral-matrix estimates are compared using the largest-root statistic. The comparisons, which are tested simultaneously, are between estimates obtained from upper and…

观测序列位置参数突变的检验AI 解读

A possible alternative to the hypothesis that the sequence X 1, X 2, …, Xn are iid N(ξ, σ2) random variables is that at some unknown instant the expectation ξ shifts. The likelihood ratio test for the alternative of a location shift is studied and its distribution under the null hypothesis found. Tables of standard fractiles are given, along with asymptotic results.

经济时间序列的联系及其缺失：货币与利率AI 解读

Extensions of time-series modeling procedures of Box and Jenkins [5] reveal that numerous economic variables which are generally regarded as being strongly interrelated may with equal validity, based on recent empirical evidence, be regarded as independent or only weakly related. Differences between these results and the bulk of econometric literature are attributed to the failure of the latter to satisfactorily account for autocorrelation. Due to limitations in the data, it…

连接两条时间序列的动态回归与分布滞后模型识别AI 解读

A methodology is introduced for identifying dynamic regression or distributed lag models relating two time series. First, specification of a bivariate time-series model is discussed, and its relationship to the usual dynamic regression model is indicated. Then, a two-stage identification procedure is presented which involves fitting univariate time-series models to each series, and identifying a dynamic shock model relating the two univariate model innovation series. The…

检验回归系数稳定性的两种方法AI 解读

This paper investigates the power of two methodologies, the tests of Brown, Durbin, and Evans [2] and variable parameter regression, to detect several varieties of instability in the coefficients of a linear regression model. The study reported by Khan [10] on the stability of the demand for money is replicated with variable parameter regression, and his results are in part questioned and in part sharpened.

一阶随机差分方程相关有限样本分布的近似AI 解读

Edgeworth series expansions are obtained of the finite sample distributions of the least squares estimator and the associated t ratio test statistic in the context of a first-order noncircular stochastic difference equation. General formulae are given for these expansions up to 0(Th1) where T is the sample size and explicit representations of these in terms of the true parameters are derived up to 0(12). Some numerical comparisons of the approximations and the exact…

基于相关图大样本估计的季节性移动平均模型估计程序AI 解读

Summary In recent years considerable interest has centred on a family of moving average models proposed by Box and Jenkins (1970) for the description of time series which contain a seasonal component. A method is given in the paper for estimating the parameters of the seasonal models based on a principle due to Walker (1961) for the estimation of non-zero members of the autocorrelation function. An illustration of the method is given.

平稳双变量点过程中事件间隔的谱分析AI 解读

Summary A method is developed for analysing stationary bivariate point processes through their interval properties. The technique is based on representing the intervals as processes in continuous time. Expressions for a cross-covariance function and the corresponding cross-spectrum are given and some examples are considered. We note that use of this technique together with the device of smoothing makes computation of spectral estimates for point processes more efficient.

关于ARMA过程参数估计及Akaike、Hannan估计程序的札记AI 解读

Patterson & Thompson (1971) have described a modified maximum likelihood technique for estimating variance components in the additive mixed model. We consider the use of this method in estimating the parameters of the autoregressive-moving average model, and examine its performance relative to some established techniques for 200 simulations of a firstorder moving average process.

自回归移动平均模型分析：估计与预测AI 解读

The exact likelihood function from a set of observations generated by univariate stationary normal autoregressive–moving average models is derived. Convenient methods are developed to evaluate the exact likelihood function, specifically the inverse and determinant of the T × T covariance matrix of the observations, ΣT and the quadratic form, Z′ΣT-1Z, where Z is a T × 1 vector of observations. Computations of the least squares and the maximum likelihood estimates of the…

改进的Box–Jenkins估计量AI 解读

An easily implemented modification of the estimation procedure given by Box & Jenkins (1970) for the autoregressive–moving average time series model is suggested and some new results on covariance determinante are given. The proposed modification provides a closer approximation to the exact maximum likelihood estimators. Simulation experiments which demonstrate the effectiveness of this modification are presented.

针对自相关的随机性检验：替代方法AI 解读

The asymptotic efficiencies of the rank serial correlation and turning–points tests with respect to the serial correlation test are evaluated for first–order autocorrelation. Tests based on the periodogram of the data are suggested. A Monte Carlo study is conducted to evaluate the relative performance of likelihood derivative, distribution–free, and periodogram tests for small to moderate sample sizes with normal and nonnormal parent distributions. The serial correlation…

有限样本中 Box–Pierce 综合检验统计量的显著性水平AI 解读

In time series model building, using the methodology of Box & Jenkins (1970), it is usual to verify the adequacy of a fitted equation by computing residual autocorrelations. Following Box & Pierce (1970), an overall, or ’portmanteau’, test of fit can be based on these quantities. Recent experience suggests that surprisingly low values of the portmanteau statistic are often found. This paper shows that, even for moderately large sample sizes, the true significance levels are…

关于自回归移动平均过程的 Akaike 与 Hannan 估计程序AI 解读

We demonstrate that the estimator proposed by Akaike (1973) is exactly the first step of a Gauss-Newton algorithm applied to the exponent of a Gaussian likelihood and show its relationship to the estimator proposed by Hannan (1969).