Maximum likelihood estimators in regression models with infinite variance innovations

被引：0

作者：

Vygantas Paulaauskas

Svetlozar T. Rachev

机构：

[1] Vilnius University,Department of Mathematics

[2] University of Karlsrhue,Institut of Statistics and Mathematical Economics, Department of Economics

[3] University of California,Department of Statistics and Applied Probability

来源：

Statistical Papers | 2003年 / 44卷

关键词：

60E07; 60P17; 62F12; 62J05; Autoregression; stable distributions; Lévy processes; maximum likelihood estimators;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

In this paper we consider the problem of maximum likelihood (ML) estimation in the classical AR(1) model with i.i.d. symmetric stable innovations with known characteristic exponent and unknown scale parameter. We present an approach that allows us to investigate the properties of ML estimators without making use of numerical procedures. Finally, we introduce a generalization to the multivariate case.

引用

页码：47 / 65

页数：18

共 25 条

[1]

Anderson T. W.(1959)On asymptotic distributions of estimates of parameters of stochastic difference equations Annals of Mathematical Statistics 30 676-687

[2]

Chan N. H.(1989)On the first order autoregressive process with infinite variance Econometric Theory 5 354-362

[3]

Tran L. T.(1983)Stable limits for partial sums of dependent random variables Annals of Probability 11 262-269

[4]

Davis R.(1986)Limit theory for the sample covariance and correlation functions of moving averages Annals of Statistics 14 543-558

[5]

Davis R.(2000)More on P-Stable Convex Sets in Banach Spaces J. Theoretical Probab. 13 39-64

[6]

Resnick S.(1984)α-stable limit theorems for sums of dependent random vectors Journal of Multivariate Analysis 29 219-251

[7]

Davydov Yu.(1988)Statistical analysis of cointegration vectors Journal of Economics and Dynamics and Control 12 231-254

[8]

Paulauskas V.(1943)On the statistical treatment of linear stochastic difference equations Econometrica 11 173-220

[9]

Račkauskas A.(1997)Asymptotic inference for AR(1) processes with (nonnormal) stable errors Journal of Mathematical Sciences 83 401-406

[10]

Jakubowski A.(1998)Cointegrated processes with infinite variance innovations Annals of Applied Probability 8 775-792

← 1 2 3 →