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扩展参数空间与相似性权重下的空间自回归AI 解读

We provide in this paper asymptotic theory for a spatial autoregressive model (SAR, henceforth) in which the spatial coefficient, λ, is allowed to be less than or equal to unity, as well as consistent with a local to unit root (LUR) model and of the moderate integration (MI) from unity type, and the spatial weights are allowed to be similarity-based and data driven. Other special cases of our setting include the random walk, a model in which all the weights are equal, the…

金融指数峰度的时间聚合效应AI 解读

Indices of financial returns typically display sample kurtosis that declines towards the Gaussian value 3 as the sampling interval increases. This paper uses stochastic unit root (STUR) and continuous time analysis to explain the phenomenon. Limit theory for the sample kurtosis reveals that STUR specifications provide two sources of excess kurtosis, both of which decline with the sampling interval. Limiting kurtosis is shown to be random and is a functional of the limiting…

局部随机单位根回归理论与金融收益指数样本相关系数的不稳定性AI 解读

Summary It is well known that the sample correlation coefficient between many financial return indices exhibits substantial variation on any reasonable sampling window. This stylised fact contradicts a unit root model for the underlying processes in levels, as the statistic converges in probability to a constant under this modeling scheme. In this paper, we establish asymptotic theory for regression in local stochastic unit root (LSTUR) variables. An empirical application…

混合随机局部单位根模型AI 解读

Two approaches have dominated formulations designed to capture small departures from unit root autoregressions. The first involves deterministic departures that include local-to-unity (LUR) and mildly (or moderately) integrated (MI) specifications where departures shrink to zero as the sample size n→∞. The second approach allows for stochastic departures from unity, leading to stochastic unit root (STUR) specifications. This paper introduces a hybrid local stochastic unit…

内生随机单位根模型中的 IV 与 GMM 推断AI 解读

Lieberman and Phillips (2017; LP) introduced a multivariate stochastic unit root (STUR) model, which allows for random, time varying local departures from a unit root (UR) model, where nonlinear least squares (NLLS) may be used for estimation and inference on the STUR coefficient. In a structural version of this model where the driver variables of the STUR coefficient are endogenous, the NLLS estimate of the STUR parameter is inconsistent, as are the corresponding estimates…

多元随机单位根模型及其衍生品定价应用AI 解读

This paper extends recent findings of Lieberman and Phillips (2014) on stochastic unit root (STUR) models to a multivariate case including asymptotic theory for estimation of the model’s parameters. The extensions are useful for applications of STUR modeling and because they lead to a generalization of the Black–Scholes formula for derivative pricing. In place of the standard assumption that the price process follows a geometric Brownian motion, we derive a new form of the…

平稳高斯过程记忆参数极大似然估计的渐近理论AI 解读

Consistency, asymptotic normality, and efficiency of the maximum likelihood estimator for stationary Gaussian time series were shown to hold in the short memory case by Hannan (1973, Journal of Applied Probability 10, 130–145) and in the long memory case by Dahlhaus (1989, Annals of Statistics 34, 1045–1047). In this paper we extend these results to the entire stationarity region, including the case of antipersistence and noninvertibility.

基于相似性的预测方法AI 解读

Assume we are asked to predict a real-valued variable yt based on certain characteristics , and on a database consisting of for i=1,...,n. Analogical reasoning suggests to combine past observations of x and y with the current values of x to generate an assessment of y by similarity-weighted averaging. Specifically, the predicted value of y, , is the weighted average of all previously observed values yi, where the weight of yi, for every i=1,...,n, is the similarity between…

经验相似性模型的渐近理论AI 解读

We consider the stochastic process $Y_t = \sum\nolimits_{i < t} {s_w } (x_t ,x_i)Y_i /\sum\nolimits_{i < t} {s_w } (x_t ,x_i) + \varepsilon _t$ , t = 2, …, n , where s w ( x t , x i ) is a similarity function between the t th and the i th observations and { ε t } is a random disturbance term. This process was originally axiomatized by Gilboa, Lieberman, and Schmeidler (2006, Review of Economics and Statistics 88, 433–444) as a way by which agents, or…

广义自回归条件相关模型AI 解读

This paper develops a generalized autoregressive conditional correlation (GARCC) model when the standardized residuals follow a random coefficient vector autoregressive process. As a multivariate generalization of the Tsay (1987, Journal of the American Statistical Association 82, 590–604) random coefficient autoregressive (RCA) model, the GARCC model provides a motivation for the conditional correlations to be time varying. GARCC is also more general than the Engle (2002,…

长记忆过程自协方差函数的完整渐近级数AI 解读

An infinite-order asymptotic expansion is given for the autocovariance function of a general stationary long-memory process with memory parameter d[set membership, variant](-1/2,1/2). The class of spectral densities considered includes as a special case the stationary and invertible ARFIMA(p,d,q) model. The leading term of the expansion is of the order O(1/k1-2d), where k is the autocovariance order, consistent with the well known power law decay for such processes, and is…

