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状态空间模型的吉布斯抽样AI 解读

We show how to use the Gibbs sampler to carry out Bayesian inference on a linear state space model with errors that are a mixture of normals and coefficients that can switch over time. Our approach simultaneously generates the whole of the state vector given the mixture and coefficient indicator variables and simultaneously generates all the indicator variables conditional on the state vectors. The states are generated efficiently using the Kalman filter. We illustrate our…

交叉相关建模：双曲正割回归AI 解读

The problem of determining if a bivariate normal correlation changes with respect to time or some other covariate is considered. It is assumed that the means and standard deviations of the normal random variables can be consistently estimated from the entire data run, and do not need to be re-estimated for each covariate value. A new estimator of a bivariate normal correlation is given that has useful performance down to samples of size one. This allows regression type…

椭圆轮廓误差下的贝叶斯卡尔曼滤波AI 解读

SUMMARY The basic recursive equations of the Kalman filter, for independent normally distributed error sources in both the observation and the system equations, are shown to hold for a larger class of distributions. It is shown that, for error sources following jointly a general elliptical distribution, the conditional posterior distribution of the parameters and the one-step ahead predictive distribution at every stage t are also elliptical. This generalizes some recent…

适用于相依数据的交叉验证方法AI 解读

In this paper we extend the technique of cross-validation to the case where observations form a general stationary sequence. We call it h-block cross-validation, because the idea is to reduce the training set by removing the h observations preceding and following the observation in the test set. We propose taking h to be a fixed fraction of the sample size, and we add a term to our h-block cross-validated estimate to compensate for the underuse of the sample. The advantages…

弱依赖平稳序列的极值指数估计AI 解读

Under stationarity and weak dependence, the statistical significance and the estimation of the extremal index are considered. It is shown that the distribution of the sample maximum can be uniformly approximated given the extremal index and the marginal distribution as the sample size increases. An adaptive procedure is proposed for estimating the extremal index. The procedure is shown to be asymptotically optimal in a class of estimators.

非因果平稳自回归过程的自适应估计AI 解读

We consider the estimation problem of the parameter $b$ of a stationary AR($p$) process without any of the usual causality assumptions. The aim of the paper is to derive asymptotic minimax bounds for estimators of $b$. When the distribution of the noise is known, we show LAN properties of the model and derive locally asymptotically minimax (LAM) estimators. The most important results are about the case of unknown distribution: The main result shows that, if one uses the…

反卷积、频带限制与四阶谱AI 解读

In the largest application area of time series analysis—geophysical exploration—the underlying innovations sequence is of primary interest and must be estimated. This sequence is estimated by deconvolving the non-Gaussian, noninvertible time series. This involves estimation of a phase-shift correction from the time series, which can be carried out by maximizing the kurtosis of the series. Unfortunately, the method is hampered by the fact that the time series is typically…

反卷积、带宽与四阶谱AI 解读

In the largest application area of time series analysis—geophysical exploration—the underlying innovations sequence is of primary interest and must be estimated. This sequence is estimated by deconvolving the non-Gaussian, noninvertible time series. This involves estimation of a phase-shift correction from the time series, which can be carried out by maximizing the kurtosis of the series. Unfortunately, the method is hampered by the fact that the time series is typically…

带确定性趋势的 ARIMA 模型中的若干单位根检验AI 解读

For a nonstationary time series we consider a model which can accommodate the possibility of deterministic and stochastic trends. Assuming that we are primarily interested in testing for the stochastic trend, that is, for a unit root in the time series, we employ the Lagrange multiplier principle and obtain test statistics. The asymptotic distributions of the test statistics. The asymptotic distributions of the test statistics are characterized by functionals of stochastic…

动态回归模型中的异常值检测与处理AI 解读

This paper offers an approach to detecting outliers in multiple time series by studying transfer functions with one input where outliers in the input may or may not be passed to the output.

