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无限方差下的不可逆移动平均时间序列AI 解读

The limiting distribution of the least squares estimate of the derived process of a noninvertible and nearly noninvertible moving average model with infinite variance innovations is established as a functional of a Lévy process. The form of the limiting law depends on the initial value of the innovation and the stable index α. This result enables one to perform asymptotic testing for the presence of a unit root for a noninvertible moving average model through the constructed…

错设线性回归中 Stein 规则与正部 Stein 规则估计量的比较AI 解读

In this paper, we examine the performance of the predictive risk of the Steinrule (SR) and positive-part Stein-rule (PSR) estimators when relevant regressors are omitted in the specified model. The exact formula of the predictive risk of the PSR estimator is derived, and the sufficient condition for the PSR estimator to dominate the SR estimator under a specification error is given. It is shown by numerical computation that the PSR estimator seems to be the best choice among…

近非平稳时间序列渐近功效计算的一点说明AI 解读

In the AR(2) model, with a double root at unity, we consider the asymptotic distribution of the likelihood ratio with respect to a nearly nonstationary alternative. It is shown how the distribution can be represented as a Radon-Nikodym derivative of an Ito process with respect to Brownian motion. Using this result, we point out how standard contiguity arguments can be applied to obtain a representation of the asymptotic power function in nearly nonstationary alternatives.

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自回归单位根拉格朗日乘数检验的一则说明AI 解读

It is shown that in a first-order mixed autoregressive moving average model, a Lagrange multiplier test for the autoregressive unit-root hypothesis can be inconsistent against stationary alternatives.

稳健模型选择与 M 估计AI 解读

This paper studies the qualitative robustness properties of the Schwarz information criterion (SIC) based on objective functions defining M -estimators. A definition of qualitative robustness appropriate for model selection is provided and it is shown that the crucial restriction needed to achieve robustness in model selection is the uniform boundedness of the objective function. In the process, the asymptotic performance of the SIC for general M -estimators is also studied.…

VPRT：相较 SPRT 的可变样本量序贯检验程序AI 解读

Under more general assumptions than those usually made in the sequential analysis literature, a variable-sample-size-sequential probability ratio test (VPRT) of two simple hypotheses is found that maximizes the expected net gain over all sequential decision procedures. In contrast, Wald and Wolfowitz [25] developed the sequential probability ratio test (SPRT) to minimize expected sample size, but their assumptions on the parameters of the decision problem were restrictive.…

信息矩阵奇异时随机前沿模型最大似然估计的渐近分布AI 解读

This paper investigates the asymptotic distribution of the maximum likelihood estimator in a stochastic frontier function when the firms are all technically efficient. For such a situation the true parameter vector is on the boundary of the parameter space, and the scores are linearly dependent. The asymptotic distribution of the maximum likelihood estimator is shown to be a mixture of certain truncated distributions. The maximum likelihood estimates for different parameters…

MA(1) 与局部水平模型最大似然估计量的分布AI 解读

Although considerable attention has recently been paid to the behavior of the maximum likelihood estimator of simple moving average models, little progress has been made in finding a good approximation to its distribution in cases where the process is close to being noninvertible. In this paper a method is produced that gives an excellent approximation to the distribution function, even in the case where the process is strictly noninvertible. Also studied is the related…

ARIMA 模型差分阶数的点最优检验AI 解读

Deciding the order of differencing is an important part in the specification of an autoregressive integrated moving average (ARIMA) mode. In most, though not all, cases this means deciding whether to use the original observations or their first differences. Common test procedures used in this context are some variants of autoregressive unit root tests. In these tests, one tests the null hypothesis that the order of differencing is one against the alternative that it is zero.…

多变量时间序列的多项式误差修正表示定理AI 解读

We consider a class of multivariate processes which, when differenced enough, yield covariance stationary processes whose determinants of the Wold representation have I as their only root on the unit circle. A representation theorem is proved for this class of processes that generalizes the Granger representation theorem.