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AR(1) 模型分析中的平坦先验与无知先验AI 解读

Abstract The paper compares, by a Monte‐Carlo study based on an AR(1) model, the performance of the flat prior and the ignorance prior suggested by Phillips. It argues that the ignorance prior gives heavy weight to values of the autoregressive parameter p higher than 1, and hence distorts the sample evidence as summarized in the likelihood function. It yields bimodal posterior distributions, with the second mode at p higher than 1, even when the true value of p is…

批评批评者：随机趋势的客观贝叶斯分析AI 解读

Abstract In two recent articles, Sims (1988) and Sims and Uhlig (1988/1991) question the value of much of the ongoing literature on unit roots and stochastic trends. They characterize the seeds of this literature as ‘sterile ideas’, the application of nonstationary limit theory as ‘wrongheaded and unenlightening’, and the use of classical methods of inference as ‘unreasonable’ and ‘logically unsound’. They advocate in place of classical methods an explicit Bayesian approach…

单位根贝叶斯推断的不同路径AI 解读

Abstract This paper is a comment on P. C. B. Phillips, ‘To criticise the critics: an objective Bayesian analysis of stochastic trends’ [Phillips, (1991)]. Departing from the likelihood of an univariate autoregressive model different routes that lead to a posterior odds analysis of the unit root hypothesis are explored, where the differences in routes are due to the different choices of the prior. Improper priors like the uniform and the Jeffreys prior are less suited for…

线性估计方程的刀切法：渐近理论与随机过程应用AI 解读

SUMMARY Let (X 1, X 2, ..., Xn) be a vector of (possibly dependent) random variables having distribution F(X, θ). Let θn be an estimating equation for θ, e.g. the score function or the maximum pseudolikelihood estimating equation in spatial processes. Let θn be the estimator obtained from G such that θn → θ0 in probability and n1/2(θn−θ0)→N(0,V) in distribution. In many situations, it is difficult to derive an analytical expression for V, e.g. for maximum pseudolikelihood…

无需固定模型集上界的自回归阶数递归估计AI 解读

SUMMARY In a recent paper, we proved that Rissanen's 'predictive least squares' (PLS) criterion for model selection provides strongly consistent order estimates for autoregressive (AR) processes, i.e. the PLS order estimate p̂(n) based on the first n data points converges almost surely to p 0 as n → ∞ when the data are generated by an AR process of order p 0, and p 0 is known to belong to the finite model set M = {1, 2, ..., K}, K < ∞. In the present paper we strengthen this…

具有时间序列误差的核回归估计AI 解读

SUMMARY Suppose that data y 1, ..., yn are observed according to the model yi=f((i−12)/n)+ϵi,i=1,…,n, where f is a smooth function and {ϵ1,…,ϵn} is a sample from a zero-mean, covariance stationary time series. The problem of objectively choosing the bandwidth of a kernel estimate for f is addressed. It is shown both theoretically and by simulation that cross-validation produces extremely rough kernel estimates when the data are sufficiently positively correlated. This makes…

单调增益、一阶自相关与过零率AI 解读

The effect of a linear filter with monotone gain on the first-order autocorrelation of a weakly stationary time series is discussed. When the gain is monotone increasing, the first-order autocorrelation cannot increase. Otherwise, when the gain is monotone decreasing, the correlation cannot decrease. Further, when the gain is strictly monotone, the first-order autocorrelation is unchanged if and only if the process is a pure sinusoid with probability 1. Under the Gaussian…

依赖数据下的尾指数估计AI 解读

Let $X_1, X_2,\ldots$ be possibly dependent random variables having the same marginal distribution. Consider the situation where $\bar{F}(x) := P\lbrack X_1 > x\rbrack$ is regularly varying at $\infty$ with an unknown index $- \alpha < 0$ which is to be estimated. In the i.i.d. setting, it is well known that Hill's estimator is consistent for $\alpha^{-1}$, and is asymptotically normally distributed. It is the purpose of this paper to demonstrate that such properties of…

若干非参数变点估计量的渐近行为AI 解读

Consider a sequence $X_1, X_2,\ldots, X_n$ of independent random variables, where $X_1, X_2,\ldots, X_{n\theta}$ have distribution $P,$ and $X_{n\theta + 1}, X_{n\theta + 2},\ldots, X_n$ have distribution $Q$. The change-point $\theta \in (0,1)$ is an unknown parameter to be estimated, and $P$ and $Q$ are two unknown probability distributions. The nonparametric estimators of Darkhovskh and Carlstein are imbedded in a more general framework, where random seminorms are applied…

未知阶自回归过程系数最小二乘估计量的矩收敛AI 解读

Given a realization of $T$ consecutive observations of a stationary autoregressive process of unknown, possibly infinite, order $m$, it is assumed that a process of arbitrary finite order $p$ is fitted by least squares. Under appropriate conditions it is known that the estimators of the autoregressive coefficients are asymptotically normal. The question considered here is whether the moments of the (scaled) estimators converge, as $T \rightarrow \infty$, to the moments of…

非线性约束下线性时间序列模型的参数估计AI 解读

Least squares estimators of the parameters of a linear time series model, where the parameters are constrained by a set of nonlinear restrictions, are studied. The model may contain lags of the dependent variable as regressors and the sums of squares of the explanatory variables may grow at different rates as the sample size increases. The estimation procedures can be applied to a regression model with an error process that satisfies either a stationary or a nonstationary…

