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自回归单位根的高效检验AI 解读

The asymptotic power envelope is derived for point-optimal tests of a unit root in the autoregressive representation of a Gaussian time series. The authors propose a family of tests whose asymptotic power functions are tangent to the power envelope at one point and are never far below. When the series has an unknown mean or linear trend, commonly used tests are found to be dominated by members of the family of point-optimal invariant tests. The authors propose a modified…

计量经济模型的确定AI 解读

This paper is concerned with model determination methods and their use in the prediction of economic time series. The methods are Bayesian but they can be justified by classical arguments as well. The paper continues some recent work on Bayesian asymptotic, develops embedding techniques for vector martingales, and implements the modeling ideas in a multivariate regression framework that includes Bayesian vector autoregression (BVAR's) and reduced rank regressions (RRR's). It…

相关误差下若干单位根检验的改进及其局部渐近性质AI 解读

Many unit root tests have distorted sizes when the root of the error process is close to the unit circle. This paper analyses the properties of the Phillips-Perron tests and some of their variants in the problematic parameter space. We use local asymptotic analyses to explain why the Phillips-Perron tests suffer from severe size distortions regardless of the choice of the spectral density estimator but that the modified statistics show dramatic improvements in size when used…

用于经济周期分析的 GMM 小样本性质AI 解读

We investigate, by Monte Carlo methods, the finite-sample properties of generalized method of moment procedures for conducting inference about statistics that are of interest in the business-cycle literature. These statistics include the second moments of data filtered using the first-difference and Hodrick–Prescott filters, and they include statistics for evaluating model fit. Our results indicate that, for the procedures considered, the existing asymptotic theory is not a…

动态线性模型中不同工具变量估计量的比较AI 解读

Using a dynamic linear equation that has a conditionally homoskedastic moving average disturbance, the authors compare two parameterizations of a commonly used instrumental variables estimator (Hansen (1982)) to one that is asymptotically optimal in a class of estimators that includes the conventional one (Hansen (1985)). They find that for some plausible data generating processes, the optimal one is distinctly more efficient asymptotically. Simulations indicate that, in…

季节调整是线性还是非线性的数据滤波过程？AI 解读

The authors investigate whether seasonal adjustment procedures are linear data transformations. This question was addressed by A. H. Young (1968) and is important for the estimation of regression models with seasonally adjustment data. The authors focus on the X-11 program and rely on simulation evidence, involving linear unobserved component autorgressive integrated moving average models. They define and test a set of properties for the adequacy of a linear approximation to…

非线性协方差结构模型估计量的小样本性质AI 解读

This study examines the small sample properties of generalized method of moments (GMM) and maximood likelihood estimators of nonlinear models of covariance structure. It considers the properties of estimates for a simple factor model, the Hall and Mishkin (1982) model of consumption and income, and a simple structural vector-autoregression-type error model. This analysis establishes three basic results. First, optimally weighted GMM estimation yields some biased parameter…

季节性过程中的冲击持续性AI 解读

The paper addresses the issue of measuring the persistence of shocks on seasonally integrated processes observed at quarterly intervals. We show that the amplitude of the limiting cycle described by the cumulated impulse response function provides a parametric measure of persistence and that Cochrane's normalized variance ratio can correspondingly be extended as a non-parametric counterpart. For illustrative purposes the latter is applied to the Italian GDP and to the output…

宏观经济理论视角下的应用协整分析AI 解读

Cointegration analyses of macroeconomic time series are often not based on fully specified theoretical models. We use a theoretical model to scrutinize common procedures in applied cointegration analysis. Monte Carlo experiments show that 1) some tests of the cointegration vectors do not work well on series generated by an equilibrium cycle model; (2) cointegration restrictions add little to forecasting; (3) structural VAR models based on weak long-run restrictions seem to…

宏观计量模型中中位数无偏估计的计算AI 解读

A stochastic simulation model is proposed in this paper for obtaining median unbiased (MU) estimates in macroeconometric models. MU estimates are computed for the lagged dependent variable (LDV) coefficients in 18 equations of a macroeconometric model. The 2SLS bias for a coefficient, defined as the difference between the 2SLS estimate and the MU estimate, is on average smaller in absolute value than would be expected from Andrews' exact results for an equation with only a…

季节性过程中的冲击持续性AI 解读

The paper addresses the issue of measuring the persistence of shocks on seasonally integrated processes observed at quarterly intervals. We show that the amplitude of the limiting cycle described by the cumulated impulse response function provides a parametric measure of persistence and that Cochrane's normalized variance ratio can correspondingly be extended as a non-parametric counterpart. For illustrative purposes the latter is applied to the Italian GDP and to the output…

从宏观经济理论审视应用协整分析AI 解读

Cointegration analyses of macroeconomic time series are often not based on fully specified theoretical models. We use a theoretical model to scrutinize common procedures in applied cointegration analysis. Monte Carlo experiments show that 1) some tests of the cointegration vectors do not work well on series generated by an equilibrium cycle model; (2) cointegration restrictions add little to forecasting; (3) structural VAR models based on weak long-run restrictions seem to…

