CONDITIONAL MOMENTS AND LINEAR-REGRESSION FOR STABLE RANDOM-VARIABLES

[摘要] Jointly alpha-stable random variables with index 0 < alpha < 2 have only finite moments of order less than alpha, but their conditional moments can be higher than alpha. We provide conditions for this to happen and use the existence of the conditional moments to study the regression E(X2\X1 = x). We show that if (X1, X2) is a symmetric alpha-stable random vector, then under appropriate conditions, the regression is well-defined even when alpha less-than-or-equal-to 1 and is linear in x. The results are applied to different classes of symmetric alpha-stable processes.

[发布日期] 1991-12-01

[关键词] STABLE RANDOM VECTORS;LINEAR REGRESSION;AUTOREGRESSIVE MODELS;MOVING AVERAGES;SUB-GAUSSIAN VECTORS;HARMONIZABLE VECTORS