THE DIFFUSION LIMIT OF A TVP-GQARCH-M(1,1) MODEL
研究了TVP-GQARCH-M(1,1)过程的弱收敛问题，发现其弱极限是外生随机波动率连续时间过程，并推导了不同情况下的不变分布，揭示了GARCH与非对称GQARCH方差过程与连续时间Ornstein-Uhlenbeck模型之间的近似分布关系。
This paper presents results on the issue of weak convergence of a TVP-GQARCH-M(1,1) process. These suggest that the weak limit of this endogenous volatility model is an exogenous (stochastic) volatility continuous time process. Under the appropriate assumptions, we derive the invariant distributions at which the process converges in various cases. They reveal an approximate distributional relation between the GARCH or the asymmetric GQARCH variance processes and the continuous time Ornstein–Uhlenbeck models with respect to appropriate nonnegative Levy processes.I am grateful to Ritsa Panagiotou, Phyllis Alexander, Antonis Demos, Bruce Hansen, Nicholas Magginas, Nour Meddahi, Enrique Sentana, Paolo Zaffaroni, two anonymous referees, and the seminar participants at the Department of International and European Economic Studies for their valuable comments.