Garch(1,1) process can have arbitrarily heavy power tails

We study the structure of solutions of Kesten’s equation (1.5), where a, b ⩾ 0 are the coefficients of the GARCH(1,1) process in (1.1). We prove that, for any b ∈ (0, 1) and any κ > 0 small enough, there exists a stationary GARCH(1,1) process with tail index κ. The research was partially supported by the bilateral France-Lithuania scientific project Gilibert and the Lithuanian State Science and Studies Foundation, grant no. T-15/07. Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 2, pp. 196–210, April–June, 2007.