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非稳定自回归误差下时间序列回归估计量极限分布的一般方法AI 解读

The authors consider the time series regression model where the error term follows a nonstable autoregressive process and present a general approach for delivering the limiting distribution of a normalized estimator for the autoregressive parameter. The present approach is quite straightforward and leads them to an accurate evaluation of the distribution function, unlike the other approaches suggested in the literature. The authors' methodology is illustrated and percent…

非线性理性预期模型的求解：利率的随机均衡模型AI 解读

The authors introduce, in this paper, a method for solving nonlinear quadratic Pareto problems. The method provides the analyst with a set of time series realizations for the variables in the economy. By obtaining a large number of these realizations, they can approximate the empirical distributions of a variety of statistics, which will give a detailed description of the model's properties. In particular, those statistics can be compared with the similar ones obtained from…

基于残差的协整检验的渐近性质AI 解读

This paper develops an asymptotic theory for residual based tests for cointegration. These tests involve procedures that are designed to detect the presence of a unit root in the residuals of (cointegrating) regressions among the levels of economic time series. Attention is given to the augmented Dickey-Fuller (ADF) test that is recommended by Engle-Granger (1987) and the Z(a) and Z(t) unit root tests recently proposed by Phillips (1987). Two new tests are also introduced,…

含部分单位根的线性时间序列模型中的推断AI 解读

This paper considers estimation and hypothesis testing in linear time series when some or all of the variables have (possibly multiple) unit roots. The motivating example is a vector autoregression with some unit roots in the companion matrix, which might include polynomials in time as regressors. Parameters that can be written as coefficients on mean zero, nonintegrated regressors have jointly normal asymptotic distribution, converging at the rate of T(superscript…

This paper studies the asymptotic properties of instrumental variable (IV) estimates of multivariate cointegrating regressions and allows for deterministic and stochastic regressors as well as quite general deterministic processes in the data-generating mechanism. It is found that IV regressions are consistent even when the instruments are stochastically independent of the regressors. This phenomenon, which contrasts with traditional theory for stationary time series, is a…

利用总量时间序列估计跨期替代模型AI 解读

In conducting empirical investigations of the permanent income model of consumption and the consumption-based intertemporal asset pricing model, various authors have imposed restrictions on the nature of the substitutability of consumption across goods and over time.In this paper we suggest a method for testing some of these restrictions and present empirical results using this approach.Our empirical analyses focuses on three questions: (1) Can the services from durable and…

随机水平突变时间序列模型、ARIMA 近似与水平突变检测AI 解读

The main purpose of this article is to assess the performance of autoregressive integrated moving average (ARIMA) models when occasional level shifts occur in the time series under study. A random level-shift time series model that allows the level of the process to change occasionally is introduced. Between two consecutive changes, the process behaves like the usual autoregressive moving average (ARMA) process. In practice, a series generated from a random level-shift ARMA…

似不相关时间序列方程与同质性检验AI 解读

A multivariate structural time series model made up of unobserved components such as trends and seasonals is formulated. A homogeneous system, in which any linear combination of the observations follows the same time series process, is shown to correspond to a multivariate structural model in which the covariance matrices of the disturbances are proportional. A homogeneous model is considerably easier to estimate than the more general model and a score test of homogeneity…

误差修正模型的解释：部分调整、前瞻行为与国际动态货币需求AI 解读

Abstract An error correction model is derived from a stochastic dynamic programming problem incorporating rational expectations. A parametric restriction is derived that allows a test for the theoretical proposition that the optimal strategy behind the error correction from entails the failure to asymptotically close the gap between the choice variable and the growing target. This is accomplished by nesting a partial adjustment model with forward‐looking expectations within…

不等间隔纵向数据中的序列相关AI 解读

Serial correlation in the within subject error structure in longitudinal data with unequally spaced observations is modelled using continuous time autoregressive moving averages. The models considered have both fixed and random effects in addition to serially correlated within subject errors. Two approaches are presented for calculating the exact likelihood for a model when the errors are Gaussian. The first calculates the covariance matrices for each subject for assumed…

小样本自回归模型选择中 Kullback–Leibler 信息的改进估计AI 解读

A new estimator, AICl, of the Kuliback-Leibler information is proposed for Gaussian autoregressive time series model selection. The expected information is decomposed into two terms, the first being estimated without bias. The second term is a penalty function which depends only weakly on the model parameters, and hence can be tabulated by simulation from a white noise process. The estimated information, AICl, is very nearly unbiased when the model is either correct or…

