Essays on Econometrics : Nonlinearities and Nonnormalities

Doutoramento em Matemática Aplicada à Economia e à GestãoThis Dissertation consists of three independent papers on econometrics, having in common the fact that each of them proposes a new methodology to deal with issues caused by the departure from linearity and gaussianity assumptions. We start by introducing a simple and easy to implement procedure to test for multiple structural changes in persistence. An in-depth Monte Carlo analysis shows that the new procedure performs well under various DGPs with persistence changes. The application of the proposed test to OECD countries inflation reveals relevant statistical evidence of breaks in persistence for all countries. Overall, the persistence was high and non-mean-reverting until the early 80’s and subsequently decreased, which coincides with the beginning of the Great Moderation. Then, the second paper introduce a flexible framework able to capture some aspects of the potential nonlinear causal relationships between economic variables. More precisely, the proposed procedure estimates the expected time (ET) an outcome variable takes to cross a fixed threshold given a starting value and conditional on covariates. An application to the economic activity-yield spread relationship for the U.S. suggests that the yield spread may have an important role in stimulating a faster return to desirable growth rates when the economy is in contraction or faces weak growth. Moreover, negative yield spread values in the presence of positive and high industrial production growth rates leads to a quick return to negative growth rates and may trigger a recession. Finally, the third paper proposes a simple framework that allows us to take into account the magnitude of potential losses incurred throughout the investment horizon, denoted intra-horizon risk, in portfolio optimization. To this end, we introduce a novel nonparametric method to estimate the first passage probability function that only make use of the Markovian property of the returns. An empirical application is provided considering equity, bond and commodity Exchange Traded funds (ETFs). Our results suggest that the proposed framework indicates portfolios with lower expected time to reach the target return than those indicated by the Markowitz’ mean-variance approach with similar levels of intra-horizon risk, which may result in higher expected annualized return if the lower threshold that triggers a stop-loss decision is not crossed.info:eu-repo/semantics/publishedVersio

Assimetrias nos ciclos económicos : modelação não linear do PIB de alguns países

Mestrado em Econometria Aplicada e PrevisãoEsta dissertação pretende investigar a existência de não-linearidades nos ciclos económicos de vários países através dos modelos STAR(Smooth Transition AR), à semelhança de Bradley e Jansen(2000). Os vários testes de linearidade realizados fornecem evidência de não-linearidades na taxa de crescimento do PIB para a grande maioria dos países, sendo a evidência contra a hipótese nula de linearidade mais forte que no artigo acima referido.No entanto, tal como nesse trabalho, não foi possível encontrar características comuns nos ciclos económicos dos países estudados.A heterogeneidade revela-se quer na utilização de modelos adequados diferentes quer, para o mesmo modelo, em estimativas bastante diferentes dos parâmetros e dos números de desfasamentos.The purpose of this dissertation is to investigate business cycle nonlinearities for several countries using STAR(Smooth Transition AR). Linearity tests provide evidence of nonlinear dynamics for the GDP growth rate of most countries, with evidence against the null hypothesis of linearity stronger than in Bradley and Jansen (2000). However, as in this work, it was not possible to find common business cycle characteristics for the countries under scrutiny. Heterogeneity shows up through different adequate models and also through rather different parameter estimates and lag numbers

Are linear models really unuseful to describe business cycle data?

We use first differenced logged quarterly series for the GDP of 29 countries and the euro area to assess the need to use non-linear models to describe business cycle dynamic behaviour. Our approach is model (estimation)-free, based on testing only. We aim to maximize power to detect non-linearities while, simultaneously, avoiding the pitfalls of data mining. The evidence we find does not support some descriptions because the presence of significant non-linearities is observed for two-thirds of the countries only. Linear models cannot be simply dismissed as they are frequently useful. Contrarily to common knowledge, non-linear business cycle variation does not seem to be a universal, undisputable and clearly dominant stylized fact. This finding is particularly surprising for the U.S. case. Some support for non-linear dynamics for some further countries is obtained indirectly, through unit root tests, but this can hardly be invoked to support non-linearity in classical business cycles.info:eu-repo/semantics/publishedVersio

Are linear models really unuseful to describe business cycle data?