二元时间序列互谱的自动估计AI 解读

The penalised Whittle likelihood has recently been shown to have good properties in nonparametric estimation of spectral density functions. This paper extends the approach to the estimation of the cross-spectrum of a bivariate time series. One major difference from the univariate case is that the cross-spectrum estimate is not constrained to be positive, but must result in a positive definite spectral density matrix. An efficient computational method based on iterative…

随机系数自回归模型中的自适应估计AI 解读

This paper proves the local asymptotic normality of a stationary and ergodic first order random coefficient autoregressive model in a semiparametric setting. This result is used to show that Stein's necessary condition for adaptive estimation of the mean of the random coefficient is satisfied if the distributions of the innovations and the errors in the random coefficients are symmetric around zero. Under these symmetry assumptions, a locally asymptotically minimax adaptive…

长记忆移动平均过程经验过程的渐近展开AI 解读

Let $X_n = \Sigma_{i=1}^{\infty} a_i \varepsilon_{n-i}$, where the $\varepsilon_i$ are iid with mean 0 finite fourth moment and the $a_i$ are regularly varying with index $-\beta$ where $\beta \epsilon (1/2, 1)$ so that ${X_n}$ has long-range dependence. This covers an important class of the fractional ARIMA process. For $r \geq 0$, let $Y_{N, r} = \sum_{n=1}^N \sum_{1\leq j_1 < \dots < j_r} \Pi_{s=1}^r a_{j_s}, Y_{N, 0} = N, \sigma_{N, r}^2 = \Var(Y_{N, r})$ and $F^{(r)} =$…

误设时间序列模型中的渐近最优估计AI 解读

A concept of asymptotically efficient estimation is presented when a misspecified parametric time series model is fitted to a stationary process. Efficiency of several minimum distance estimates is proved and the behavior of the Gaussian maximum likelihood estimate is studied. Furthermore, the behavior of estimates that minimize the h-step prediction error is discussed briefly. The paper answers to some extent the question what happens when a misspecified model is fitted to…

线性时间序列下的固定设计回归AI 解读

This investigation is concerned with recovering a regression function $g(x_i)$ on the basis of noisy observations taken at uniformly spaced design points $x_i$. It is presumed that the corresponding observations are corrupted by additive dependent noise, and that the noise is, in fact, induced by a general linear process in which the summand law can be discrete, as well as continuously distributed. Discreteness induces a complication because such noise is not known to be…

离散化事件序列的若干模型AI 解读

A discretized series of events is a binary time series that indicates whether or not events of a point process in the line occur in successive intervals. Such data are common in environmental applications. We describe a class of models for them, based on an unobserved continuous-time discrete-state Markov process, which determines the rate of a doubly stochastic Poisson process, from which the binary time series is constructed by discretization. We discuss likelihood…

弱假设下的自相关推断AI 解读

In this article we consider the large-sample behavior of estimates of autocorrelations and autoregressive moving average (ARMA) coefficients, as well as their distributions, under weak conditions. Specifically, the usual text book formulas for variances of these estimates are based on strong assumptions and should not be routinely applied without careful consideration. Such is the case when the time series follows an ARMA process with uncorrelated innovations that may not be…

重复样本直方图AI 解读

The “replicate histogram” is introduced as a simple diagnostic tool for describing the sampling distribution of a general statistic. It can be applied to virtually any statistic that has an asymptotic distribution, and the data on which the statistic is computed may be serially or spatially dependent. The method is completely sample based, requiring no theoretical analysis by the user, no knowledge of the proper standardization for the statistic, and no specification of the…

Bootstrap 模型选择AI 解读

In a regression problem, typically there are p explanatory variables possibly related to a response variable, and we wish to select a subset of the p explanatory variables to fit a model between these variables and the response. A bootstrap variable/model selection procedure is to select the subset of variables by minimizing bootstrap estimates of the prediction error, where the bootstrap estimates are constructed based on a data set of size n. Although the bootstrap…

连续时间长记忆时间序列模型的估计AI 解读

A class of univariate fractional ARIMA models with a continuous time parameter is developed for the purpose of modeling long-memory time series. The spectral density of discretely observed data is derived for both point observations (stock variables) and integral observations (flow variables). A frequency domain maximum likelihood method is proposed for estimating the longmemory parameter and is shown to be consistent and asymptotically normally distributed, and some issues…

具有共同随机趋势的连续时间动态模型的高斯估计AI 解读

We derive the exact discrete model and the Gaussian likelihood function of a first-order system of linear stochastic differential equations driven by an observable vector of stochastic trends and a vector of stationary innovations.

连续时间模型中的非因果性AI 解读

In this paper, we study new definitions of noncausality, set in a continuous time framework, illustrated by the intuitive example of stochastic volatility models. Then, we define CIMA processes (i.e., processes admitting a continuous time invertible moving average representation), for which canonical representations and sufficient conditions of invertibility are given. We can provide for those CIMA processes parametric characterizations of noncausality relations as well as…