通过广义线性回归拟合长记忆模型AI 解读

There is an increasing awareness of the importance of long-memory models in statistical applications.If long memory is present, it has to be taken into account in order to obtain reliable tests and confidence intervals.One obstacle to using models with long memory in routine statistical analysis has been the lack of easily available and sufficiently versatile statistical software.Here we propose a simple but flexible class of parametric models, which can be used to model…

加速高斯重要性抽样及其在动态潜变量模型中的应用AI 解读

We propose a new generic and highly efficient Accelerated Gaussian Importance Sampler (AGIS) for the numerical evaluation of (very) high-dimensional density functions. A specific case of interest to us is the evaluation of likelihood functions for a broad class of dynamic latent variable models. The feasibility of our method is strikingly illustrated by means of an application to a first-order dynamic stochastic volatility model for daily stock returns, whose likelihood for…

非线性时间序列模型的拟合及随机方差模型应用AI 解读

New strategies for the implementation of maximum likelihood estimation of nonlinear time series models are suggested. They make use of recent work on the EM algorithm and iterative simulation techniques. The estimation procedures are applied to the problem of fitting stochastic variance models to exchange rate data.

利用模拟向量自回归估计非线性时间序列模型AI 解读

This paper develops two new methods for conducting formal statistical inference in nonlinear dynamic economic models. The two methods require very little analytical tractability, relying instead on numerical simulation of the model's dynamic behaviour. Although one of the estimators is asymptotically more efficient than the other, a Monte Carlo study shows that, for a specific application, the less efficient estimator has smaller mean squared error in samples of the size…

GARCH 模型的非平稳性：贝叶斯分析AI 解读

First, the non-stationarity properties of the conditional variances in the GARCH(1, 1) model are analysed using the concept of infinite persistence of shocks. Given a time sequence of probabilities for increasing/decreasing conditional variances, a theoretical formula for quasi-strict non-stationarity is defined. The resulting conditions for the GARCH(1,1) model are shown to differ from the weak stationarity conditions mainly used in the literature. Bayesian statistical…

独立 Student-t 误差线性模型的贝叶斯分析AI 解读

This article takes up methods for Bayesian inference in a linear model in which the disturbances are independent and have identical Student-t distributions. It exploits the equivalence of the Student-t distribution and an appropriate scale mixture of normals, and uses a Gibbs sampler to perform the computations. The new method is applied to some well-known macroeconomic time series. It is found that posterior odds ratios favour the independent Student-t linear model over the…

向量自回归与因果性AI 解读

A limit theory for Wald tests of Granger causality in levels vector autoregressions (VAR's) and error correction models (ECM's) is developed, which allows for stochastic trends and cointegration. Earlier work is extended to the general case, thereby characterizing when these Wald tests are asymptotically valid as 'x'(superscript 2) criteria. Our results for inference from unrestricted levels VAR are not encouraging: the limit theory often involves nuisance parameters and…

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单位根对向量自回归的伪影响AI 解读

This paper analyzes whether inclusion of a statistically independent random walk in a vector autoregression can result in spurious inference. The problem was raised originally by Ohanian (1988). In a Monte Carlo simulation based on the VAR's estimated by Sims (1980, 1982), Ohanian found that ‘block exogeneity’ of the genuine variables with respect to an artificially generated random walk variable was rejected too often. In the present paper we attempt a full analytical study…

评论AI 解读

I show that the Engle–Kozicki formulation of common features—applied to international business cycles—has some surprising, counterintuitive, and, I argue, undesirable implications. Such implications can be derived only on a case-by-case basis, however, and are necessarily specific to each application. Therefore, some attention to those possibilities might usefully accompany each application of the general common-features principle.

《共同特征检验》评论AI 解读

I show that the Engle-Kozicki formulation of common features--applied to international business cycles--has some surprising, counterintuitive, and, I argue, undesirable implications. Such implications can be derived only on a case-by-case basis, however, and are necessarily specific to each application. Therefore, some attention to those possibilities might usefully accompany each application of the general common-features principle.

共同特征检验AI 解读

This article introduces a class of statistical tests for the hypothesis that some feature that is present in each of several variables is common to them. Features are data properties such as serial correlation, trends, seasonality, heteroscedasticity, autoregressive conditional heteroscedasticity, and excess kurtosis. A feature is detected by a hypothesis test taking no feature as the null, and a common feature is detected by a test that finds linear combinations of…