摘要暂缺

经验相似性AI 解读

An agent is asked to assess a real-valued variable Yp based on certain characteristics Xp = (Xp-super-1, ..., Xp-super-m), and on a database consisting of Xi-super-1, ... Xi-super-m, Yi) for i = 1, ..., n. A possible approach to combine past observations of X and Y with the current values of X to generate an assessment of Y is similarity-weighted averaging. It suggests that the predicted value of Y, Ȳp-super-s, be the weighted average of all previously observed values Yi,…

This paper derives second‐order expansions for the distributions of the Whittle and profile plug‐in maximum likelihood estimators of the fractional difference parameter in the ‘Autoregressive Fractionally Integrated Moving Average of order (0, d, 0)’ with unknown mean and variance. Both estimators are shown to be second‐order pivotal. This extends earlier findings of Lieberman and Phillips (2004a, Econometric Theory, 20, 464–84), who derived expansions for the Gaussian…

平稳长记忆高斯时间序列中 Whittle 最大似然估计量的有效 Edgeworth 展开AI 解读

In this paper, we prove the validity of an Edgeworth expansion to the distribution of the Whittle maximum likelihood estimator for stationary long-memory Gaussian models with unknown parameter . The error of the ( s − 2)-order expansion is shown to be o ( n −( s −2)/2 )—the usual independent and identically distributed rate—for a wide range of models, including the popular ARFIMA( p , d , q ) models. The expansion is valid under mild assumptions on the behavior of the…

长记忆模型的代入估计AI 解读

We consider the Gaussian ARFIMA(j,d,l) model, with spectral density and an unknown mean . For this class of models, the n−1-normalized information matrix of the full parameter vector, (μ,θ), is asymptotically degenerate. To estimate θ, Dahlhaus (1989, Annals of Statistics 17, 1749–1766) suggested using the maximizer of the plug-in log-likelihood, , where is any n(1−2d)/2-consistent estimator of μ. The resulting estimator is a plug-in maximum likelihood estimator (PMLE). This…

分数差分参数极大似然估计量的分布展开AI 解读

The maximum likelihood estimator (MLE) of the fractional difference parameter in the Gaussian ARFIMA(0,d,0) model is well known to be asymptotically N(0,6/π2). This paper develops asymptotic expansions to the distribution of this statistic under the assumption of a known unit variance. The correction term for the density is shown to be independent of d, so that the MLE is second-order pivotal for d. This feature of the MLE is unusual, at least in time series contexts.…

平稳高斯强相依过程参数最大似然估计的有效渐近展开AI 解读

We establish the validity of an Edgeworth expansion to the distribution of the maximum likelihood estimator of the parameter of a stationary, Gaussian, strongly dependent process. The result covers ARFIMA-type models, including fractional Gaussian noise. The method of proof consists of three main ingredients: (i) verification of a suitably modified version of Durbin's general conditions for the validity of the Edgeworth expansion to the joint density of the log-likelihood…

时间序列统计推断的渐近理论AI 解读

Modern time series econometrics involves a diversity of models. In addition to the more traditional vector autoregressive (VAR) and autoregressive moving average (ARMA) systems, cointegration and unit root models are in widespread use for macroeconomic data, nonlinear and non-Gaussian models are popular for financial data, and long memory models are becoming more common in both macroeconomic and financial applications. Much econometric thought relates to issues of estimation…

长程依赖下样本自相关函数的有效 Edgeworth 展开AI 解读

We prove in this paper the validity of an Edgeworth expansion to the joint distribution of the sample autocorrelations of a stationary Gaussian long memory process. The method of proof relies on a verification of the suitably modified conditions for the validity of a multivariate Edgeworth expansion of Durbin (1980, Biometrika 67, 311–333). A simulation study proves the expansion to be useful and accurate.

混合线性模型的小样本推断改进：Bartlett 校正与调整似然AI 解读

Summary The mixed linear model is a popular method for analysing unbalanced repeated measurement data. The classical statistical tests for parameters in this model are based on asymptotic theory that is unreliable in the small samples that are often encountered in practice. For testing a given fixed effect parameter with a small sample, we develop and investigate refined likelihood ratio (LR) tests. The refinements considered are the Bartlett correction and use of the…

ARFIMA 模型中基于似然的小样本推断AI 解读

The autoregressive fractionally integrated moving average (ARFIMA) model has become a popular approach for analyzing time series that exhibit long-range dependence. For the Gaussian case, there have been substantial advances in the area of likelihood-based inference, including development of the asymptotic properties of the maximum likelihood estimates and formulation of procedures for their computation. Small-sample inference, however, has not to date been studied. Here we…

摘要暂缺

非正态性的影响AI 解读

A typical statistic encountered can be characterized as a ratio of polynomials of arbitrary degree in a random vector. This vector may possess any admissible cumulant structure. We provide in this paper general formulae for the effect of nonnormality on the density and distribution functions of this ratio. The results appear in terms of generalized cumulants, a theory developed by McCullagh (1984, Biometrika 71, 461–476). With the aid of suitable notation, the expressions…