Vinod, H. D. (2003), Constructive Ensembles for Time Series in Econometrics and Finance Computing Science and Statistics, 35, I2003Proceedings/VinodHD/VinodHD.paper.pdf
The ensemble plays a key role as the notional ‘population’ for the observed time series. I propose a new method of constructing the ensemble by using maximum entropy (ME) methods. The ME distribution satisfies the mean preserving constraint by construction and is computer intensive. My seven-step algorithm for constructing ensembles is designed to satisfy the ergodic theorem and Doob’s theorem, without assuming stationarity and without using asymptotics. Proposed methods are particularly convenient for short nonstationary time series and can potentially simplify several inference problems in time series analysis. Three examples illustrate them. A consumption function example explicitly shows that: (i) the constructed ensemble retains the basic shape and dependence structure of autocorrelation function (acf) and partial autocorrelation function (pacf) of the original time series, (ii) one can avoid shape-destroying transformations (differencing) and the underlying need for achieving stationarity, and (iii) one can provide confidence intervals for coefficients of lagged dependent variables. A demand function example shows that traditional inference methods are consistent and conservative when viewed in terms of the proposed ensemble.