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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…

最小截尾平方估计量成为最大似然估计量的一种模型AI 解读

Abstract The least trimmed squares (LTS) estimator is a popular robust regression estimator. It finds a subsample of h ‘good’ observations among n observations and applies least squares on that subsample. We formulate a model in which this estimator is maximum likelihood. The model has ‘outliers’ of a new type, where the outlying observations are drawn from a distribution with values outside the realized range of h ‘good’, normal observations. The LTS estimator is found to…

时间序列线性回归中 M 估计量的有界性AI 解读

We show boundedness in probability uniformly in sample size of a general M-estimator for multiple linear regression in time series. The positive criterion function for the M-estimator is assumed lower semicontinuous and sufficiently large for large argument. Particular cases are the Huber-skip and quantile regression. Boundedness requires an assumption on the frequency of small regressors. We show that this is satisfied for a variety of deterministic and stochastic…

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…

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…

模型发现与 Haavelmo 的学术遗产AI 解读

Trygve Haavelmo’s Probability Approach aimed to implement economic theories, but he later recognized their incompleteness. Although he did not explicitly consider model selection, we apply it when theory-relevant variables, { X t }, are retained without selection while selecting other candidate variables, { W t }. Under the null that the { W t } are irrelevant, by orthogonalizing with respect to the { X t }, the estimator distributions of the X t ’s parameters are unaffected…

数据线性变换下共同趋势的渐近不变性AI 解读

It is well known that if Xt is a nonstationary process and Yt is a linear function of Xt, then cointegration of Yt implies cointegration of Xt. We want to find an analogous result for common trends if Xt is generated by a finite order VAR with i.i.d. (0,Ωx) errors εxt. We first show that Yt has an infinite order VAR representation in terms of its white noise prediction errors, εyt, which are a linear process in εxt, the prediction error for Xt. We then apply this result to…

简单随机系数自回归模型中的最小二乘估计AI 解读

The question we discuss is whether a simple random coefficient autoregressive model with infinite variance can create the long swings, or persistence, which are observed in many macroeconomic variables. The model is defined by yt=stρyt−1+εt,t=1,…,n, where st is an i.i.d. binary variable with p=P(st=1), independent of εt i.i.d. with mean zero and finite variance. We say that the process yt is persistent if the autoregressive coefficient ρˆn of yt on yt−1 is close to one. We…

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.…

协整向量自回归模型中的若干识别问题AI 解读

The paper analyses some identification problems in the cointegrated vector autoregressive model. A criteria for identification by linear restrictions on individual relations is given. The asymptotic distribution of the estimators of [alpha] and [beta] is derived when they are identified by linear restrictions on [beta], and when they are identified by linear restrictions on [alpha]. It it shown that, in the latter case, a component of is asymptotically Gaussian. Finally we…

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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…

一类分数阶过程向量自回归模型的表示理论AI 解读

Based on an idea of Granger (1986, Oxford Bulletin of Economics and Statistics 48, 213–228), we analyze a new vector autoregressive model defined from the fractional lag operator 1 − (1 − L ) d . We first derive conditions in terms of the coefficients for the model to generate processes that are fractional of order zero. We then show that if there is a unit root, the model generates a fractional process X t of order d , d > 0, for which there are vectors β so that β‼ X t is…

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含 I(2) 变量的 VAR 协整参数约束检验札记AI 解读

We give a brief introduction to the vector autoregressive model for cointegrated I(2) variables and show how some plausible economic relations can be formulated in the I(2) framework in such a way that likelihood ratio tests for their validity are asymptotically χ2 distributed.The authors thank Paolo Paruolo for helpful comments and the ESF for financial support in the framework of the EMM network.

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协整关系检验的 Bartlett 修正因子AI 解读

Likelihood ratio tests for restrictions on cointegrating vectors are asymptotically χ 2 distributed. For some values of the parameters this asymptotic distribution does not give a good approximation to the finite sample distribution. In this paper we derive the Bartlett correction factor for the likelihood ratio test and show by some simulation experiments that it can be a useful tool for making inference.

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季节性协整的似然分析AI 解读

The error correction model for seasonal cointegration is analyzed. Conditions are found under which the process is integrated of order 1 and cointegrated at seasonal frequency, and a representation theorem is given. The likelihood function is analyzed and the numerical calculation of the maximum likelihood estimators is discussed. The asymptotic distribution of the likelihood ratio test for cointegrating rank is given. It is shown that the estimated cointegrating vectors are…

部分系统中协整秩的渐近推断AI 解读

The likelihood ratio test for cointegrating rank is analyzed for partial (or conditional) systems in the vector autoregressive error-correction model. Under the assumption of weak exogeneity for the cointegrating parameters, the asymptotic distributions are given and tables of critical values are provided. A discussion is given of some of the assumptions of the model, why they are needed, and how they are tested.

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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…

长期与短期结构的识别：ISLM 模型应用AI 解读

In this paper we discuss the problem of identification in a model with cointegration. It is pointed out that there is an identification problem for both long-run parameters and short-run parameters. The identification of the equations and the cointegrating relations is achieved by linear restrictions on the parameters and a criterion for a statistical model to be identifying is given. We also define empirical identification of an estimated structure. A switching algorithm…