Quantile regression methods in economics and finance - PhDData

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Quantile regression methods in economics and finance

The thesis was published by Bonaccolto, Giovanni, in January 2016, University of Padova.

Abstract:

In the recent years, quantile regression methods have attracted relevant interest in the statistical and econometric literature. This phenomenon is due to the advantages arising from the quantile regression approach, mainly the robustness of the results and the possibility to analyse several quantiles of a given random variable. Such as features are particularly appealing in the context of economic and financial data, where extreme events assume critical importance. The present thesis is based on quantile regression, with focus on the economic and financial environment. First of all, we propose new approaches in developing asset allocation strategies on the basis of quantile regression and regularization techniques. It is well known that quantile regression model minimizes the portfolio extreme risk, whenever the attention is placed on the estimation of the response variable left quantiles. We show that, by considering the entire conditional distribution of the dependent variable, it is possible to optimize different risk and performance indicators. In particular, we introduce a risk-adjusted profitability measure, useful in evaluating financial portfolios under a pessimistic perspective, since the reward contribution is net of the most favorable outcomes. Moreover, as we consider large portfolios, we also cope with the dimensionality issue by introducing an l1-norm penalty on the assets weights. Secondly, we focus on the determinants of equity risk and their forecasting implications. Several market and macro-level variables influence the evolution of equity risk in addition to the well-known volatility persistence. However, the impact of those covariates might change depending on the risk level, being different between low and high volatility states. By combining equity risk estimates, obtained from the Realized Range Volatility, corrected for microstructure noise and jumps, and quantile regression methods, we evaluate, in a forecasting perspective, the impact of the equity risk determinants in different volatility states and, without distributional assumptions on the realized range innovations, we recover both the points and the conditional distribution forecasts. In addition, we analyse how the relationships among the involved variables evolve over time, through a rolling window procedure. The results show evidence of the selected variables’ relevant impacts and, particularly during periods of market stress, highlight heterogeneous effects across quantiles. Finally, we study the dynamic impact of uncertainty in causing and forecasting the distribution of oil returns and risk. We analyse the relevance of recently developed news-based measures of economic policy uncertainty and equity market uncertainty in causing and predicting the conditional quantiles and distribution of the crude oil variations, defined both as returns and squared returns. For this purpose, on the one hand, we study the causality relations in quantiles through a non-parametric testing method; on the other hand, we forecast the conditional distribution on the basis of the quantile regression approach and the predictive accuracy is evaluated by means of several suitable tests. Given the presence of structural breaks over time, we implement a rolling window procedure to capture the dynamic relations among the variables.



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