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周期自回归的若干结果AI 解读

Several properties of a periodic autoregressive process {xs} are examined by considering a related stationary multivariate autoregressive process. The properties of interest include: the representation of xs as an infinite linear combination of independent, periodically distributed random variables, constraints on the parameters which permit such a representation, the covariance and spectral properties of {xs}, and the asymptotic behaviour of cumulative sums of {xs} and of…

贝叶斯稳态预测模型的推广AI 解读

Summary The Bayesian Steady Forecasting model is generalized to a very wide class of processes other than the normal by defining the time series on the decision space. Examples of such processes are presented including a Beta-Binomial process, a Poisson-Gamma process and a Student-t sample distribution steady model. Simple updating relations are given for most of the processes discussed.

功率谱的稳健估计AI 解读

Summary Outliers in time series can play havoc with conventional power spectrum density estimation techniques when the spectrum features of interest consist of one or more peaks of relatively low amplitude. Furthermore, the outliers need not be large relative to the scale of the process in order to have considerable impact on the estimate; they only need to be large relative to the scale of the innovations process. Following a tutorial review of the central notions of…

基于不精确观测的时间序列预测函数AI 解读

Let $T \subseteq I$ be sets of real numbers. Let $\{Y(t): t\in I\}$ be a real time series whose covariance kernel is assumed known and positive definite. The mean is assumed either to be known or to be an unknown member of a known class of functions on $I$. 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 that the sample path…

向量线性时间序列模型的渐近估计与假设检验结果AI 解读

For a general vector linear time series model we prove the strong consistency and asymptotic normality of parameter estimates obtained by maximizing a particular time domain approximation to a Gaussian likelihood, although we do not assume that the observations are necessarily normally distributed. To solve the normal equations we set up a constrained Gauss-Newton iteration and obtain the properties of the iterates when the sample size is large. In particular we show that…

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正态总体位置突变的似然比检验AI 解读

An alternative to the hypothesis that the sequence X 1 ···, X n are independent and identically distributed normal random variables, with mean μ and variance σ2, is that the location parameter μ shifts at some unknown instant. The null distributions of likelihood ratio test statistics are given by Hawkins (1977) for the two cases of known and unknown σ2. Unfortunately, the null distribution for unknown σ2 obtained in that article is incorrect. In this article the correct…

历史时间序列的Karhunen–Loève分析：牙买加种植园出生数据应用AI 解读

A comparison of two spectral analysis procedures is presented: the frequency domain (Fourier transform) model and the Karhunen-Loève time domain model. Both models are used in turn to analyze a plantation births series during the period 1880–1938. The principal components model can be adapted as the discrete analogue of the Karhunen-Loève stochastic integral equation in order to decompose a single time series into trend, cycle, and seasonality. The results indicate that the…

非线性时间序列模型滞后结构的估计AI 解读

Suppose that the time series {Y(t)} is the output of a linear plus quadratic filter observed with additive noise. The relationship is a second-order approximation to a nonlinear distributed lag model. Assume that the input to the filter {X(t)} is a stationary Gaussian process. This article presents a relatively simple procedure for determining the values of the parameters of the quadratic filter by using the sample cross bispectrum between the two series. The asymptotic…

具有单位根的自回归时间序列估计量分布AI 解读

Let n observations Y 1, Y 2, ···, Y n be generated by the model Y t = pY t−1 + e t , where Y 0 is a fixed constant and {e t } t-1 n is a sequence of independent normal random variables with mean 0 and variance σ2. Properties of the regression estimator of p are obtained under the assumption that p = ±1. Representations for the limit distributions of the estimator of p and of the regression t test are derived. The estimator of p and the regression t test furnish methods of…

马尔可夫转移函数的非参数估计AI 解读

Let $\{X_n\}$ be a Markov chain having a stationary transition function and assume that the state set is an arbitrary set in a Euclidean space. The state transition law of the chain is given by a function $F(y|x) = P\lbrack X_{n+1} \leqslant y|X_n = x\rbrack$, which is assumed defined and continuous for all $x$. In this paper we give a statistical procedure for determining a function $F_n(y\mid x)$ on the basis of the sample $\{X_j\}^n_{j=1}, n = 1, 2,\cdots,$ and prove that…

线性过程估计的高阶效率AI 解读

Estimation as a reduction of data is usually accompanied by some loss of information. This paper theoretically compares asymptotically efficient estimation methods for parameters in Gaussian linear processes. By means of the concept of "asymptotic information loss" suitably defined, estimates equivalent to the order of $N^{-\frac{1}{2}}$ are differentiated. This problem was studied by C. R. Rao for multinomial distributions and by K. Takeuchi for the exponential family of…

线性时不变系统的分布滞后近似AI 解读

An infinite distributed lag system is approximated by a truncated one, which can be consistently estimated. We investigate the rate at which the parameter space in the approximate model can be increased as sample size increases, in such a way that these estimates will provide consistent estimates of the underlying system.

