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无限方差 ARMA 模型的加权最小绝对偏差估计AI 解读

For autoregressive moving average (ARMA) models with infinite variance innovations, quasi-likelihood-based estimators (such as Whittle estimators) suffer from complex asymptotic distributions depending on unknown tail indices. This makes statistical inference for such models difficult. In contrast, the least absolute deviations estimators (LADE) are more appealing in dealing with heavy tailed processes. In this paper, we propose a weighted least absolute deviations estimator…

计量经济推断的性质与逻辑：1942 年希尔赛德讲座AI 解读

This paper by Trygve Haavelmo was never submitted to a journal. The paper has been transcribed from Haavelmo's handwritten notes for a seminar given in 1942. The notes were kept by Haavelmo and were not known to exist by anyone else until Haavelmo died in 1999 and left his scientific remains to the Department of Economics, University of Oslo. The paper was retrieved from these personal archives by Olav Bjerkholt, who transcribed it from the original handwritten manuscript…

非线性过程分数阶单整参数的局部 Whittle 估计AI 解读

We study asymptotic properties of the local Whittle estimator of the long memory parameter for a wide class of fractionally integrated nonlinear time series models. In particular, we solve the conjecture posed by Phillips and Shimotsu (2004, Annals of Statistics 32, 656–692) for Type I processes under our framework, which requires a global smoothness condition on the spectral density of the short memory component. The formulation allows the widely used fractional…

遍历及几何遍历马尔可夫链的大数定律AI 解读

For use in asymptotic analysis of nonlinear time series models, we show that with (Xt,t ≥ 0) a (geometrically) ergodic Markov chain, the general version of the strong law of large numbers applies. That is, the average converges almost surely to the expectation of φ(Xt,Xt+1,…) irrespective of the choice of initial distribution of, or value of, X0. In the existing literature, the less general form has been studied.We thank Paolo Paruolo (the co-editor) and the referee for…

平稳模型的贝叶斯一致性AI 解读

In this paper, we provide a Doob-style consistency theorem for stationary models. Many applications involving Bayesian inference deal with non independent and identically distributed data, in particular, with stationary data. However, for such models, there is still a theoretical gap to be filled regarding the asymptotic properties of Bayesian procedures. The primary goal to be achieved is establishing consistency of the sequence of posterior distributions. Here we provide…

基于 VAR 近似的协整检验修正信息准则AI 解读

We consider the cointegration tests of Johansen (1988, Journal of Economic Dynamics and Control 12, 231–254; 1991, Econometrica 59, 1551–1580) when a vector autoregressive (VAR) process of order k is used to approximate a more general linear process with a possibly infinite VAR representation. Traditional methods to select the lag order, such as Akaike's information criterion (AIC) or the Bayesian information criterion, often lead to too parsimonious a model with the…

I(2) 模型协整秩的似然比检验AI 解读

This paper presents the likelihood ratio (LR) test for the number of cointegrating relations in the I(2) vector autoregressive model. It is shown that the asymptotic distribution of the LR test for the cointegration ranks is identical to the asymptotic distribution of the much applied test statistic based on the two-step estimation procedure in Johansen (1995, Econometric Theory 11, 25–59), Paruolo (1996, Journal of Econometrics 72, 313–356), and Rahbek, Kongsted, and…

一般误差分布下平稳一阶自回归模型预测的有限样本性质AI 解读

We study the properties of the multi-period-ahead least-squares forecast for the stationary AR(1) model under a general error distribution. We find that the forecast is unbiased up to O(T−1), where T is the in-sample size, regardless of the error distribution and that the mean squared forecast error, up to O(T−3/2), is robust against nonnormality.The author is grateful to the co-editor Paolo Paruolo and two anonymous referees for helpful comments. The author is solely…

单位根不变检验的可用信息AI 解读

This paper considers the information available to invariant unit root tests at and near the unit root. Because all invariant tests will be functions of the maximal invariant, the Fisher information in this statistic will be the available information. The main finding of the paper is that the available information for all tests invariant to a linear trend is zero at the unit root. This result applies for any sample size, over a variety of distributions and correlation…

缓慢变化回归变量与非线性趋势回归AI 解读

Slowly varying (SV) regressors arise commonly in empirical econometric work, particularly in the form of semilogarithmic regression and log periodogram regression. These regressors are asymptotically collinear. Usual regression formulas for asymptotic standard errors are shown to remain valid, but rates of convergence are affected and the limit distribution of the regression coefficients is shown to be one dimensional. Some asymptotic representations of partial sums of SV…

复数 ARMA 过程的实部AI 解读

In what follows all processes referred to are weakly stationary. Let us call the real part of a complex ARMA(p,q) process a Re CARMA(p,q) process. Every real ARMA(p,q) process can trivially be written as a Re CARMA(p,q) process. Provided the moment properties of complex linear processes are appropriately specified, the following inverse result is available: every Re CARMA(p,q) process is spectrally equivalent to a real ARMA(2p,p + q) process or some simpler process. Thus the…

马尔可夫状态转换 GARCH 过程的平稳性AI 解读

Generalized autoregressive conditional heteroskedasticity (GARCH) models with Markov-switching regimes are often used for volatility analysis of financial time series. Such models imply less persistence in the conditional variance than the standard GARCH model and potentially provide a significant improvement in volatility forecast. Nevertheless, conditions for asymptotic wide-sense stationarity have been derived only for some degenerated models. In this paper, we introduce…

