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函数型时间序列共同趋势的统计推断AI 解读

We study statistical inference on unit roots and cointegration for time series in a Hilbert space. We develop statistical inference on the number of common stochastic trends embedded in the time series, that is, the dimension of the nonstationary subspace. We also consider tests of hypotheses on the nonstationary and stationary subspaces themselves. The Hilbert space can be of an arbitrarily large dimension, and our methods remain asymptotically valid even when the time…

存在偏差时的自助法推断AI 解读

We consider bootstrap inference for estimators which are (asymptotically) biased. We show that, even when the bias term cannot be consistently estimated, valid inference can be obtained by proper implementations of the bootstrap. Specifically, we show that the prepivoting approach of Beran (1987, 1988), originally proposed to deliver higher-order refinements, restores bootstrap validity by transforming the original bootstrap p-value into an asymptotically uniform random…

任意阶自回归模型中近乎有效的单位根似然比检验AI 解读

We study large sample properties of likelihood ratio tests of the unit-root hypothesis in an autoregressive model of arbitrary order. Earlier research on this testing problem has developed likelihood ratio tests in the autoregressive model of order 1, but resorted to a plug-in approach when dealing with higher-order models. In contrast, we consider the full model and derive the relevant large sample properties of likelihood ratio tests under a local-to-unity asymptotic…

向分数布朗运动导数的弱收敛AI 解读

It is well known that, under suitable regularity conditions, the normalized fractional process with fractional parameter d converges weakly to fractional Brownian motion (fBm) for $d>\frac {1}{2}$ . We show that, for any nonnegative integer M , derivatives of order $m=0,1,\dots ,M$ of the normalized fractional process with respect to the fractional parameter d jointly converge weakly to the corresponding derivatives of fBm. As an illustration, we apply the results to the…

线性回归中适当聚类层级的检验AI 解读

The overwhelming majority of empirical research that uses cluster-robust inference assumes that the clustering structure is known, even though there are often several possible ways in which a dataset could be clustered. We propose two tests for the correct level of clustering in regression models. One test focuses on inference about a single coefficient, and the other on inference about two or more coefficients. We provide both asymptotic and wild bootstrap implementations.…

快速可靠的聚类稳健刀切与自助推断方法AI 解读

Summary We provide computationally attractive methods to obtain jackknife‐based cluster‐robust variance matrix estimators (CRVEs) for linear regression models estimated by least squares. We also propose several new variants of the wild cluster bootstrap, which involve these CRVEs, jackknife‐based bootstrap data‐generating processes, or both. Extensive simulation experiments suggest that the new methods can provide much more reliable inferences than existing ones in cases…

函数型时间序列非平稳子空间维数的推断AI 解读

We propose a statistical procedure to determine the dimension of the nonstationary subspace of cointegrated functional time series taking values in the Hilbert space of square-integrable functions defined on a compact interval. The procedure is based on sequential application of a proposed test for the dimension of the nonstationary subspace. To avoid estimation of the long-run covariance operator, our test is based on a variance ratio-type statistic. We derive the…

聚类稳健推断：实证实践指南AI 解读

Methods for cluster-robust inference are routinely used in economics and many other disciplines. However, it is only recently that theoretical foundations for the use of these methods in many empirically relevant situations have been developed. In this paper, we use these theoretical results to provide a guide to empirical practice. We do not attempt to present a comprehensive survey of the (very large) literature. Instead, we bridge theory and practice by providing a…

可能存在水平突变时的积分阶数半参数检验AI 解读

Lobato and Robinson developed semiparametric tests for the null hypothesis that a series is weakly autocorrelated, or I(0), about a constant level, against fractionally integrated alternatives. These tests have the advantage that the user is not required to specify a parametric model for any weak autocorrelation present in the series. We extend this approach in two distinct ways. First, we show that it can be generalized to allow for testing of the null hypothesis that a…

异方差分数单整时间序列模型中的自适应推断AI 解读

We consider estimation and inference in fractionally integrated time series models driven by shocks which can display conditional and unconditional heteroscedasticity of unknown form. Although the standard conditional sum-of-squares (CSS) estimator remains consistent and asymptotically normal in such cases, unconditional heteroscedasticity inflates its variance matrix by a scalar quantity, λ>1, thereby inducing a loss in efficiency relative to the unconditionally…

多维聚类下的野生自助法与渐近推断AI 解读

We study two cluster-robust variance estimators (CRVEs) for regression models with clustering in two dimensions and give conditions under which t-statistics based on each of them yield asymptotically valid inferences. In particular, one of the CRVEs requires stronger assumptions about the nature of the intra-cluster correlations. We then propose several wild bootstrap procedures and state conditions under which they are asymptotically valid for each type of t-statistic.…

含确定性趋势的分数阶时间序列模型：截断平方和估计AI 解读

We consider truncated (or conditional) sum of squares estimation of a parametric model composed of a fractional time series and an additive generalized polynomial trend. Both the memory parameter, which characterizes the behavior of the stochastic component of the model, and the exponent parameter, which drives the shape of the deterministic component, are considered not only unknown real numbers but also lying in arbitrarily large (but finite) intervals. Thus, our model…

