2015/02 | LEM Working Paper Series | |
An Information Theoretic Criterion for Empirical Validation of Time Series Models |
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Stefano Lamperti |
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Keywords | ||
Simulations, Empirical Validation, Time Series, Agent Based Models
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JEL Classifications | ||
C15, C52, C63
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Abstract | ||
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.
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