Abstract
In this paper we develop an asymptotic theory for the Real-time GARCH model of Smetanina (2016a), which can be thought of as a generalization of the standard GARCH(1,1) theory. We first establish ergodicity and mixing property of the joint process for squared returns and volatility process. We also prove strong consistency and asymptotic normality for the parameter vector. Finally we present simulations that show that the theory works quite well in finite sample even when the error terms are npot normally distributed.
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