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高阶连续时间自回归模型的估计AI 解读

A method is presented for computing maximum likelihood, or Gaussian, estimators of the structural parameters in a continuous time system of higherorder stochastic differential equations. It is argued that it is computationally efficient in the standard case of exact observations made at equally spaced intervals. Furthermore it can be applied in situations where the observations are at unequally spaced intervals, some observations are missing and/or the endogenous variables…

局部备择下高斯 ARMA 过程似然比统计量分布的渐近展开AI 解读

In this paper, we shall derive the asymptotic expansion for the distribution of the likelihood ratio criterion for a Gaussian autoregressive moving average process under a sequence of local alternative hypotheses converging to the null hypothesis with rate of convergence where n is the sample size. Explicit algebraic formulae are presented for certain special cases, including the ARMA(1,1).

联合及条件数据生成过程与向量自回归的非参数时间序列估计AI 解读

In this paper we develop nonparametric estimators of the joint time series data generating process (DGP) of ( x t , y t ) at different t -values, of conditional DGP, of the conditional mean of x t given the past values of x and y , and, more generally, the conditional mean of ( x t , y t ) given their past values (vector autoregression). We establish, among other results, the central limit theorems for these estimators under far weaker mixing conditions than those used in…

分布变化的最优检测AI 解读

Suppose one is able to observe sequentially a series of independent observations $X_1, X_2, \cdots$ such that $X_1, X_2, \cdots, X_{\nu-1}$ are iid distributed according to a known distribution $F_0$ and $X_\nu, X_{\nu+1}, \cdots$ are iid distributed according to a known distribution $F_1$. Assume that $\nu$ is unknown and the problem is to raise an alarm as soon as possible after the distribution changes from $F_0$ to $F_1$. Formally, the problem is to find a stopping rule $N$…

马尔可夫序列的非参数密度估计、预测与回归AI 解读

Let {Xi } be a stationary Markov sequence having a transition probability density function f(y | x) giving the pdf of X i +1 | (Xi = x). In this study, nonparametric density and regression techniques are employed to infer f(y | x) and m(x) = E[X i + 1 | Xi = x]. It is seen that under certain regularity and Markovian assumptions, the asymptotic convergence rate of the nonparametric estimator mn (x) to the predictor m(x) is the same as it would have been had the Xi 's been…

时间序列与系统分析及其应用AI 解读

A comprehensive, applications-oriented treatment of time series analysis. Integrates time series theory with methods of systems analysis. Clearly explains the use of ARMA forecasts and includes a complete treatment of the Box/Jenkins approach to modelling. Provides worked examples.

自回归时间序列残差方差与阶数的估计AI 解读

SUMMARY We study the bias of Yule-Walker, least squares and Burg-type estimates of the residual variance of autoregressive processes. Both simulations and theory indicate that Yule-Walker estimates are inferior to least squares and Burg-type estimates. The effect on order determination is also studied, and we extend the results on overestimation of the AIC criterion to the general multivariate case. For strongly autocorrelated processes, Yule-Walker estimates of residual…

指数边际非线性自回归时间序列的建模与残差分析AI 解读

SUMMARY An approach to modelling and residual analysis of nonlinear autoregressive time series in exponential variables is presented; the approach is illustrated by an analysis of a long series of wind velocity data which has first been detrended and then transformed into a stationary series with an exponential marginal distribution. The stationary series is modelled with a newly developed type of second order autoregressive process with random coefficients, called the…

动态线性模型的递归估计AI 解读

SUMMARY A dynamic, linear model for the analysis of univariate time series is proposed. It encompasses many of the common statistical models as special cases such as multiple regression, exponential smoothing and mixed autoregressive-moving average processes. its distinguishing feature is that it relies on only one primary source of randomness. It therefore not only provides a simpler framework for the study of dynamic models but also eliminates the need for the contentious…

非因果性的线性理论AI 解读

Abstract : Different definitions of noncausality (according to Granger, Sims, Haugh and Pierce,...) are analyzed in terms of orthogonality in the Hilbert space of square integrable variables. Conditions, when necessary, are given for their respective equivalence. Some problems of testability are mentioned. Finally noncausality is also analyzed in terms of rational expectations, extending previous results of Sims. (Author)

日度股票收益非线性的证据AI 解读

This article applies a newly developed statistical technique to time series of daily rates of return of 15 common stocks. The technique involves estimating the bispectrum of the observed time series. The bispectrum is defined as the double Fourier transform of the third-order cumulant function. If the process generating rates of return is linear with independent innovations, then the skewness of the bispectrum will be constant. The article describes a test that can detect…

基于模型的季节调整程序的变异性度量AI 解读

An algorithm is derived that develops measures of variability for the estimates of the nonseasonal component computed from a model-based seasonal adjustment procedure. The measures of variability are developed from signal extraction theory. Properties of components of the variance are developed, and the behavior of the variance is investigated for one popular time series model. The results are illustrated by using real data.