多元 GARCH 模型的参数化AI 解读

This paper deals with issues of structure and parametrization of VECH models proposed in Bollerslev, Engle, and Wooldridge (1988) and Baba, Engle, Kraft, and Kroner (BEKK) models. Both general models and also restricted versions such as the widely used diagonal VECH (DVECH) and factor generalized autoregressive conditional heteroskedastic (F-GARCH) models are discussed. A simple algorithm is presented that checks whether a given VECH model may be cast as a BEKK model. It is…

单位根检验的稳健贝叶斯方法AI 解读

In this paper we deal with the identification of an autoregressive model for an observed time series and the detection of a unit root in its characteristic polynomial. This is a big issue concerned with distinguishing stationary time series from time series for which differencing is required to induce stationarity. We consider a Bayesian approach, and particular attention is devoted to the problem of the sensitivity of the standard Bayesian analysis with respect to the…

适应未知误差分布的非参数回归估计量AI 解读

We propose a new kernel estimator for nonparametric regression with unknown error distribution. We show that the proposed estimator is adaptive in the sense that it is asymptotically equivalent to the infeasible local likelihood estimator (Staniswalis, 1989, Journal of the American Statistical Association 84, 276–283; Fan, Farmen, and Gijbels, 1998, Journal of the Royal Statistical Society, Series B 60, 591–608; and Fan and Chen, 1999, Journal of the Royal Statistical…

向量自回归过程的单整阶数AI 解读

We show that the order of integration of a vector autoregressive process is equal to the difference between the multiplicity of the unit root in the characteristic equation and the multiplicity of the unit root in the adjoint matrix polynomial. The equivalence with the standard I(1) and I(2) conditions (Johansen, 1996, Likelihood-Based Inference in Cointegrated Vector Auto-Regressive Models) is proved.I am very grateful to Søren Johansen for his precious insights and his…

协方差平稳与单位根面板 AR(1) 模型的有效线性 GMM 估计AI 解读

This paper considers generalized method of moments (GMM) estimation of the inclusive panel AR(1) model that contains the covariance stationary panel AR(1) model and the panel AR(1) model with a unit root as special cases. The paper presents a two-step optimal linear GMM (OLGMM) estimator for the inclusive model that is asymptotically equivalent to the optimal nonlinear GMM estimator of Ahn and Schmidt (1997, Journal of Econometrics 76, 309–321) when the data are covariance…

重尾下线性估计量的效率：α 对称分布的卷积AI 解读

This paper focuses on the analysis of efficiency, peakedness, and majorization properties of linear estimators under heavy-tailedness assumptions. We demonstrate that peakedness and majorization properties of log-concavely distributed random samples continue to hold for convolutions of α-symmetric distributions with α > 1. However, these properties are reversed in the case of convolutions of α-symmetric distributions with α < 1.We show that the sample mean is the best linear…

二元失效时间数据的模型选择检验AI 解读

In this paper, we address two important issues in semiparametric survival model selection for censored data generated by the Archimedean copula family: method of estimating the parametric copulas and data reuse. We demonstrate that for selection among candidate copula models that might all be misspecified, estimators of the parametric copulas based on minimizing the selection criterion function may be preferred to other estimators. To handle the issue of data reuse, we put…

滞后解释变量冗余性的再考察AI 解读

In a recent Econometric Theory problem, it was demonstrated that in a conditionally heteroskedastic time series regression with martingale difference errors the use of lagged values of regressors as instruments may not increase the efficiency of estimation relative to ordinary least squares. We provide an example of an analogous phenomenon in a model with serially correlated errors, where the optimal instrumental variables estimator is asymptotically as efficient as the…

针对近积分过程的修正 KPSS 检验AI 解读

This note suggests a simple modification to the Kwiatkowski, Phillips, Schmidt, and Shin (1992, Journal of Econometrics , 54, 159–178) test (KPSS test) so that it is applicable to testing the null hypothesis of near integration against a unit root alternative. The modified KPSS test is shown not to suffer from the asymptotic size distortion problems of the original KPSS test that are described by Müller (2005, Journal of Econometrics 128, 195–213). The test also has good…

含时变协变量的混合风险率模型的非参数识别AI 解读

Most nonparametric identification results for the mixed proportional hazards model for single spell duration data depend crucially on the proportional hazards assumption. Here, it is shown that variation in covariates over time, combined with variation across observations, is sufficient to ensure identification without the proportional hazards assumption. The required variation over time is minimal, and the mixed hazards model is identified without the proportional hazards…

半参数截断回归模型的加权与两阶段最小二乘估计AI 解读

This paper provides a root-n consistent, asymptotically normal weighted least squares estimator of the coefficients in a truncated regression model. The distribution of the errors is unknown and permits general forms of unknown heteroskedasticity. Also provided is an instrumental variables based two-stage least squares estimator for this model, which can be used when some regressors are endogenous, mismeasured, or otherwise correlated with the errors. A simulation study…

具有稳定型误差的温和爆炸自回归的极限定理AI 解读

We discuss the limiting behavior of the serial correlation coefficient in mildly explosive autoregression, where the error sequence is in the domain of attraction of an α-stable law, α ∈ (0,2]. Therein, the autoregressive coefficient ρ = ρn > 1 is assumed to satisfy the condition ρn → 1 such that n(ρn − 1) → ∞ as n → ∞. In contrast to the vast majority of existing literature in the area, no specific form of ρ is required. We show that the serial correlation coefficient…