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无限方差创新下 ARMA 模型的参数估计AI 解读

We consider a standard ARMA process of the form $\phi(B)X_t = \theta(B)Z_t$, where the innovations $Z_t$ belong to the domain of attraction of a stable law, so that neither the $Z_t$ nor the $X_t$ have a finite variance. Our aim is to estimate the coefficients of $\phi$ and $\theta$. Since maximum likelihood estimation is not a viable possibility (due to the unknown form of the marginal density of the innovation sequence), we adopt the so-called Whittle estimator, based on…

自回归模型参数与阶数变化的检验AI 解读

The problem of testing whether or not a change has occurred in the parameter values and order of an autoregressive model is considered. It is shown that if the white noise in the AR model is weakly stationary with finite fourth moments, then under the null hypothesis of no changepoint, the normalized Gaussian likelihood ratio test statistic converges in distribution to the Gumbel extreme value distribution. An asymptotically distribution-free procedure for testing a change…

变点检测策略误报运行长度的一则注记AI 解读

A new proof is given to a known result on the average run length to false alarm of the Shiryayev-Roberts change-point detection policy when the observations are nonlattice. Via the approach of this new proof, the average run length to false alarm can be calculated in the lattice case and for the mixed-type Shiryayev-Roberts scheme.

用广义似然比统计量序贯检测变点AI 解读

We study sequential detection of a change-point using the generalized likelihood ratio statistic. For the special case of detecting a change in a normal mean with known variance, we give approximations to the average run lengths and compare our procedure to standard CUSUM tests and combined CUSUM-Shewhart tests. Several examples indicating extensions to problems involving multiple parameters are discussed.

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近积分 AR 过程中若干检验统计量的渐近分布AI 解读

Asymptotic distributions of some test statistics in near-integrated AR processes are studied. Some exact formulas for the distribution functions are given as well as approximative results obtained by saddlepoint approximation techniques.

非线性 ARCH 时间序列的非参数估计与识别：强收敛和渐近正态性AI 解读

We consider the estimation and identification of the functional structures of nonlinear econometric systems of the ARCH type. We employ nonparametric kernel estimates for the nonlinear functions characterizing the systems, and we establish strong consistency along with sharp rates of convergence under mild regularity conditions. We also prove the asymptotic normality of the estimates.

动态计量模型的检验、涵盖与模拟AI 解读

We define, in a dynamic framework, the notions of binding functions, images, reflecting sets, indirect identification, indirect information, and encompassing. We study the properties of the notion of encompassing when the true distribution does not necessarily belong to one of the two competing models of interest. In this context we propose various test procedures of the encompassing hypothesis. Some of these procedures are based on simulations, and some of them are linked…

基于 M 估计量的单位根检验AI 解读

This paper considers unit root tests based on M estimators. The asymptotic theory for these tests is developed. It is shown how the asymptotic distributions of the tests depend on nuisance parameters and how tests can be constructed that are invariant to these parameters. It is also shown that a particular linear combination of a unit root test based on the ordinary least-squares (OLS) estimator and on an M estimator converges to a normal random variate. The interpretation…

变量测量误差与协整AI 解读

In this article it is shown how the cointegration or joint trending behavior of economic time series helps to alleviate the errors in variables problem.

含 I(2) 过程的协整系统估计AI 解读

This paper considers the properties of systems likelihood procedures for cointegrated systems when the I(2) variables are present. Two alternative methods are proposed: one is based on the full system likelihood, whereas another is based on the subsystem likelihood. By eliminating all unit roots in the system by the use of prior information concerning the presence of unit roots, these procedures yield estimates whose asymptotic distributions are mixed normal, free from…

以稳定过程为备择的非平稳性新检验AI 解读

It was recently shown (Abadir, 1993b) that nonstationarity causes the limiting distributions of the Wald ( W ) and Lagrange multiplier ( LM ) statistics to become different from each other. This paper demonstrates that such a divergence between the two distributions can be used as an indicator of the presence of a unit root. A test based on this idea is devised by modifying the normalized autocorrelation coefficient ( NAC ). It is then shown to be an improvement on NAC in…

