TY - JOUR
T1 - A note on the relationship between GARCH and symmetric stable processes
AU - Groenendijk, Patrick A.
AU - Lucas, André
AU - de Vries, Casper G.
PY - 1995
Y1 - 1995
N2 - This note provides some explanations and extensions for the interesting results in Ghose and Kroner (1995). Specifically, we address the following points: (1) It is shown that the stable distribution and the stationary ARCH distributions are partially nested with respect to their tail shapes; (2) A novel interpretation of the McCulloch estimator is developed from the vantage point of extreme value theory; (3) This interpretation not only explains the apparent bias in some of the reported estimates, but it also helps in remedying the problem. Taken together, all three points reinforce the main conclusion of Ghose and Kroner.
AB - This note provides some explanations and extensions for the interesting results in Ghose and Kroner (1995). Specifically, we address the following points: (1) It is shown that the stable distribution and the stationary ARCH distributions are partially nested with respect to their tail shapes; (2) A novel interpretation of the McCulloch estimator is developed from the vantage point of extreme value theory; (3) This interpretation not only explains the apparent bias in some of the reported estimates, but it also helps in remedying the problem. Taken together, all three points reinforce the main conclusion of Ghose and Kroner.
KW - GARCH
KW - Stable distributions
KW - Tail index estimators
UR - http://www.scopus.com/inward/record.url?scp=0003191872&partnerID=8YFLogxK
U2 - 10.1016/0927-5398(95)00005-F
DO - 10.1016/0927-5398(95)00005-F
M3 - Article
AN - SCOPUS:0003191872
VL - 2
SP - 253
EP - 264
JO - Journal of Empirical Finance
JF - Journal of Empirical Finance
SN - 0927-5398
IS - 3
ER -