Earth’s gravitational field provides invaluable insights into the changing nature of our planet. It reflects mass change caused by geophysical processes like continental hydrology, changes in cryosphere or flux ocean. Satellite missions such as NASA/DLR operated Gravity Recovery and Climate Experiment (GRACE), its successor GRACE Follow-On (GRACE-FO) continuously monitor these temporal variatio...

Given a stationary first-order autoregressive process X t (with lag-one correlation ρ satisfying |ρ| < 1), we examine the Central Limit Theorem for 1 n ln |X 1 · · · X n | and compute variances to high precision. Given a nonstationary process X t (with |ρ| > 1), we examine instead

When modeling time series data using autoregressive-moving average processes, it is a common practice to presume that the residuals are normally distributed. However, sometimes we encounter non-normal residuals and asymmetry of data marginal distribution. Despite widespread use of pure autoregressive processes for modeling non-normal time series, the autoregressive-moving average models have le...

Consider a discrete-time risk model in which the insurer is allowed to invest a proportion of its wealth in a risky stock and keep the rest in a risk-free bond. Assume that the claim amounts within individual periods follow an autoregressive process with heavy-tailed innovations and that the log-returns of the stock follow another autoregressive process, independent of the former one. We derive...

A dynamic model for limited dependent variables is proposed, which estimation does not rely on simulation methods. A latent conditional mean function which is measurable with respect to past and observable information circumvents the solution of a T -dimensional integral and yields a simple and computationally parsimonious maximum likelihood estimation. It can be shown that the latent process i...