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共同随机趋势检验AI 解读

This paper is concerned with tests in multivariate time series models made up of random walk (with drift) and stationary components. When the stationary component is white noise, a Lagrange multiplier test of the hypothesis that the covariance matrix of the disturbances driving the multivariate random walk is null is shown to be locally best invariant, something that does not automatically follow in the multivariate case. The asymptotic distribution of the test statistic is…

向量自回归谱的渐近同时置信带AI 解读

Asymptotic simultaneous confidence bands for all ω in [0, 0.5] are obtained for each scalar function in a spectral density matrix, as well as for the logarithm of the autospectra, the squared coherence and the phase spectra. The bands are illustrated using a simulation study and surface elevation data.

回归误差序列独立性的非参数检验AI 解读

A test for serial independence of regression errors is proposed that is consistent in the direction of serial dependence alternatives of first order. The test statistic is a function of a Hoeffding-Blum-Kiefer-Rosenblatt type of empirical process, based on residuals. The resultant statistic converges, surprisingly, to the same limiting distribution as the corresponding statistic based on true errors.

估计函数的窗口子抽样及其在回归模型中的应用AI 解读

We propose a subsampling method for estimating the asymptotic standard error of a statistic β n that is the solution to an estimating equation 1/n Σn j=1 Uj(Y j Xj, β) = 0 where the data Yj may be temporally or spatially correlated and the estimating function may depend on covariates Xj . A key statistic that we consider in detail is a generalized linear model regression coefficient computed under the assumption of independence. The availability of a consistent variance…

时间序列尺度分析中小波方差估计量的统计性质与应用AI 解读

Many physical processes are an amalgam of components operating on different scales, and scientific questions about observed data are often inherently linked to understanding the behavior at different scales. We explore time-scale properties of time series through the variance at different scales derived using wavelet methods. The great advantage of wavelet methods over ad hoc modifications of existing techniques is that wavelets provide exact scale-based decomposition…

转移回归模型及其在环境时间序列中的应用AI 解读

Environmental epidemiologists often encounter time series data in the form of discrete or other nonnormal outcomes; for example, in modeling the relationship between air pollution and hospital admissions or mortality rates. We present a case study examining the association between pollen counts and meteorologic covariates. Although such time series data are inadequately described by standard methods for Gaussian time series, they are often autocorrelated, and warrant an…

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异方差与自相关协方差矩阵核估计量的一致性AI 解读

Conditions are derived for the consistency of kernel estimators of the covariance matrix of a sum of vectors of dependent heterogeneous random variables, which match those of the currently best-known conditions for the central limit theorem, as required for a unified theory of asymptotic inference. These include finite moments of order no more than 2 + for > 0, trending variances, and variables which are near-epoch dependent on a mixing process, but not necessarily mixing.…

短期利率的漂移函数真的非线性吗？AI 解读

Aït‐Sahalia (1996) and Stanton (1997) use nonparametric estimators applied to short‐term interest rate data to conclude that the drift function contains important nonlinearities. We study the finite‐sample properties of their estimators by applying them to simulated sample paths of a square‐root diffusion. Although the drift function is linear, both estimators suggest nonlinearities of the type and magnitude reported in Aït‐Sahalia (1996) and Stanton (1997) . Combined with…

协整与信息集之间的距离AI 解读

This paper investigates Granger noncausality and the cointegrating relation between two time series in the Hilbert space framework. This framework allows us to analyze the relationship between cointegration and distance between two information sets. In particular, we prove that if two variables, X and Y , are cointegrated, then the distance between two information sets, concerning the differenced series Δ X and Δ Y , must be less than the standard deviation of Δ X .

非高斯对数周期图回归AI 解读

We show the consistency of the log-periodogram regression estimate of the long memory parameter for long range dependent linear, not necessarily Gaussian, time series when we make a pooling of periodogram ordinates. Then, we study the asymptotic behavior of the tapered periodogram of long range dependent time series for frequencies near the origin, and we obtain the asymptotic distribution of the log-periodogram estimate for possibly non-Gaussian observation when the tapered…

系数具有马尔可夫切换的向量自回归过程的若干性质AI 解读

Some statistical properties of a vector autoregressive process with Markov-switching coefficients are considered. Sufficient conditions for this nonlinear process to be covariance stationary are given. The second moments of the process are derived under the conditions. The autocovariance matrix decays at exponential rate, permitting the application of the law of large numbers. Under the stationarity conditions, although sharing the “mean-reverting” property with conventional…

平稳 ARCH 模型：依赖结构与中心极限定理AI 解读

This paper studies a broad class of nonnegative ARCH(∞) models. Sufficient conditions for the existence of a stationary solution are established and an explicit representation of the solution as a Volterra type series is found. Under our assumptions, the covariance function can decay slowly like a power function, falling just short of the long memory structure. A moving average representation in martingale differences is established, and the central limit theorem is proved.

