Monte Carlo Experiments on Maximum entropy Constructive Ensembles for Time Series Analysis and Inference

In econometric analysis, the traditional bootstrap and related methods often require the assumption of stationarity. This assumption says that the distribution function of the process remains unchanged when shifted in time by an arbitrary value, imposing perfect time-homogeneity. In terms of the joint distribution, stationarity implies that the date of the first time index is not relevant. There are many problems with this assumption however for time series data. With time series, the order in which random realizations occur is crucial. This is why theorists work with stochastic processes, with two implicit arguments, w and t, where w represents the sample space and t represents the order. The question becomes, is there a bootstrap procedure that can preserve the ordering without assuming stationarity? The new method for maximum entropy ensembles proposed by Dr. H. D. Vinod might satisfy the Ergodic and Kolmogorov theorems, without assuming stationarity.