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相关时间序列的预测AI 解读

ABSTRACT A collection of time series are “related” if they follow similar stochastic processes and/or they are statistically dependent. This paper proposes a related time series (RTS) forecasting model that exploits these relationships. The model's foundation is a set of univariate Gaussian autoregressions, one for each series, which are then augmented to incorporate stochastic volatility, heavy‐tailed innovations, additive outliers, time‐varying parameters and common…

广义局部单位根模型AI 解读

We introduce a generalization of the popular local‐to‐unity model of time series persistence by allowing for p autoregressive (AR) roots and p − 1 moving average (MA) roots close to unity. This generalized local‐to‐unity model, GLTU( p ), induces convergence of the suitably scaled time series to a continuous time Gaussian ARMA( p , p − 1) process on the unit interval. Our main theoretical result establishes the richness of this model class, in the sense that it can well…

近似加权风险最小的无偏估计AI 解读

Consider a small-sample parametric estimation problem, such as the estimation of the coefficient in a Gaussian AR(1). We develop a numerical algorithm that determines an estimator that is nearly (mean or median) unbiased, and among all such estimators, comes close to minimizing a weighted average risk criterion. We also apply our generic approach to the median unbiased estimation of the degree of time variation in a Gaussian local-level model, and to a quantile unbiased…

非标准计量问题中置信集的可信性AI 解读

Confidence intervals are commonly used to describe parameter uncertainty. In nonstandard problems, however, their frequentist coverage property does not guarantee that they do so in a reasonable fashion. For instance, confidence intervals may be empty or extremely short with positive probability, even if they are based on inverting powerful tests. We apply a betting framework to formalize the “reasonableness ” of confidence intervals as descriptions of parameter uncertainty,…

原假设下存在干扰参数时的近最优检验AI 解读

This paper considers nonstandard hypothesis testing problems that involve a nuisance parameter. We establish an upper bound on the weighted average power of all valid tests, and develop a numerical algorithm that determines a feasible test with power close to the bound. The approach is illustrated in six applications: inference about a linear regression coefficient when the sign of a control coefficient is known; small sample inference about the difference in means from two…

强自相关时间序列的 HAC 修正AI 解读

Applied work routinely relies on heteroscedasticity and autocorrelation consistent (HAC) standard errors when conducting inference in a time series setting. As is well known, however, these corrections perform poorly in small samples under pronounced autocorrelations. In this article, I first provide a review of popular methods to clarify the reasons for this failure. I then derive inference that remains valid under a specific form of strong dependence. In particular, I…

结构断点前后参数的推断AI 解读

Consider inference about the pre and post break value of a scalar parameter in a time series model with a single break at an unknown date. Unless the break is large, treating the break date estimated by least squares as the true break date leads to substantially oversized tests and confidence intervals. To develop a suitable alternative, we first establish convergence to a Gaussian process limit experiment. We then determine a nearly weighted average power maximizing test in…

低频稳健协整检验AI 解读

Standard inference in cointegrating models is fragile because it relies on an assumption of an I(1) model for the common stochastic trends, which may not accurately describe the data’s persistence. This paper considers low-frequency tests about cointegrating vectors under a range of restrictions on the common stochastic trends. We quantify how much power can potentially be gained by exploiting correct restrictions, as well as the magnitude of size distortions if such…

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部分不稳定广义矩模型中的有效推断AI 解读

This paper considers time series Generalized Method of Moments (GMM) models where a subset of the parameters are time varying. We focus on an empirically relevant case with moderately large instabilities, which are well approximated by a local asymptotic embedding that does not allow the instability to be detected with certainty, even in the limit. We show that for many forms of the instability and a large class of GMM models, usual GMM inference on the subset of stable…

一致区分 I(0) 与 I(1) 过程的不可能性AI 解读

An I(0) process is commonly defined as a process that satisfies a functional central limit theorem, i.e., whose scaled partial sums converge weakly to a Wiener process, and an I(1) process as a process whose first differences are I(0). This paper establishes that with this definition, it is impossible to consistently discriminate between I(0) and I(1) processes. At the same time, on a more constructive note, there exist consistent unit root tests and also nontrivial…

稳健长期方差估计理论AI 解读

Long-run variance estimation can typically be viewed as the problem of estimating the scale of a limiting continuous time Gaussian process on the unit interval. A natural benchmark model is given by a sample that consists of equally spaced observations of this limiting process. The paper analyzes the asymptotic robustness of long-run variance estimators to contaminations of this benchmark model. It is shown that any equivariant long-run variance estimator that is consistent…

线性时间序列回归中单一突变日期的置信集AI 解读

This paper considers the problem of constructing confidence sets for the date of a single break in a linear time series regression. We establish analytically and by small sample simulation that the currently standard method in econometrics to construct such confidence intervals has a coverage rate far below nominal levels when breaks are of moderate magnitude. Given that breaks of moderate magnitude are a theoretically and empirically highly relevant phenomenon, we proceed…

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回归系数一般持续性时变的有效检验AI 解读

There are a large number of tests for instability or breaks in coefficients in regression models designed for different possible departures from the stable model. We make two contributions to this literature. First, we consider a large class of persistent breaking processes that lead to asymptotically equivalent efficient tests. Our class allows for many or relatively few breaks, clustered breaks, regularly occurring breaks, or smooth transitions to changes in the regression…