聚类误差下的渐近理论与野生自助推断AI 解读

We study inference based on cluster-robust variance estimators for regression models with clustered errors, focusing on the wild cluster bootstrap. We state conditions under which asymptotic and bootstrap tests and confidence intervals are asymptotically valid. These conditions put limits on the rates at which the cluster sizes can increase as the number of clusters tends to infinity. We also derive Edgeworth expansions for the asymptotic and bootstrap test statistics.…

含一般确定性项的协整向量自回归模型AI 解读

In the cointegrated vector autoregression (CVAR) literature, deterministic terms have until now been analyzed on a case-by-case, or as-needed basis. We give a comprehensive unified treatment of deterministic terms in the additive model Xt=γZt+Yt, where Zt belongs to a large class of deterministic regressors and Yt is a zero-mean CVAR. We suggest an extended model that can be estimated by reduced rank regression, and give a condition for when the additive and extended models…

未知形式异方差下分数阶时间序列的准极大似然与 bootstrap 推断AI 解读

We consider the problem of conducting estimation and inference on the parameters of univariate heteroskedastic fractionally integrated time series models. We first extend existing results in the literature, developed for conditional sum-of-squares estimators in the context of parametric fractional time series models driven by conditionally homoskedastic shocks, to allow for conditional and unconditional heteroskedasticity both of a quite general and unknown form. Global…

初始值对非平稳分数时间序列条件平方和估计的影响AI 解读

In this paper, we analyze the influence of observed and unobserved initial values on the bias of the conditional maximum likelihood or conditional sum-of-squares (CSS, or least squares) estimator of the fractional parameter, d , in a nonstationary fractional time series model. The CSS estimator is popular in empirical work due, at least in part, to its simplicity and its feasibility, even in very complicated nonstationary models. We consider a process, X t , for which data…

异方差ARFIMA模型的分数单整自助得分检验及商品价格应用AI 解读

Empirical evidence from time series methods which assume the usual I(0)/I(1) paradigm suggests that the efficient market hypothesis, stating that spot and futures prices of a commodity should co-integrate with a unit slope on futures prices, does not hold. However, these statistical methods are known to be unreliable if the data are fractionally integrated. Moreover, spot and futures price data tend to display clear patterns of time-varying volatility which also has the…

VAR 模型中协整秩的改进似然比检验AI 解读

We suggest improved tests for cointegration rank in the vector autoregressive (VAR) model and develop asymptotic distribution theory and local power results. The tests are (quasi-)likelihood ratio tests based on a Gaussian likelihood, but as usual the asymptotic results do not require normally distributed innovations. Our tests differ from existing tests in two respects. First, instead of basing our tests on the conditional (with respect to the initial observations)…

分数阶单位根与协整检验的数值分布函数AI 解读

SUMMARY We calculate, by simulations, numerical asymptotic distribution functions of likelihood ratio tests for fractional unit roots and cointegration rank. Because these distributions depend on a real‐valued parameter b which must be estimated, simple tabulation is not feasible. Partly owing to the presence of this parameter, the choice of model specification for the response surface regressions used to obtain the numerical distribution functions is more involved than is…

分数型函数中心极限定理的必要矩条件AI 解读

We discuss the moment condition for the fractional functional central limit theorem (FCLT) for partial sums of x t = Δ − d u t , where $d\, \in \,\left({ - {1 \over 2}\,,\,{1 \over 2}} \right)$ is the fractional integration parameter and u t is weakly dependent. The classical condition is existence of q ≥ 2 and $q\, > \,\left( {d\, + \,{1 \over 2}} \right)^{ - 1} $ moments of the innovation sequence. When d is close to $ - {1 \over 2}$ this moment condition is very strong.…

受扰动分数过程的局部多项式 Whittle 估计AI 解读

We propose a semiparametric local polynomial Whittle with noise estimator of the memory parameter in long memory time series perturbed by a noise term which may be serially correlated. The estimator approximates the log-spectrum of the short-memory component of the signal as well as that of the perturbation by two separate polynomials. Including these polynomials we obtain a reduction in the order of magnitude of the bias, but also inflate the asymptotic variance of the long…

弱分数协整的完全修正窄带最小二乘估计AI 解读

We consider estimation of the cointegrating relation in the weak fractional cointegration model, where the strength of the cointegrating relation (difference in memory parameters) is less than one‐half. A special case is the stationary fractional cointegration model, which has found important applications recently, especially in financial economics. Previous research on this model has considered a semi‐parametric narrow‐band least squares (NBLS) estimator in the frequency…

隐含波动率对外汇、股票与债券波动率及跳跃预测的作用AI 解读

We study the forecasting of future realized volatility in the foreign exchange, stock, and bond markets from variables in our information set, including implied volatility backed out from option prices. Realized volatility is separated into its continuous and jump components, and the heterogeneous autoregressive (HAR) model is applied with implied volatility as an additional forecasting variable. A vector HAR (VecHAR) model for the resulting simultaneous system is…

非平稳分数自回归模型的似然推断AI 解读

This paper discusses model-based inference in an autoregressive model for fractional processes which allows the process to be fractional of order d or d-b. Fractional differencing involves infinitely many past values and because we are interested in nonstationary processes we model the data X1,...,XT given the initial values , as is usually done. The initial values are not modeled but assumed to be bounded. This represents a considerable generalization relative to previous…