Hypermonogenic Functions and their Cauchy-Type Theorems

2004 ◽  
pp. 97-112 ◽  
Author(s):  
Sirkka-Liisa Eriksson ◽  
Heinz Leutwiler
Keyword(s):  
Cauchy Type ◽  
Hypermonogenic Functions

scholarly journals A family of the Cauchy type mean-value theorems

2005 ◽  
Vol 306 (2) ◽  
pp. 730-739 ◽  
Author(s):  
Josip E. Pečarić ◽  
Ivan Perić ◽  
H.M. Srivastava
Keyword(s):  
Mean Value ◽  
Cauchy Type ◽  
Mean Value Theorems

Cauchy-type integrals in domains with smooth boundary

1989 ◽  
Vol 44 (6) ◽  
pp. 866-867
Author(s):  
V. I. Morkunas
Keyword(s):  
Smooth Boundary ◽  
Cauchy Type ◽  
Cauchy Type Integrals

scholarly journals LIMIT THEORY FOR COINTEGRATED SYSTEMS WITH MODERATELY INTEGRATED AND MODERATELY EXPLOSIVE REGRESSORS

2009 ◽  
Vol 25 (2) ◽  
pp. 482-526 ◽  
Author(s):  
Tassos Magdalinos ◽  
Peter C.B. Phillips
Keyword(s):  
Multivariate Regression ◽  
Cauchy Type ◽  
Tail Behavior ◽  
Least Squares Regression ◽  
Moment Conditions ◽  
Limit Theory ◽  
Asymptotically Normal ◽  
Significant Bias ◽  
Integrated Or ◽  
Special Case

An asymptotic theory is developed for multivariate regression in cointegrated systems whose variables are moderately integrated or moderately explosive in the sense that they have autoregressive roots of the form ρni = 1 + ci/nα, involving moderate deviations from unity when α ∈ (0, 1) and ci ∈ ℝ are constant parameters. When the data are moderately integrated in the stationary direction (with ci < 0), it is shown that least squares regression is consistent and asymptotically normal but suffers from significant bias, related to simultaneous equations bias. In the moderately explosive case (where ci > 0) the limit theory is mixed normal with Cauchy-type tail behavior, and the rate of convergence is explosive, as in the case of a moderately explosive scalar autoregression (Phillips and Magdalinos, 2007, Journal of Econometrics 136, 115–130). Moreover, the limit theory applies without any distributional assumptions and for weakly dependent errors under conventional moment conditions, so an invariance principle holds, unlike the well-known case of an explosive autoregression. This theory validates inference in cointegrating regression with mildly explosive regressors. The special case in which the regressors themselves have a common explosive component is also considered.

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