An Information Theoretic Criterion for Empirical Validation of Time Series Models

Simulated models suffer intrinsically from validation and comparison problems. The choice of a suitable indicator quantifying the distance between the model and the data is pivotal to model selection. However, how to validate and discriminate between alternative models is still an open problem calling for further investigation, especially in light of the increasing use of simulations in social sciences. In this paper, we present an information theoretic criterion to measure how close models' synthetic output replicates the properties of observable time series without the need to resort to any likelihood function or to impose stationarity requirements. The indicator is sufficiently general to be applied to any kind of model able to simulate or predict time series data, from simple univariate models such as Auto Regressive Moving Average (ARMA) and Markov processes to more complex objects including agent-based or dynamic stochastic general equilibrium models. More specifically, we use a simple function of the L-divergence computed at different block lengths in order to select the model that is better able to reproduce the distributions of time changes in the data. To evaluate the L-divergence, probabilities are estimated across frequencies including a correction for the systematic bias. Finally, using a known data generating process, we show how this indicator can be used to validate and discriminate between different models providing a precise measure of the distance between each of them and the data.