In the first chapter; we consider nonlinear transformations of random walks driven by thick-tailed innovations with infinite means or variances. In particular, we show how nonlinearity, nonstationarity, and thick tails interact to generate persistency in memory, and we clearly demonstrate that...

We consider a volatility model, named ARCH-NNH model, that is specifically an ARCH process with a nonlinear function of a persistent, integrated or nearly integrated, explanatory variable.We first establish the asymptotic theories showing that the time series properties of our model successfully...