检验产出与通胀权衡中的卢卡斯假说AI 解读

A Bayesian highest-posterior interval test that accounts for heteroscedasticity and for two regimes of autocorrelation is derived to test the Lucas variance hypothesis on output-inflation trade-offs. Japanese and U.S. data show that heteroscedasticity and autocorrelation tend to influence the test results. A Bayesian procedure and Akaike's information criterion are used to determine the order or autoregressive schemes, and a join point to partition the sample is estimated by…

评 Bell 与 Hillmer《经济时间序列季节调整涉及的问题》AI 解读

Christopher A. Sims, Comment on "Issues Involved with the Seasonal Adjustment of Economic Time Series" by William R. Bell and Steven C. Hillmer, Journal of Business & Economic Statistics, Vol. 3, No. 1 (Jan., 1985), pp. 92-94

时间序列回归模型中的高效估计与预测AI 解读

For a time series regression model with correlated residuals we show how to compute efficiently the likelihood, predict future values and interpolate missing values. As an illustration we consider a regression model with autoregressive moving average residuals.

多元自回归指数模型中残差自相关的分布AI 解读

The asymptotic distribution of residual autocorrelations in multivariate autoregressive index models is derived. Generalization of the classical portmanteau statistic for checking model adequacy is discussed.

自回归移动平均过程的 Levinson–Durbin 递推AI 解读

We discuss an algorithm which allows for recursive-in-order calculation of the parameters of autoregressive-moving average processes. The proposed procedure generalizes the recursion of Levinson (1946) and Durbin (1960), which applies in the pure autoregressive case. We use ideas similar to the multivariate autoregressive case. Our results suggest how estimation procedures for autoregressive-moving average parameters, which include an automatic choice of model order, for…

时间序列的稳健检验及其在一阶自回归过程中的应用AI 解读

Robust analogues of the Wald and the Rao score statistics are presented for testing composite hypotheses in time series models involving dependent observations. Asymptotic efficiency and empirical power comparisons using moderate size samples are given for first-order autoregressive processes. Our method of robustifying the estimating equation gives a simple and unified approach which is useful in a large class of problems including regression with dependent errors, and…

样本时空自协方差与自相关函数的矩AI 解读

Pfeifer & Deutsch (1981) have derived expressions for the means and variances of the sampled autocovariances and autocorrelations, in the case of a white-noise space-time process. This note shows how their work can be extended to general space-time autoregressive moving average processes. The results are useful for testing the significance of observed space-time autocorrelations, given a hypothesized space-time process.

平稳单变量时间序列新息方差的频域估计AI 解读

The innovation variance σ2 of a linear stochastic time series model can be estimated using periodogram ordinates. However, since the periodogram ordinates as estimators of the corresponding spectrum ordinates can show appreciable small-sample bias, it is believed that the estimator of σ2 is biased. One way of reducing the small-sample bias in the periodogram ordinates is by tapering. In this paper an estimator of σ2 based on tapered time series is defined and evaluated…

典型分析在时间序列模型识别中的应用AI 解读

The second-order moment structure of time series models is used to derive a canonical analysis in time series modelling. Consistency properties of certain canonical correlations and the corresponding eigenvectors are shown. Based on these properties, a canonical correlation approach for tentative order determination in building autoregressive-moving average models is proposed. This approach can handle directly nonstationary as well as stationary processes and it also…

自回归模型中的正态性检验AI 解读

It is shown that any test of normality computed from autoregressive residuals has the same limiting null distribution as for the standard case of independent, identically distributed observations with estimated parameters. Some numerical results are given to indicate that this approximation is acceptable for sample size 20 in first- and second-order models. Limited numerical results are also given to explore the effect of incorrectly specifying the order.

移动平均过程创新表示的收敛速度AI 解读

SUMMARY A moving average process of order q can be written as a linear combination of the (q+ 1) most recent innovations. We show that if the moving average polynomial has roots on the unit circle, then the coefficients of the innovations tend to the true moving average coefficients, the difference between the two being O(l/t), where t is the number of observations we consider. The results are extended to mixed autoregressive moving average models and multivariate models.

扩散过程及其在布朗运动漂移变化检测中的应用AI 解读

The classical cusum procedure of Page (1954) and a competitor suggested independently by Shiryayev (1963) and Roberts (1966) for detecting a change in distribution are systematically compared, when the change point v = 0 and when v is large. The specific model considered is that of detecting a change in the drift of Brownian motion, for which diffusion theory yields certain explicit results that seem impossible to compute in discrete time. The Shiryayev-Roberts process turns…