平稳向量时间序列参数估计的中心极限定理及含噪信号应用AI 解读

A general finite parameter model for stationary ergodic nondeterministic vector time series is considered. A central limit theorem for parameter estimates, obtained by maximising frequency domain approximations to the Gaussian likelihood, is established. The treatment given extends the central limit theorem of Dunsmuir and Hannan in that the innovations covariance matrix and the linear transfer function need not be separately parameterised. Models for a stationary vector…

动态模型中最小二乘估计的强一致性AI 解读

The least squares estimate of the parameter matrix $\mathbf{B}$ in the model $\mathbf{y}_t = \mathbf{B'x}_t + \mathbf{u}_t$, where $\mathbf{u}_t$ is an $m$-component vector of unobservable disturbances and $x_t$ is a $p$-component vector, converges to $\mathbf{B}$ with probability one under certain conditions on the behavior of $x_t$ and $\mathbf{u}_t$. When $\mathbf{x}_t$ is stochastic and the conditional expectation of $\mathbf{u}_t$ given $\mathbf{x}_s$ for $s \leqslant t$…

时间序列模型设定的综合检验功效研究AI 解读

In this note we present simulation evidence on the power of a portmanteau statistic used to detect time series model misspecification. This is related to the loss in forecasting accuracy resulting from use of the incorrectly specified model. Our conclusion is that the statistic achieves a high level of success only when sample size is large.

ARMA 过程最大似然估计量的强一致性AI 解读

The strong consistency of the maximum likelihood parameter estimation method is established for multivariate Gaussian stochastic processes possessing autoregressive moving average (ARMA) representations. The demonstration in this paper exploits the ergodic theorem together with results from linear prediction theory.

连续时间平稳马尔可夫过程的密度估计AI 解读

This paper deals with a general class of recursive estimates of the density function in a continuous-time stationary Markov process. Under the condition $G_2$ of Rosenblatt sufficient conditions for almost sure convergence of such estimates are given.

一阶自回归参数的稳健估计AI 解读

Outliers in time series can adversely affect both the least squares estimates and ordinary M-estimates of autoregressive parameters. Attention is focused here on obtaining robust estimates of the parameter for a first-order autoregressive time series xk The observations are y k = z k + v k, and two models are considered: Model IO, with v k ≡ 0, x k possibly non-Gaussian, and Model AO, with v k nonzero and possibly quite large a small fraction of the time, and x k Gaussian. A…

自回归误差回归模型多步预测的渐近均方误差AI 解读

The asymptotic prediction mean squared error is derived for the regression model with autoregressive errors. The results cover the cases where future values of the exogenous variables are known, where some exogenous variables are predicted from autoregressive processes, and where lagged endogenous variables are included in the model. A result is also obtained for the predictor that ignores autocorrelation of the errors and is based on ordinary least squares (OLS) estimates…

自相关误差下非线性最小二乘与最大似然估计的小样本性质AI 解读

Rao and Griliches (1969) compared several methods of parameter estimation in models having autocorrelated errors. They concluded that nonlinear least squares estimators were not superior to two-stage linear estimators. This study partially replicates the Rao and Griliches Monte Carlo simulation and, in addition, examines the maximum likelihood estimator as a possible competitor. The simulation results are not consistent with those of Rao and Griliches; the small-sample…

自回归误差回归模型多步预测的渐近均方误差AI 解读

The asymptotic prediction mean squared error is derived for the regression model with autoregressive errors. The results cover the cases where future values of the exogenous variables are known, where some exogenous variables are predicted from autoregressive processes, and where lagged endogenous variables are included in the model. A result is also obtained for the predictor that ignores autocorrelation of the errors and is based on ordinary least squares (OLS) estimates…

高斯向量过程自相关参数的估计AI 解读

Summary A procedure based on differences is used to yield an estimator of an unknown parameter occurring in the autocorrelation structure of a stationary Gaussian vector process. Various properties of the estimator including its existence, consistency and asymptotic normality are shown. Necessary and sufficient conditions are given for the estimator to be efficient.

自回归模型阶数的确定AI 解读

Summary It is shown that a strongly consistent estimation procedure for the order of an autoregression can be based on the law of the iterated logarithm for the partial autocorrelations. As compared to other strongly consistent procedures this procedure will underestimate the order to a lesser degree.