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两状态二阶马尔可夫链的充分统计量AI 解读

Statistical inference for binomial processes with second-order Markov dependence is worked out. Sufficient statistics for the 2 2 parameters associated with the process are found and their exact joint distribution is given in a closed form. An algorithm for finding the probability of k successes in n dependent trials is developed and a simple estimation procedure is suggested and applied to a meteorological time series.

管理与经济学统计AI 解读

What is Statistics? Describing Sets of Measurements Probability Random Variables and Probability Distributions Three Useful Discrete Probability Distributions The Normal and Other Continuous Probability Distributions Sampling and Sampling Distributions Large sample Estimation Large Sample Tests of Hypotheses Inferences from Small Samples The Analysis of Variance Linear Regression and Correlation Multiple Linear Regression Elements of Time Series Analysis Forecasting Models…

移动平均过程自相关之和的界AI 解读

Limits for the sums of the complete set of autocorrelations and their absolute values are given for the moving average process.

混合自回归移动平均过程平稳性与可逆性参数约束的递归结构AI 解读

A necessary and sufficient condition for a Schur polynomial is used to develop a method for obtaining the sets of inequalities which define the boundaries of the stationary autoregressive and invertible moving average parameter domains, given any mixed process of order (p, q).

相关数据的拟合优度检验AI 解读

Goodness-of-fit tests for stationary processes are a problem of practical importance, e.g. in the analysis of electroencephalographic data. The distribution of the chi-squared statistic under the normal hypothesis is studied by simulation; power is investigated by an inverse filtering procedure for processes which can be well represented by an autoregressive-moving average model. For a second model, consisting of a Gaussian or non-Gaussian signal plus Gaussian noise, sample…

移动平均残差自回归过程及线性结构协方差矩阵的最大似然估计AI 解读

The autoregressive process with moving average residuals is a stationary process $\{y_t\}$ satisfying $\sum^p_{s = 0} \beta_sy_{t - s} = \sum^q_{j = 0} \alpha_j\nu_{t - j}$, where the sequence $\{\nu_t\}$ consists of independently identically distributed (unobservable) random variables. The distribution of $y_1,\cdots, y_T$ can be approximated by the distribution of the $T$-component vector $\mathbf{y}$ satisfying $\sum^p_{s = 0} \beta_s\mathbf{K}_s\mathbf{y} = \sum^q_{j = 0} \alpha_j\mathbf{J}_j\mathbf{v}$…

稳健估计量在相依数据中的表现AI 解读

This paper investigates the effect of serial dependence in the data on the efficiency of some robust estimators. When the observations are from a stationary process satisfying certain mixing conditions, linear combinations of order statistics and the Hodges-Lehmann estimator are shown to be asymptotically normally distributed. Gaussian processes are studied in detail and it is shown that when all the serial correlations $(\rho_n)$ are $\geqq 0$, the efficiency of the robust…

搜索多项式阶数与滞后长度时 Almon 滞后法的性质AI 解读

Researchers who use the Almon lag technique to estimate distributed lag models have a particularly difficult problem determining the correct specification of the degree of polynomial and the length of lag. The usual procedure is to search over several possible values for the degree of polynomial and the length of lag and then choose the combination that minimizes the residual variance. This article demonstrates that if one uses this search procedure, the estimated lagged…

滞后过程的时滞估计AI 解读

Recent studies of nonlinear prediction and of nonlinear filtering of stochastic processes in addition to studies of higher-order spectra have pointed out the usefulness of lag processes. Now suppose we are given observations on a filter operating on a lag process with an unknown lag. In this article we propose a way of estimating this (delay) lag. The method involves the definition of a quantity, S 2(λ; u), termed lagged coherence, which is a function of the lag u and which…

切换回归与随机系数回归模型的贝叶斯及非贝叶斯分析AI 解读

Quandt [20] analyzed the problem of discontinuous shifts in regression regimes at unknown points in the data series. We note that Quandt's statistical approach based solely on the likelihood function can be misleading, whereas the Bayesian method based on a proper prior distribution of the unknown parameters yields sensible results. However, the exact evaluation of the posterior distribution is unusually burdensome and cannot be simplified even in large samples. To avoid…

ARIMA过程预测量的一种直接基本形式AI 解读

A direct method of formulating predictors of autoregressive integrated moving average processes is given which has certain advantages over the three basic forms proposed by Box & Jenkins (1970). Some ways of making use of this representation are discussed.

随机变量序列变点推断的贝叶斯方法AI 解读

A Bayesian approach is considered to the problem of making inferences about the point in a sequence of random variables at which the underlying distribution changes. Inferences are based on the posterior probabilities of the possible change-points. Detailed analyses are given for cases in which the distributions are binomial and normal, and numerical illustrations are provided. An informal sequential procedure is also noted.

