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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…

一类特定非线性时间序列系统的识别AI 解读

A nonlinear time series system is considered. The system has the property that the output series corresponding to a given input series is the sum of a noise series and the result of applying in turn the operations of linear filtering, instantaneous functional composition and linear filtering to the input series. Given a stretch of Gaussian input series and corresponding output series, estimates are constructed of the transfer functions of the linear filters, up to constant…

检验多个时间序列是否共享周期AI 解读

Tests are discussed for detecting the presence of common periodicities in the components of a multiple time series. Distributional results are obtained for the case of white noise, independent, normal series. These are extended, first to the case of normal linear series with specified spectra and then to the case of estimated spectra. These results are then discussed in the context of correlated series. The tests are applied to several sets of data.

基于样本自相关的一阶移动平均模型估计AI 解读

For the first order moving average we consider a proposal by Walker (Biometrika, 1961) to use $k$ sample autocorrelations $(1 < k < T, T$ sample size), to estimate the first autocorrelation of the model, and hence its basic parameter. When $k = k_T \rightarrow \infty$ as $T \rightarrow \infty$, the estimator is proved consistent and asymptotically normal and efficient, the latter provided $k_T$ dominates $\log T$ and is dominated by $T^\frac{1}{2}$. An alternative form of…

序列相关检验的一项稳健性性质AI 解读

This paper shows that the UMP or UMPU tests for serial correlation, derived under the assumption of a normal distribution, are quite robust against departure from normality. In fact, the tests are still UMP or UMPU in much broader classes of distributions and the null distributions remain unchanged under these classes. The results will be applied to a linear model.

对齐秩次过程的两端固定维纳过程近似及应用AI 解读

For independent random variables distributed symmetrically around an unknown location parameter, aligned rank order statistics are constructed by using an estimator of the location parameter based on suitable rank statistics. The sequence of these aligned rank order statistics is then incorporated in the construction of suitable stochastic processes which converge weakly to some Gaussian functions, and, in particular, to tied-down Wiener processes in the most typical cases.…

极端样本量或较多回归变量下的 Durbin–Watson 序列相关检验AI 解读

Recent studies by Durbin and Watson [5], L'Esperance and Taylor [10], Koerts and Abrahamse [8], Tillman [15], Vinod [16], Savin and White [14] and others have shown increasing interest in the test of autocorrelation based on the d statistic proposed by Durbin and Watson [3 and 4]. The focus of these papers has been the computation of the exact distribution of d and the power of the test based on d. The exact distribution of d has been developed by Imhof [7] and Pan Jie-Jian…

正自相关一阶自回归过程中 σ² 最小二乘估计量的偏差界AI 解读

H. Neudecker, Bounds for the Bias of the Least Squares Estimator of @s^2 in the Case of a First-Order Autoregressive Process (Positive Autocorrelation), Econometrica, Vol. 45, No. 8 (Nov., 1977), p. 2006

向量移动平均过程的精确与近似最大似然估计AI 解读

Summary This paper derives the exact likelihood function for the vector moving average process; the method used is a generalization of that adopted by Box and Jenkins (1970, Appendix A7.4) for the univariate process. Tunnicliffe Wilson (1973) has previously considered the estimation of parameters in multivariate time series models, and his procedure for moving averages is shown to be an approximation to maximum likelihood. A procedure for the computation of the exact…

Wiener–Kolmogorov 预测器的渐近性质（二）AI 解读

Summary The asymptotic properties of the autoregressive estimates a (T)(u) obtained using the fles method (Bhansali, 1974) suggest that, in practice, a decision on truncating the a (T)(u) at u = p, say, will need to be taken. This truncated sequence of the auto-regressive estimates is used to form alternative estimates of the linear predictor, the autoregressive spectral density function and the innovation variance. Some of the asymptotic properties of these estimates are…

平稳点过程中事件间隔的连续时间谱分析AI 解读

Summary The sequence of intervals between events in a stationary point process is considered as a process in continuous time. Expressions are given for a covariance function and the corresponding spectrum. Some examples are given to illustrate that the properties of the intervals as a process in continuous time are not the same as those of the intervals as a sequence. The methods developed are used to analyse a process consisting of times of R peaks in an electrocardiogram…

自回归移动平均模型的时域与频域估计AI 解读

The autoregressive moving average model is a stationary stochastic process $\{y_t\}$ satisfying $\sum^p_{k=0} \beta_ky_{t-k} = \sum^q_{g=0} \alpha_g\nu_{t-g}$, where the (unobservable) process $\{v_t\}$ consists of independently identically distributed random variables. The coefficients in this equation and the variance of $v_t$ are to be estimated from an observed sequence $y_1, \cdots, y_T$. To apply the method of maximum likelihood under normality the model is modified…