时间序列统计带宽的估计AI 解读

In many time series and signal processing applications such as spectral estimation, signal-to-noise estimation and frequency response estimation it is imperative to have a good estimate of the bandwidth of the time series. In many scientific applications deconvolution is carried out over the signal-dominated part of the spectrum resulting in a spectrum which is dominantly unimodal, and hence a technique like that used for smoothing windows can be used to define the…

时间序列情形下相关积分的行为AI 解读

The behaviour of the correlation integral is well known when applied to simple chaotic regimes and to pure random noise. The asymptotic behaviour of a chaotic system is represented by an infinite set of points called an attractor, the dimension of which can be estimated by the correlation integral. Essentially, the correlation integral of a time series is a normalized count of the number of close pairs of points of the series lying in phase space. We examine the expected…

非线性时间序列的识别：一阶刻画与阶数确定AI 解读

We study the possibility of identifying nonlinear time series using nonparametric estimates of the conditional mean and conditional variance. It is shown that most nonlinear models satisfy the assumptions needed to apply nonparametric asymptotic theory. Sampling variations of the conditional quantities are studied by simulation and explained by asymptotic arguments for a number of first-order nonlinear autoregressive processes. The conditional mean and variance can be used…

谐波回归模型参数估计的渐近分布AI 解读

The harmonic regression signal plus noise model is used extensively in applied statistics. This note establishes the joint asymptotic normality of the generalized least squares estimates of the harmonic regression parameters and gives an explicit exprètaion for the limiting covanance matrix. It also clarifies misstatements concerning the model's properties that have appeared in the literature.

多个变点的极大似然估计AI 解读

Maximum likelihood estimation of the locations of changes in sequences of independent categorical random variables when there are known lower bounds on the lengths of the sub-sequences between the change points is discussed. A method is developed which finds one of the maximum likelihood solutions. The problem of estimating the number of changed segments is discussed and some numerical results about the precision of the estimates of the locations of changes are presented.…

ARMA模型的阶数识别AI 解读

We present a new powerful method for determining the order of ARMA (p, q) models having small sets of observations. The procedure is based on an autoregressive order determination criterion and on linear estimation methods. Simulated data are used to demonstrate the capabilities of the approach.

均值变化极大似然检验的渐近分布AI 解读

For the maximum likelihood tests for a change in the mean of independent random variables, it is proved that the limit distribution is a double exponential, i.e. Gumbel, distribution. Our results also explain why the maximum likelihood methods are very powerful on the tails.

伯努利变量序列中变化区段的定位AI 解读

The theory underlying inferences about a single change point in a sequence of independent Bernoulli variables is extended to the two change points problem where the distance between the two change points is known, namely a changed segment. Both null and nonnull distributions of the log likelihood ratio for testing the hypothesis that there is no changed segment against the alternative that there is one of specified length are derived using recurrence equations. The…

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爆炸性自回归中残差经验过程的弱收敛AI 解读

This paper proves the weak convergence of the residual empirical process in an explosive autoregression model to the Brownian bridge. As an application the Kolmogorov-Smirnov goodness-of-fit test for testing that the errors have a specified distribution is shown to be asymptotically distribution-free.

若干长程依赖序列的经验过程及其在U统计量中的应用AI 解读

Let $(X_j)^\infty_{j = 1}$ be a stationary, mean-zero Gaussian process with covariances $r(k) = EX_{k + 1} X_1$ satisfying $r(0) = 1$ and $r(k) = k^{-D}L(k)$ where $D$ is small and $L$ is slowly varying at infinity. Consider the two-parameter empirical process for $G(X_j),$ $\bigg\{F_N(x, t) = \frac{1}{N} \sum^{\lbrack Nt \rbrack}_{j = 1} \lbrack 1\{G(X_j) \leq x\} - P(G(X_1) \leq x) \rbrack; // -\infty < x < + \infty, 0 \leq t \leq 1\bigg\},$ where $G$ is any measurable…

爆炸性自回归过程的 BootstrapAI 解读

Asymptotic validity of the bootstrap is established for the least squares estimate of the parameter of an explosive first-order autoregressive process. It is noted that nonnormal limit distributions are obtained for both the traditional and the bootstrap estimates. The theoretical bootstrap validity results are supported by appropriate simulation.

自相似过程的有效参数估计AI 解读

Asymptotic normality of the maximum likelihood estimator for the parameters of a long range dependent Gaussian process is proved. Furthermore, the limit of the Fisher information matrix is derived for such processes which implies efficiency of the estimator and of an approximate maximum likelihood estimator studied by Fox and Taqqu. The results are derived by using asymptotic properties of Toeplitz matrices and an equicontinuity property of quadratic forms.