While theory of autoregressive conditional heteroskedasticity (ARCH) models is well understood for strictly stationary processes, some recent interest has focused on the nonstationary case. In the classical model including a positive intercept parameter, the volatility process diverges to...

We generalize the BM-local time fractional symmetric α-stable motion introduced in Cohen and Samorodnitsky (2006) by replacing the local time with a general continuous additive functional (CAF). We show that the resulting process is again symmetric α-stable with stationary increments....

Throughout the past 3 decades, the random walk model served as exchange rate forecasting benchmark to verify that a model is able to outperform a random process. However, its application as forecasting benchmark is contradictory. Rather than serving as a benchmark that explains exchange rate...