ARIMA过程预测器的一种直接基本形式AI 解读

A direct method of formulating predictors of autoregressive integrated moving average processes is given which has certain advantages over the three basic forms proposed by Box & Jenkins (1970). Some ways of making use of this representation are discussed.

参考值与估计方差对CUSUM检验平均运行长度的影响AI 解读

Summary An approximation, based on the Wiener process, is applied to Page's cusum statistic. Based on the average run length, the optimal reference value is determined analytically and shown to agree with results from studies using numerically determined run lengths. Next, we study the effect of using an estimate for variance and how this interacts with the choice of a reference value.

混合过程的次序统计量函数AI 解读

Recent results of Shorack (Ann. Math. Statist. (1972) 412-427) on the asymptotic normality of functions of order statistics are extended to stationary $\phi$-mixing processes and to a class of strong mixing processes. The results of this paper are based on the weak convergence of empirical processes relative to the metric $d_q$ as developed in Fears and Mehra (Ann. Statist. (1974) 586-596). Some remarks on trimmed and Winsorized means in the strong mixing case are also…

混合随机过程经验累积分布函数的渐近分布理论AI 解读

This paper introduces a new mixing condition for stationary processes which is weaker than $\phi$-mixing but stronger than strong mixing. Many processes arising in applications, e.g., first order autoregressive processes, obey the conditions. The main result is that the empiric cdf of a sample from such processes converges to a Gaussian process.

ARMA 模型的估计AI 解读

In estimating a vector model, $\Sigma B(j)x(n-j)=\Sigma A(j)\epsilon(n-j), A(0)=I_r, E(\epsilon(m)\epsilon(n)')=\delta_{mn}K$ it is suggested that attention be confined to cases where $g(z) =\Sigma A(j)z^j, h(z)=\Sigma B(j)z^j$ have determinants with no zeroes inside the unit circle and have $I_r$ as greatest common left divisor and where $\1brack A(p)\vdots B(q) \rbrack$ is of rank r, where p, q are the degrees of g, h, respectively. It is shown that these conditions ensure…

含滞后内生变量时一阶向量自回归误差的检验AI 解读

This paper derives an asymptotically valid test for first-order autoregressive errors. The test is derived in a simultaneous system of equations context, and allows lagged endogenous variables to be present in the model.

使用离散数据的连续时间回归AI 解读

A general continuous time distributed lag model is considered. The problem is that of estimating the parameters of the kernel when, as is often the case, the available data consist not of a continuous record but of discrete observations recorded at regular intervals of time. Fourier transformation of the model and insertion of the computable, discrete Fourier transforms of the variables produce an approximate model which is of non-linear regression type and is relatively…

This paper discusses the asymptotic behavior of the neoclassical two-sector growth model when the steady-state conditions are not fulfilled, and derives the asymptotic growth rates for cases in which Hicks neutral technical progress occurs in the investment sector, or Harrod neutral technical progress occurs at different rates in the two sectors. The last section compares the asymptotic properties of this model with the standard steady-state properties of the two-sector…

最小预测均方误差的估计AI 解读

Bloomfield (1973) and Jones (1964) have discussed the estimation of the error of prediction of a time series. Their results use the asymptotic normality of their estimates and we attempt to examine the validity of this approximation in the simplest case. We show that one can approximate the distribution of the mean square error in small-sample situations, and in consequence obtain some idea of the rate of convergence to normality.

移动平均与自回归过程协方差矩阵的近似逆AI 解读

Let $\mathbf{\Sigma}$ denote the convariance matrix of a vector $\mathbf{x} = (x_1, \cdots, x_T)'$ of $T$ successive observations from a stationary process $\{ x_t\}$ with continuous positive spectral density $f(\lambda)$. Let $\mathbf{\Gamma}$ be the $T \times T$ matrix with elements $\gamma(s, t) = (2\pi)^{-2} \int^\pi_{-\pi} e^{i\lambda (s-t)} f^{-1}(\lambda) d\lambda$. The properties of $\mathbf{\Gamma}$ considered as an approximate inverse of $\mathbf{\Sigma}$ are…

关于序列相关精确检验的一则说明AI 解读

A transformation of the OLS residual vector to achieve a desired covariance structure, proposed earlier by Durbin [3], is shown to be capable of substantially changing the OLS residual vector even when that vector already has nearly the desired covariance structure. This may explain its substantially inferior performance in Monte Carlo comparisons with the transform proposed by the Abrahamse and Koerts [1]. A new transform, involving only small alterations in Durbin's…

检验Almon滞后法的约束AI 解读

This article considers testing the restrictions imposed by Almon's approach to estimation of distributed lag relationships. The conventional likelihood ratio test procedure requires that the regression equation be estimated in unrestricted form and then subject to the Almon restrictions. An alternative test is suggested which has the advantage of requiring only that the unrestricted version be estimated. The problem of selecting the order of the polynomial is discussed and a…