近非平稳 AR(1) 过程的高斯似然估计AI 解读

An asymptotic analysis is presented for estimation in the three-parameter first-order autoregressive model, where the parameters are the mean, autoregressive coefficient and variance of the shocks. The nearly nonstationary asymptotic model is considered wherein the autoregressive coefficient tends to 1 as sample size tends to $\infty$. Three different estimators are considered: the exact Gaussian maximum likelihood estimator, the conditional maximum likelihood or least…

近非平稳自回归时间序列的最大似然型估计AI 解读

The nearly nonstationary first-order autoregression is a sequence of autoregressive processes $y_n(k + 1) = \phi_ny_n(k) + \varepsilon(k + 1), 0 \leq k \leq n$, where the $\varepsilon(k)$'s are iid mean zero shocks and the autoregressive coefficient $\phi_n = 1 - \beta/n$ for some $\beta > 0$, so that $\phi_n \rightarrow 1$ as $n \rightarrow \infty$. We consider a class of maximum likelihood type estimators called $M$ estimators, which are not necessarily robust. The…

缓慢衰减相关下的正态性检验与干扰参数AI 解读

Slowly decaying serial correlations can cause goodness-of-fit tests for a distribution to reject the null hypothesis with probability tending to one with increasing sample size. When the null distribution is completely specified (simple null hypothesis) the problem is actually worse than for the case where there are nuisance parameters to be estimated (composite null hypothesis). In particular, we consider here testing normality. We discuss limit theorems and propose…

缓慢衰减序列相关下高斯及相关过程的位置 M 估计AI 解读

We investigate the behavior of M estimators of the location parameter for stochastic processes with long-range dependence. The processes considered are Gaussian or one-dimensional transformations of Gaussian processes. It turns out that, up to a constant, all M estimators are asymptotically equivalent to the arithmetic mean. For Gaussian processes this constant is always equal to one, independently of the ψ function. In view of the case of iid observations, the results are…

暂定死亡率序列的调整：含结构化测量误差的动态线性模型AI 解读

The authors "consider the problem of adjusting provisional time series using a bivariate structural model with correlated measurement errors. Maximum likelihood estimators and a minimum mean squared error adjustment procedure are derived for a provisional and final series containing common trend and seasonal components. The model also includes measurement errors common to both series and errors that are specific to the provisional series. [The authors] illustrate the…

带切换的动态线性模型AI 解读

The problem of modeling change in a vector time series is studied using a dynamic linear model with measurement matrices that switch according to a time-varying independent random process. We derive filtered estimators for the usual state vectors and also for the state occupancy probabilities of the underlying nonstationary measurement process. A maximum likelihood estimation procedure is given that uses a pseudo-expectation-maximization algorithm in the initial stages and…

带切换机制的动态线性模型AI 解读

The problem of modeling change in a vector time series is studied using a dynamic linear model with measurement matrices that switch according to a time-varying independent random process. We derive filtered estimators for the usual state vectors and also for the state occupancy probabilities of the underlying nonstationary measurement process. A maximum likelihood estimation procedure is given that uses a pseudo-expectation-maximization algorithm in the initial stages and…

回归参数稳定性的贝叶斯显著性检验AI 解读

This paper presents a Bayesian significance test for stationarity of a regression equation using the highest posterior density credible set. In addition, a solution to the Behrens-Fisher problem is provided. From a Monte Carlo simulation study, it has been shown that the Bayesian significance test has stronger power than the Cusum and the Cusum of squares tests. The Bayesian significance test may be useful in detecting individual parameter nonstationarity.

一种快速有效的频率估计技术AI 解读

A technique is presented for the estimation of the frequency of a sinusoid in the presence of noise. The technique is based on fitting ARMA (2, 2) models iteratively, in a special way. The estimator is shown to be strongly consistent and as efficient as the least squares estimator of the frequency, or the periodogram maximizer. A simple accelerated version of the technique is shown to converge in a small number of iterations, the number depending on the accuracy of the…

半参数与非参数模型的自动频域推断AI 解读

The author considers frequency domain time series analysis, where smoothing in nonparametric spectrum estimation is data-dependent. Uniform convergence of spectrum estimates is established and applied to a semiparametric model, parameterized over possibly only a subset of the frequencies, in which disturbances have nonparametric autocorrelation. Optimal instruments depend on the disturbance spectrum and frequency response function, which is nonparametric in incomplete…

工具变量统计量检验嵌套与非嵌套假设的蒙特卡洛研究及有限样本性质AI 解读

Using Monte Carlo methodology, this paper investigates the effect of dynamics and simultaneity on the finite sample properties of instrumental variables statistics for testing nested and nonnested hypotheses. Simple numerical-analytical formulae (response surfaces) are obtained which closely approximate the statistics' unknown size and power functions for a dynamic simultaneous-equations model. The analysis illustrates the value and limitations of asymptotic theory in…

股票市场价格的长期记忆AI 解读

A test for long-term memory that is robust to short-range dependence is developed. It is a modification of the R/S statistic, and the relevant asymptotic sampling theory is derived via functional central limit theory. Contrary to previous findings, when applied to daily and monthly stock returns indexes over several time periods this test yields no evidence of long-range dependence once short-range dependence is accounted for. Monte Carlo experiments show that the modified…