Maximum entropy ensembles for time series inference in economics

Abstract

This paper uses three examples of potential interest to Asian economists to support a new tool for statistical inference with time series data. In traditional theory, an ensemble Ω represents the ‘population’ behind the observed time series. Vinod [Vinod, H. D., 2004. Ranking mutual funds using unconventional utility theory and stochastic dominance, Journal of Empirical Finance, 11(3) 2004, 353–377] proposed new maximum entropy (ME) bootstrap to construct J (=999, say) elements of Ω for inference using a seven-step algorithm designed to satisfy the ergodic theorem. The algorithm's practical appeal to applied econometricians is that it avoids all structural change and unit root type testing involving complicated asymptotics and all shape-destroying transformations like de-trending or differencing to achieve stationarity. This paper simplifies and speeds up the algorithm, extends it to panel data, discusses underlying assumptions and formal properties including proving that it satisfies Doob's theorem. We show that the constructed ensemble elements retain the basic shape and dependence structure of autocorrelation function (acf) and partial autocorrelation function (pacf) of the original time series.