Publication: Specification and casualty of distribution models
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2015-06
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2015-07-07
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Abstract
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.
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Keywords
Teoría de la distribución, Modelo matemático, Análisis de regresión, Análisis de series temporales, Estimación de parámetros