We use first differenced logged quarterly series for the GDP of 29 countries and the euro area to assess the need to use nonlinear models to describe business cycle dynamic behaviour. Our approach is model (estimation)-free, based on testing only. We aim to maximize power to detect non-linearities and, simultaneously, we purport avoiding the pitfalls of data mining. The evidence we find does not support some descriptions because the presence of significant non-linearities is observed for 2/3 of the countries only. Linear models cannot be simply dismissed as they are frequently useful. Contrarily to common knowledge, nonlinear business cycle variation does not seem to be an universal, undisputable and clearly dominant stylized fact. This finding is particularly surprising for the U.S. case. Some support for nonlinear dynamics for some further countries is obtained indirectly, through unit root tests, but this is marginal to our study, based on indirectmethods only and can hardly be invoked to support nonlinearity in classical business cycles

Revisiting non-linearities in business cycles around the world

We use first differenced logged quarterly series for the GDP of 29 countries and the euro area to (re)assess the need to use nonlinear models to describe business cycle dynamic behaviour. Our approach is model (estimation)-free, based on testing only. We aim to maximize power to detect non-linearities and, simultaneously, we purport avoiding the pitfalls of data mining. We find evidence supporting the presence of significant non-linearities in 2/3 of the cases only. Hence, it does not provide full support to some descriptions. Linear models cannot be simply dismissed as they are sometimes useful and in many cases they do not seem to leave a substantial fraction of variation to be explained by nonlinear rivals. Nonlinear business cycle variation does not seem to be an universal, undisputable and clearly dominant stylized fact. Therefore, our evidence broadly agrees with the one that has recently emerged from the ``features approach''. Some support for nonlinear dynamics for some further countries is obtained indirectly, through unit root tests, but this marginal to our study, based on indirect methods only and can hardly be invoked to support nonlinearity in classical business cycles. However, it is relevant from the output gap perspective

Revisiting non-linearities in business cycles around the world

We use first differenced logged quarterly series for the GDP of 29 countries and the euro area to (re)assess the need to use nonlinear models to describe business cycle dynamic behaviour. Our approach is model (estimation)-free, based on testing only. We aim to maximize power to detect non-linearities and, simultaneously, we purport avoiding the pitfalls of data mining. We find evidence supporting the presence of significant non-linearities in 2/3 of the cases only. Hence, it does not provide full support to some descriptions. Linear models cannot be simply dismissed as they are sometimes useful and in many cases they do not seem to leave a substantial fraction of variation to be explained by nonlinear rivals. Nonlinear business cycle variation does not seem to be an universal, undisputable and clearly dominant stylized fact. Therefore, our evidence broadly agrees with the one that has recently emerged from the ``features approach''. Some support for nonlinear dynamics for some further countries is obtained indirectly, through unit root tests, but this marginal to our study, based on indirect methods only and can hardly be invoked to support nonlinearity in classical business cycles. However, it is relevant from the output gap perspective

Are linear models really unuseful to describe business cycle data?

We use first differenced logged quarterly series for the GDP of 29 countries and the euro area to assess the need to use nonlinear models to describe business cycle dynamic behaviour. Our approach is model (estimation)-free, based on testing only. We aim to maximize power to detect non-linearities and, simultaneously, we purport avoiding the pitfalls of data mining. The evidence we find does not support some descriptions because the presence of significant non-linearities is observed for 2/3 of the countries only. Linear models cannot be simply dismissed as they are frequently useful. Contrarily to common knowledge, nonlinear business cycle variation does not seem to be an universal, undisputable and clearly dominant stylized fact. This finding is particularly surprising for the U.S. case. Some support for nonlinear dynamics for some further countries is obtained indirectly, through unit root tests, but this is marginal to our study, based on indirectmethods only and can hardly be invoked to support nonlinearity in classical business cycles

Are linear models really unuseful to describe business cycle data?

The authors use first differenced logged quarterly series for the GDP of 29 countries and the euro area to assess the need to use nonlinear models to describe business cycle dynamic behaviour. Their approach is model (estimation)-free, based on testing only. The authors aim to maximize power to detect non-linearities and, simultaneously, they purport avoiding the pitfalls of data mining. The evidence the authors find does not support some descriptions because the presence of significant non-linearities is observed for 2/3 of the countries only. Linear models cannot be simply dismissed as they are frequently useful. Contrarily to common knowledge, nonlinear business cycle variation does not seem to be a universal, undisputable and clearly dominant stylized fact. This finding is particularly surprising for the U.S. case. Some support for nonlinear dynamics for some further countries is obtained indirectly, through unit root tests, but this can hardly be invoked to support nonlinearity in classical business cycles