Resumen de Specification and casualty of distribution models
Many important economic and finance hypotheses are investigated through testing the specification of restrictions on the conditional distribution of a time series, such as conditional goodness-of- t (Box and Pierce (1970)), conditional quantiles (Koenker and Machado (1999)), and distributional Granger non-causality (Taamouti, Bouezmarni, and El Ghouch, 2014). This PhD Thesis contributes to the study of specification and causality tests that provide a more flexible and detailed approach to evaluate economic relationships, which are useful in many relevant empirical applications. In the first chapter, we propose a practical and consistent specification test of conditional distribution models for dependent data in a very general setting. Our approach covers conditional distribution models possibly indexed by function-valued parameters, which allows for a wide range of important empirical applications, such as the linear quantile auto-regressive, the CAViaR, and the distributional regression models. Our test statistic is based on a comparison between the estimated parametric and the empirical distribution functions. The new specification test (i) is valid for general linear and nonlinear dynamic models under parameter estimation error, (ii) allows for dynamic misspecification, (iii) is consistent against fixed alternatives, and (iv) has nontrivial power against ?T -local alternatives, with T the sample size. As the test statistic is non-pivotal, we propose and theoretically justify a block bootstrap approach to obtain valid inference. Monte Carlo simulations illustrate that the proposed test has good finite sample properties for different data generating processes and sample sizes. Finally, an empirical application to models of Value-at-Risk (VaR) highlights the benefits of our approach. The second chapter proposes a consistent parametric test of Granger-causality in quantiles. Although the concept of Granger-causality is defined in terms of the conditional distribution, the majority of papers have tested Granger-causality using conditional mean regression models in which the causal relations are linear. Rather than focusing on a single part of the conditional distribution, we develop a test that evaluates nonlinear causalities and possible causal relations in all conditional quantiles. The proposed test statistic has correct asymptotic size, is consistent against fixed alternatives and has power against Pitman deviations from the null hypothesis. The proposed approach allows us to evaluate nonlinear causalities, causal relations in conditional quantiles, and provides a suficient condition for Granger-causality when all quantiles are considered. As the proposed test statistic is asymptotically non-pivotal, we tabulate critical values via a subsampling approach. We present Monte Carlo evidence and an application considering the causal relation between the gold price, the USD/GBP exchange rate, and the oil price. The last chapter of the thesis studies the co-integration relationship between industry stock returns and excess stock market returns, and it is co-authored with Prof José Penalva and Prof Abderrahim Taamouti. We find that the equilibrium error term from this co-integrating relationship has strong predictive power for excess stock returns, which is increased if combined with the previous month's excess stock returns. Our results suggest that short-term return reversals and liquidity measures are primary reasons for the negative relation between the equilibrium error and expected excess stock returns. We provide new evidence on the out-of-sample stock return predictability, in contrast to Welch and Goyal (2008), among others, who found negligible out-of-sample predictive power using standard variables. We also show that the out-of-sample explanatory power is economically meaningful for investors. Simple trading strategies implied by the proposed predictability provide portfolios with higher mean returns and Sharpe ratios than a buyand- hold or a benchmark strategy does.