不同采样频率下过程的极值分析AI 解读

Summary The observed extremes of a discrete time process depend on the process itself and the sampling frequency. We develop theoretical results which show how to account for the effect of sampling frequency on extreme values, thus enabling us to analyse systematically extremal data from series with different sampling rates. We present statistical methodology based on these results which we illustrate though simulations and by applications to sea-waves and rainfall data.

一种混合自回归模型AI 解读

Summary We generalize the Gaussian mixture transition distribution (GMTD) model introduced by Le and co-workers to the mixture autoregressive (MAR) model for the modelling of non-linear time series. The models consist of a mixture of K stationary or non-stationary AR components. The advantages of the MAR model over the GMTD model include a more full range of shape changing predictive distributions and the ability to handle cycles and conditional heteroscedasticity in the…

通过可逆跳跃 MCMC 进行隐马尔可夫模型的贝叶斯推断AI 解读

Summary Hidden Markov models form an extension of mixture models which provides a flexible class of models exhibiting dependence and a possibly large degree of variability. We show how reversible jump Markov chain Monte Carlo techniques can be used to estimate the parameters as well as the number of components of a hidden Markov model in a Bayesian framework. We employ a mixture of zero-mean normal distributions as our main example and apply this model to three sets of data…

非高斯观测的状态空间时间序列分析：经典与贝叶斯视角AI 解读

Summary The analysis of non-Gaussian time series by using state space models is considered from both classical and Bayesian perspectives. The treatment in both cases is based on simulation using importance sampling and antithetic variables; Markov chain Monte Carlo methods are not employed. Non-Gaussian disturbances for the state equation as well as for the observation equation are considered. Methods for estimating conditional and posterior means of functions of the state…

受限协整向量的估计AI 解读

This article suggests the use of simple minimum-distance methods to estimate restricted cointegrating vectors. The method directly employs minimum-distance methods on unrestricted cointegrating matrices estimated in the usual way to estimate restricted parameters that are linearly or nonlinearly related to the unrestricted cointegrating vector coefficients. The limiting distribution of the estimates and the usual test for the restrictions are derived. A Monte Carlo…

层级趋势的高效计算AI 解读

To model a large database containing selling prices for houses, in which local trends, general trends, and specific characteristics play a role, we derived a new procedure to implement a state-space model for repeated measurements. The original model is decomposed into two parts, which are treated differently. The first part is ordinary least squares on data in deviation from means. This step provides a prior for coefficients to be used in the second step, which is a Kalman…

自回归模型中基于残差的正态性检验：渐近理论与模拟证据AI 解读

Existing results for the asymptotic validity of the Jarque-Bera test in vector autoregressive (VAR) models assume stationarity. In applied work, however, researchers often work with possibly integrated and cointegrated process. We prove the asymptotic validity of the Jarque-Bera test for vector error-correction (VEC) models and for unrestricted VAR models with possibly integrated or cointegrated variables. We also propose the use of bootstrap critical values in stationary…

基于典型相关的协整秩强一致判定AI 解读

This article is concerned with the statistical analysis of nonstationary, cointegrated time series. The estimation of the cointegrating structure of such time series is considered, and the problem of identifying the cointegrating rank is addressed. A methodology is presented that leads to strongly consistent estimates of this quantity. The identification is based on a canonical correlation analysis of the original variables and presents an alternative approach to those…

基于秩与符号的替代方差比检验AI 解读

This article proposes using variance-ratio tests based on the ranks and signs of a time series to test the null that the series is a martingale difference sequence. Unlike conventional variance-ratio tests, these tests can be exact. In Monte Carlo simulations, I find that they can also be more powerful than conventional variance-ratio tests. I apply the proposed tests to five exchange-rate series and find that they are capable of detecting violations of the martingale…

美国赤字的可持续性：基于多个内生断点的新方法AI 解读

Recent empirical work has questioned the consistency of US fiscal policy with an intertemporal budget constraint. Empirical results have tended to indicate that the deficit process has undergone at least one structural shift during recent decades, with the deficit becoming either unsustainable or sustainable in only a weak sense in the post-shift period. In this paper, we re-examine sustainability using a new approach, based on a cointegration model with multiple endogenous…