检测时间序列模型参数变化的序贯程序AI 解读

Procedures are proposed for monitoring forecast errors in order to detect changes in a time-series model. These procedures are based on likelihood ratio statistics which consist of cumulative sums. An extension of Page's method is presented which tests for changes in the parameter values of autoregressive integrated moving average (arima) models. The distributional properties of the statistics are approximated under the assumption that the series follows an integrated…

多重时间序列分析与计量经济模型的最终形式AI 解读

Univariate autoregressive moving average models for the endogenous variables of a dynamic simultaneous equations system can be interpreted as a form of solution of that system. This paper considers the interrelationships between the various representations of the system, and develops joint estimation and model selection procedures for the multiple time series model which arises as a multivariate representation of the individual autoregressive moving average models. A test of…

稳定分布滞后的存在性AI 解读

This paper attempts to determine conditions under which distributed lag analysis is appropriate. Results indicate that lag functions are stable and linear under fairly general (but constant) objective criteria and decision constraints as long as the underlying economic environment is characterized by a stationary Gauss-Markov process, and observed environmental variables are Gaussian perturbations of that process. The results appear particularly useful for specifying the lag…

积分移动平均过程样本自协方差函数的渐近行为AI 解读

In this paper, we derive the first two asymptotic moments of the autooovariance function of a time series generated from an integrated moving average process of order (1,1). In particular, it is found that the expected value of the sample autocovariance at lag k is approximately proportional to the length of the series. This result suggests a method of checking whether a nonstationary time series can be described by an integrated moving average process of order (1,1) and its…

多变量时间序列的典型分析AI 解读

This paper proposes a canonical transformation of a k-dimensional stationary autoregressive process. The components of the transformed process are ordered from least to most predictable. The least predictable components are often nearly white noise which can reflect stable contemporaneous relationships among the original variables. The most predictable can be nearly nonstationary representing the dynamic growth characteristic of the series. The method is illustrated with a…

有理谱密度连续时间高斯平稳过程的参数估计AI 解读

The estimation of parameters in a continuous time Gaussian stationary process with zero mean and rational spectral density is achieved by an adaptation of the maximum likelihood method. It consists of minimizing something analogous to the sum of the squares of the residuals in the discrete case. The estimate is shown to be asymptotically normal and efficient. A simple computational procedure is also given to construct the estimate.

高斯移动平均过程最大似然估计量的直接表示AI 解读

It has been known for several years that the maTin-mm likelihood estimator of the parameters of a discrete Gaussian moving average process is efficient and asymptotically normally distributed. A procedure is described in this paper which gives an expression for the maximum likelihood estimator of each parameter as a linear combination of a suitable large set of sample serial correlations. An illustration of this procedure is given.

高斯移动平均过程最大似然估计量的直接表示AI 解读

It has been known for several years that the maTin-mm likelihood estimator of the parameters of a discrete Gaussian moving average process is efficient and asymptotically normally distributed. A procedure is described in this paper which gives an expression for the maximum likelihood estimator of each parameter as a linear combination of a suitable large set of sample serial correlations. An illustration of this procedure is given.

多元时间序列的典型分析AI 解读

This paper proposes a canonical transformation of a k-dimensional stationary autoregressive process. The components of the transformed process are ordered from least to most predictable. The least predictable components are often nearly white noise which can reflect stable contemporaneous relationships among the original variables. The most predictable can be nearly nonstationary representing the dynamic growth characteristic of the series. The method is illustrated with a…

一阶积分移动平均过程样本自协方差函数的渐近行为AI 解读

In this paper, we derive the first two asymptotic moments of the autooovariance function of a time series generated from an integrated moving average process of order (1,1). In particular, it is found that the expected value of the sample autocovariance at lag k is approximately proportional to the length of the series. This result suggests a method of checking whether a nonstationary time series can be described by an integrated moving average process of order (1,1) and its…

快速傅里叶变换谱估计量AI 解读

Summary This note shows how the Fast Fourier Transform (FFT) spectral estimator can be approximately written as an average of periodograms constructed at points 2πk/N removed, where k is an integer and N is the number of observations; it also shows the properties of this approximation.

时间序列的预测函数与均值估计函数AI 解读

Let $T \subseteqq I$ be sets of real numbers. Let $\{Y(t): t \in I\}$ be a real time series whose mean is an unknown element of a known class of functions on $I$ and whose covariance kernel $k$ is assumed known. For each fixed $s \in I, Y(s)$ is predicted by a minimum mean square error unbiased linear predictor $\hat{Y}(s)$ based on $\{Y(t): t \in T\}$. If $\hat{y}(s)$ is the evaluation of $\hat{Y}(s)$ given a set of observations $\{Y(t) = g(t): t \in T\}$, then the function…