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随机回归中条件方差函数的有效估计AI 解读

Conditional heteroscedasticity has often been used in modelling and understanding the variability of statistical data. Under a general set-up which includes nonlinear time series models as a special case, we propose an efficient and adaptive method for estimating the conditional variance. The basic idea is to apply a local linear regression to the squared residuals. We demonstrate that, without knowing the regression function, we can estimate the conditional variance…

多元门限模型的检验与建模AI 解读

Threshold autoregressive models in which the process is piecewise linear in the threshold space have received much attention in recent years. In this article I use predictive residuals to construct a test statistic for detecting threshold nonlinearity in a vector time series and propose a procedure for building a multivariate threshold model. The thresholds and the model are selected jointly based on the Akaike information criterion. The finite-sample performance of the…

无限方差误差下的协整检验AI 解读

This paper develops the asymptotic theory for residual-based tests and quasi-likelihood ratio tests for cointegration under the assumption of infinite variance errors. This article extends the results of Phillips and Ouliaris (1990) and Johansen (1988, 1991) which are derived under the assumption of square-integrable errors. Here the limit laws are expressed in terms of functionals of symmetric stable laws rather than Brownian motion. Critical values of the residual-based…

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时间序列中的短期与长期因果性：理论AI 解读

Causality in Granger's sense is defined in terms of predictibility one period ahead. The notion of causality is generalized by considering causality at any given horizon 1 <= h <= inifinity, providing a rigorous formalization of indirect causal effects and causality chains in (possibly) nonstationary time series. The authors derive necessary and sufficient conditions for noncausality between vectors up to any given horizon. They observe that coefficients of lagged variables…

存在非参数自相关时的无平滑推断AI 解读

The author gives conditions under which nonparametric autocorrelation-consistent variance estimation is possible without smoothing. The conditions are relevant to inference on slope parameters in models with an intercept and strictly exogenous regressors, and allow regressors and disturbances to collectively have considerable stationary long memory and to satisfy only mild, in some cases minimal, moment conditions. His estimate dominates smoothed ones in the sense that it…

高斯动态回归时间序列模型精确信息矩阵的计算AI 解读

In this paper, the computation of the exact Fisher information matrix of a large class of Gaussian time series models is considered. This class, which is often called the single-input–single-output (SISO) model, includes dynamic regression with autocorrelated errors and the transfer function model, with autoregressive moving average errors. The method is based on a combination of two computational procedures: recursions for the covariance matrix of the derivatives of the…

一般隐马尔可夫模型极大似然估计量的渐近正态性AI 解读

Hidden Markov models (HMMs) have during the last decade become a widespread tool for modeling sequences of dependent random variables. Inference for such models is usually based on the maximum-likelihood estimator (MLE), and consistency of the MLE for general HMMs was recently proved by Leroux. In this paper we show that under mild conditions the MLE is also asymptotically normal and prove that the observed information matrix is a consistent estimator of the Fisher…

非参数自回归中的回归式推断AI 解读

We derive a strong approximation of a local polynomial estimator LPE in nonparametric autoregression by an (LPE) in a corresponding nonparametric regression model. This generally suggests the application of regression-typical tools for statistical inference in nonparametric autoregressive models. It provides an important simplification for the boot-strap method to be used: It is enough to mimic the structure of a nonparametric regression model rather than to imitate the more…

回归模型的函数型中心极限定理AI 解读

Let a linear regression be given. For detecting change-points, it is usual to consider the sequence of partial sums of least squares residuals whence a partial sums process is defined. Given a sequence of exact experimental designs, we consider for each design the corresponding partial sums process. If the sequence of designs converges to a continuous design, we derive the explicit form of the limit process of the corresponding sequence of partial sums processes. This is a…

尖锐变点的极小极大估计AI 解读

We define the sharp change point problem as an extension of earlier problems in change point analysis related to nonparametric regression. As particular cases, these include estimation of jump points in smooth curves. More generally, we give a systematic treatment of the correct rate of convergence for estimating the position of a “cusp”of an arbitrary order. We propose a test function for the local regularity of a signal that characterizes such a point as a global maximum.…

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具有 ARMA 误差的协整回归自适应估计AI 解读

Adaptive maximum likelihood estimators are derived for the parameters of a cointegrating regression whose errors follow a stationary and invertible ARMA process with innovations of unknown distribution. It is shown how to use preliminary estimates of these innovations to nonparametrically estimate their density, which can in turn be used to construct an asymptotically efficient iterative estimator of the cointegrating vector. The asymptotic distribution of this estimator is…

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分数协整的极大似然估计：美国与加拿大债券利率的应用AI 解读

We estimate a multivariate ARFIMA model to illustrate a cointegration testing methodology based on joint estimates of the fractional orders of integration of a cointegrating vector and its parent series. Previous cointegration tests relied on a two-step testing procedure and maintained the assumption in the second step that the parent series were known to have a unit root. In our empirical example of fractional cointegration, we illustrate how uncertainty regarding the order…

基于经验分布函数的两两序列独立性检验AI 解读

Summary Built on Skaug and Tjøstheim's approach, this paper proposes a new test for serial independence by comparing the pairwise empirical distribution functions of a time series with the products of its marginals for various lags, where the number of lags increases with the sample size and different lags are assigned different weights. Typically, the more recent information receives a larger weight. The test has some appealing attributes. It is consistent against all…

自相关误差下的加性非参数回归AI 解读

Summary A Bayesian approach is presented for nonparametric estimation of an additive regression model with autocorrelated errors. Each of the potentially non-linear components is modelled as a regression spline using many knots, while the errors are modelled by a high order stationary autoregressive process parameterized in terms of its autocorrelations. The distribution of significant knots and partial autocorrelations is accounted for using subset selection. Our approach…

工业时间序列中可能不连续出现的异常值检测AI 解读

Summary A method for robust estimation and multiple outlier detection in time series generated by autoregressive integrated moving average processes in industrial environments is developed. The procedure is based on reweighted maximum likelihood estimation using Huber or redescending weights and, therefore, generalizes the well-established robust M-estimation procedures used in the regression framework. When the scalar process is non-stationary, the computations required can…

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使用 GMM 方法分析协整向量AI 解读

This paper generalizes Johansen's (1988) maximum likelihood approach of the analysis of cointegrating vectors to the generalized method of moments (GMM) approach. We derive the asymptotic distribution of the cointegration vectors estimated from the fully modified generalized method of moments (FM-GMM) estimation procedure. We also introduce the FM-GMM version of Johansen's (1988) likelihood ratio (LR) test for the rank of a cointegrating matrix. Unlike the LR test which has…

多元时间序列共同断点的检验与定年AI 解读

This paper develops methods for constructing asymptotically valid confidence intervals for the date of a single break in multivariate time series, including I(0), I(1), and deterministically trending regressors. Although the width of the asymptotic confidence interval does not decrease as the sample size increases, it is inversely related to the number of series which have a common break date, so there are substantial gains to multivariate inference about break dates. These…

动态均衡经济：比较模型与数据的框架AI 解读

We propose a constructive, multivariate framework for assessing agreement between (generally misspecified) dynamic equilibrium models and data, which enables a complete second-order comparison of the dynamic properties of models and data. We use bootstrap algorithms to evaluate the significance of deviations between models and data, and we use goodness-of-fit criteria to produce estimators that optimize economically-relevant loss functions. We provide a detailed illustrative…