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基于惩罚 Whittle 似然的非参数谱密度估计AI 解读

The penalized likelihood approach is not well developed in time series analysis, even though it has been applied successfully in a number of nonparametric function estimation problems. Chow and Grenander proposed a penalized likelihood-type approach to the nonparametric estimation of the spectral density of Gaussian processes. In this article this estimator is extended to more general stationary processes, its practical implementation is developed in some detail, and some…

利用卡尔曼滤波估计、预测与插补非平稳序列AI 解读

We show how our definition of the likelihood of an autoregressive integrated moving average (ARIMA) model with missing observations, alternative to that of Kohn and Ansley and based on the usual assumptions made in estimation of and forecasting with ARIMA models, permits a direct and standard state-space representation of the nonstationary (original) data, so that the ordinary Kalman filter and fixed point smoother can be efficiently used for estimation, forecasting, and…

交叉相关建模札记：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

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 results of…

适用于依赖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…

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奇异方程系统中的自回归误差AI 解读

We consider a system of m general linear models, where the system error vector has a singular covariance matrix owing to various “adding up” requirements and, in addition, the error vector obeys an autoregressive scheme. The paper reformulates the problem considered earlier by Berndt and Savin [8] (BS), as well as others before them; the solution, thus obtained, is far simpler, being the natural extension of a restricted least-squares-like procedure to a system of equations…

自回归模型的近似中位数无偏估计AI 解读

This paper introduces approximately median-unbiased estimators and confidence intervals for univariate AR(p) models with time trends. The methods are applied to the Nelson-Plosser macroeconomic data series, the extended Nelson-Plosser series, and some annual stock dividend and price series. The results show that most of the series exhibit substantially greater persistence than least squares estimates and some Bayesian estimates suggest. For example, for the extended…

方差比检验的小样本性质：国际产出数据应用AI 解读

Two aspects of statistical inference using variance-ratio statistics are studied, (1) the accuracy of asymptotic approximations in small samples and (2) the size distortion arising from searching over many horizons in deciding whether to reject a model. A joint test combining variance-ratio statistics at various horizons is proposed and a Monte Carlo procedure for conducting exact inference is provided. The real output data of nine countries are used to discuss these issues.

单位根与协整检验的近似渐近分布函数AI 解读

Monte Carlo experiments and response surface regressions are used to calculate approximate asymptotic distribution functions for a number of well-known unit root and cointegration test statistics. These allow empirical workers to calculate approximate P values for these tests. The results of the paper are based on an extensive set of Monte Carlo experiments, which yield finite-sample quantiles for several sample sizes. Response surface regressions are then used to obtain…

一种一致的单位根检验AI 解读

This article investigates several U.S. macroeconomic time series for the presence of a unit root using a newly developed test. This test has stationarity as its null hypothesis and the alternative is a unit-root process. The test is shown to be consistent and its asymptotic null distribution is determined. The authors' findings contrast sharply with those obtained via the standard unit-root tests.

大冲击、小冲击与经济波动：宏观时间序列中的异常值AI 解读

Abstract We analyse fifteen post‐World War II US macroeconomic time series using a modified outlier identification procedure based on Tsay (1988a). ‘Large shocks’ appear to be present in all the series we examined. Furthermore, there are three basic outlier patterns: (1) outliers seem to be associated with business cycles, (2) outliers are clustered together—both over time and across series, (3) there appears to be a dichotomy between outlier behaviour of real versus nominal…

利用蒙特卡洛积分进行非线性、非正态情形下的预测、滤波与平滑AI 解读

Abstract A simulation‐based non‐linear filter is developed for prediction and smoothing in non‐linear and/or non‐normal structural time‐series models. Recursive algorithms of weighting functions are derived by applying Monte Carlo integration. Through Monte Carlo experiments, it is shown that (1) for a small number of random draws (or nodes) our simulation‐based density estimator using Monte Carlo integration (SDE) performs better than Kitagawa's numerical integration…