I(2) 变量协整的统计分析AI 解读

This paper discusses inference for I(2) variables in a VAR model. The estimation procedure suggested consists of two reduced rank regressions. The asymptotic distribution of the proposed estimators of the cointegrating coefficients is mixed Gaussian, which implies that asymptotic inference can be conducted using the χ 2 distribution. It is shown to what extent inference on the cointegration ranks can be conducted using the tables already prepared for the analysis of…

线性高斯状态空间模型的贝叶斯模型判别与贝叶斯因子AI 解读

SUMMARY It is shown how to discriminate between different linear Gaussian state space models for a given time series by means of a Bayesian approach which chooses the model that minimizes the expected loss. A practical implementation of this procedure requires a fully Bayesian analysis for both the state vector and the unknown hyperparameters and is carried out by Markov chain Monte Carlo methods. An application to some non-standard situations such as testing hypotheses on…

模型不确定性的评估与传播AI 解读

SUMMARY In most examples of inference and prediction, the expression of uncertainty about unknown quantities y on the basis of known quantities x is based on a model M that formalizes assumptions about how x and y are related. M will typically have two parts: structural assumptions S, such as the form of the link function and the choice of error distribution in a generalized linear model, and parameters θ whose meaning is specific to a given choice of S. It is common in…

通货膨胀率的长记忆：国际证据AI 解读

The authors examine monthly inflation rates of five industrial countries. The application of tests against stationarity as well as tests against a unit root yield contradictory results. Thus, fractional integration allowing for long memory is a plausible model. The authors discuss and apply the periodogram regression in order to estimate the difference parameters. For all countries, the authors find estimates significantly different from one as well as from zero. This is…

回归变量的非平稳性与实际利率行为检验AI 解读

This paper reexamines tests on the behavior of real interest rates in light of recent results which indicate that regressors are nonstationary and not strictly exogenous. Strong rejections of constancy of real interest rates that have been found previously in the literature are confirmed here. However, although there is some evidence here that real rates are negatively correlated with expected inflation, this result is not as strong as has been indicated by previous…

ARIMA 模型识别中不同定阶准则的比较AI 解读

The small-sample performance of several order-determination criteria for identification of ARIMA models is compared using simulated and economic data. The authors also demonstrate how the residual white-noise autoregressive order-determination criterion can be used to identify unit roots in nonstationary data.

协整系统中共同长记忆成分的估计AI 解读

The study of cointegration in large systems requires a reduction of their dimensionality. To achieve this, we propose to obtain the I(1) common factors in every subsystem and then analyze cointegration among them. In this article, a new way of estimating common long-memory components of a cointegrated system is proposed. The identification of these I(1) common factors is achieved by imposing that they be linear combinations of the original variables Xt , and that the…

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时变贴现因子现值模型的协整检验AI 解读

Abstract The paper analyses the impact of persistence and volatility in the discount rate in present‐value models on cointegration tests in levels and in logarithms. In simulations we find that the probability of not rejecting the null of no cointegration depends on the persistence of the discount rate process and can be very high when the expected returns process is highly persistent. In contrast, the cointegration tests are very robust with respect to the level of…

修正工具变量单位根检验的功效AI 解读

In this paper we investigate the power of Hall's (1989) instrumental variables tests for unit roots. A slight modification is made to Hall's t statistic so that the modified t statistic can be applied directly without encountering the possible negative standard error problem of Hall's original t statistic. The major finding is that the power curves of the instrumental variables tests are not monotonic functions of the autoregressive coefficient of the unit root models when…

小波方差的估计AI 解读

The wavelet variance decomposes the variance of a time series into components associated with different scales. We consider two estimators of the wavelet variance: the first based upon the discrete wavelet transform, and the second, called the maximal-overlap estimator, based upon a filtering interpretation of wavelets. We determine the large sample distribution for both estimators and show that the maximal-overlap estimator is more efficient for a class of processes of…