Four essays on the application of nonlinear techniques to time series in economics

Abstract

For years, linear modeling has been the main approach in econometrics to model dynamics and relationships between variables, due to its simplicity and accessibility both in terms of interpretation and computation. In addition, the traditional scarcity of data, both cross-sectional and longitudinal, has been another historical argument for the adoption of linear modeling to explain economic processes. Nevertheless, the economy typically does not conform to linear behavior, since it is a complex system with multiple interdependent variables interacting in many different ways: from the description of responses to shocks in persistent series by nonlinear impulse response functions, to the nonlinear propagation of economic shocks by credit, to the response of stock markets to oil price shocks. The recent increase in data generation and storage capacity has meant, together with increased computational power, a scenario where nonlinear modeling can be helpful in revealing such relationships that go beyond linearity. This thesis aims to illustrate the advantages of the correct application of nonlinear techniques in four problems in which time series dynamics applied to economic problems are modeled. First, a nonparametric nonlinear univariate model is proposed for the prediction of economic recessions. This modeling is motivated by the influential observation of the pandemic derived from Covid-19, of unprecedented economic magnitude, which caused different models to suffer in the estimation from its incorporation. In particular, based on the particular case of the GDP growth, the series is partitioned into bins of a given length, and the amount that would lead to a technical recession if placed at the period of analysis is analyzed once they are weighted by the probability of occurrence of the bins once they are embedded in a symbolic space. The robustness of the approximation is shown, with a better predictive capability than a linear autoregressive approximation or a Markov chain-based regime-changing approximation. Secondly, the determinants of the economic cycle in Spain are analyzed using the decision tree technique based on boosting. In particular, after analyzing the capacity of the technique in predicting recessions dated by the cycle committee, we analyze the variables that help the most in the prediction of a correct high probability of recession, and we analyze the interactions between these variables. In addition, the importance of these variables is analyzed dynamically. Variables such as prices or leading indicators of GDP trend or car sales are usually relevant, although in recessions such as the Great Recession, variables related to more affected sectors such as construction gain importance with respect to these. Third, we analyze the dynamics of gun homicides in the United States, a relevant problem for insurers or real estate companies in the country, using a dynamic factor model with a Kalman filter with nonlinear characteristics to take advantage of data with almost immediate availability compared to the delay of official data, up to almost two years. The results improve the predictive capability of linear and machine learning-based models. Finally, interdependencies between eleven countries of the European Monetary and Economic Union are analyzed by applying a non-linear panel model to try to explain their dynamics, creating a connectivity index with two differentiated regimes. It highlights the importance of variables such as bilateral exports or tourism for the description of the dynamics. Therefore, this paper shows in four particular cases the advantages of the correct use of nonlinear approximations in economic problems, whether they are univariate, multivariate or even panel data problems.