Stability of nonlinear stochastic recursions with application to nonlinear AR-GARCH models Academic Article uri icon


  • We characterize the Lyapunov exponent and ergodicity of nonlinear stochastic recursion models, including nonlinear AR-GARCH models, in terms of an easily defined, uniformly ergodic process. Properties of this latter process, known as the collapsed process, also determine the existence of moments for the stochastic recursion when it is stationary. As a result, both the stability of a given model and the existence of its moments may be evaluated with relative ease. The method of proof involves piggybacking a Foster-Lyapunov drift condition on certain characteristic behavior of the collapsed process.

author list (cited authors)

  • Cline, D

citation count

  • 13

complete list of authors

  • Cline, Daren BH

publication date

  • January 2007