# Estimating Time Series Models with Heuristic Methods: The Case of Economic Parity Conditions

Sebastian Deininger^{*} and Dietmar Maringer

Time series models are a common approach in economic and econometric analysis. A special case are Vector Error Correction (VEC) models where several economic variables are assumed to depend on their own and each other's recent developments. While they facilitate economically sound modeling, their actual application is often hampered by technical difficulties: Finding the optimal parameter values is usually based on maximizing some likelihood function or ``information criterion'' for which no closed-form solution exists. Even more importantly, the number of parameters increases quickly when allowing for more lags, i.e., including past observations --- which is highly desirable, e.g., when seasonalities, delayed reactions, or long memory need to be catered for. In this case, it is desirable to keep the model still as parsimonious as possible to avoid over-fitting. Ideally, one can ``cherry-pick'' the parameters which one wants and doesn't want to include; this, however, makes parameter estimation even harder as it adds challenging combinatorial problems.$\\$ In this paper, we investigate how Differential Evolution (DE), a nature-inspired search heuristic, can help to tackle the parameter selection and estimation problem simultaneously which, in traditional approaches to econometric model selection, is not possible. We also employ different criteria as basis for parameter estimation. We then apply this approach to the case of parity conditions and use data for the US, the Euro-Area and for Switzerland to investigate the uncovered interest rate parity; the expectation hypothesis of the term structure; and the purchasing power parity. The results indicate that for the considered currencies and economic regions, only some, but not all of these parities hold. Also, it is found that different approaches can lead to conflicting conclusions, which emphasizes the importance of careful economic modeling and reliable methods.

Mathematics Subject Classification: 37M10 37N40

Keywords: Differential Evolution; Lag Order Selection; UIP; PPP; Term Structure

Minisymposion: Computational Optimization Methods in Statistics, Econometrics and Finance