We present a numerical technique to visualize covariance and cross-covariance fields of a stochastic simulation. The method is local in the sense that it demonstrates the covariance structure of the solution at a point with its neighboring locations. When coupled with an efficient stochastic simulation solver, our framework allows one to effectively concurrently visualize both the mean and (cro...

We consider a class of semi-parametric dynamic models with strong white noise errors. This processes includes the standard Vector Autoregressive (VAR) model, nonfundamental structural VAR, mixed causal-noncausal models, as well nonlinear such (multivariate) ARCH-M model. For estimation in this class, we propose Generalized Covariance (GCov) estimator, which is obtained by minimizing residual-ba...

The developments of special relativity and quantum mechanics marked the beginning modern physics age. former has taught us that while space time are frame dependent notions, there is a quantity -- space-time interval whose value all inertial observers agree upon. This reveals, so to speak, genuine "fact" universe, relativistic invariant. On other hand, since dawn mechanics, no consensus on what...