发展中国家外债危机的模拟估计分析AI 解读

Abstract In this paper we develop models of the incidence and extent of external financing crises of developing countries, which lead to multiperiod multinomial discrete choice and discrete/continuous econometric specifications with flexible correlation structures in the unobservables. We show that estimation of these models based on simulation methods has attractive statistical properties and is computationally tractable. Three such simulation estimation methods are…

扩散过程离散观测的贝叶斯因子AI 解读

We present an approach to model selection for a time series of data on a fine time scale. The underlying process generating the data is modelled as a continuous time stochastic process. The underlying continuous processes are assumed to be diffusions with time varying drift and diffusion coefficient. Several approaches to modelling the diffusion coefficient are described. To perform model selection, we propose an approximation to the Bayes factor that uses only the discrete…

随机向量差分方程渐近性质的一则札记AI 解读

This note analyses a necessary condition for asymptotic normality of the maximum likelihood estimator in a stationary stochastic vector difference equation. It is shown that this condition is satisfied if the error variance matrix is positive definite.

移动平均模型的一种简单非迭代估计量AI 解读

We examine a simple noniterative estimator for the parameters of a general moving average process. This non-maximum-likelihood estimator derives moving average model parameters directly from the coefficients of an approximating autoregressive model. The estimator is evaluated through asymptotic expansions and by simulation, and is also compared with maximum likelihood and the related estimator of Durbin (1959). The comparison with maximum likelihood by simulation suggests a…

非平稳状态空间模型的快速似然计算与预测AI 解读

A recursive procedure for initializing the Kalman filter is displayed. The recursion is for nonstationary state space models. The procedure imposes small computational and programming burden over and above the Kalman filter. The procedure is superior to other suggested approaches in both computational speed and general applicability. General properties of the method are investigated. Details of the initialization for the ARIMA (p,d,q) and basic structural models are…

随机加权依赖残差经验过程的弱收敛及自回归应用AI 解读

This paper establishes the uniform closeness of a randomly weighted residual empirical process to its natural estimator via weak convergence techniques. The weights need not be independent, bounded or even square integrable. This result is used to yield the asymptotic uniform linearity of a class of rank statistics in $p$th-order autoregression models. The latter result, in turn, yields the asymptotic distributions of a class of robust and Jaeckel-type rank estimators. The…

长记忆时间序列的半参数分析AI 解读

We study problems of semiparametric statistical inference connected with long-memory covariance stationary time series, having spectrum which varies regularly at the origin: There is an unknown self-similarity parameter, but elsewhere the spectrum satisfies no parametric or smoothness conditions, it need not be in $L_p$, for any $p > 1$, and in some circumstances the slowly varying factor can be of unknown form. The basic statistic of interest is the discretely averaged…

利用一阶累积特征识别非线性时间序列AI 解读

A new approach to the problem of identifying a nonlinear time series model is considered. We argue that cumulative lagged conditional mean and variance functions are the appropriate "signatures" of a nonlinear time series for the purpose of model identification, being analogous to cumulative distribution functions or cumulative hazard functions in iid models. We introduce estimators of the cumulative lagged conditional mean and variance functions and study their asymptotic…

平滑转换自回归模型的设定、估计与评价AI 解读

This article considers the application of two families of nonlinear autoregressive models, the logistic (LSTAR) and exponential (ESTAR) autoregressive models. This includes the specification of the model based on simple statistical tests: linearity testing against smooth transition autoregression, determining the delay parameter and choosing between LSTAR and ESTAR models are discussed. Estimation by nonlinear least squares is considered as well as evaluating the properties…

用于预测的神经网络模型AI 解读

In this article we introduce a neural net designed for nonlinear statistical prediction. The net is based on a stochastic model featuring a multilayer feedforward architecture with random connections between units and noisy response functions. A Bayesian inferential procedure for this model, based on the Kalman filter, is derived. The resulting learning algorithm generalizes the so-called onedimensional Newton method, an updating algorithm currently popular in the neural net…