The aim of this study is to analyze the relevance of recently developed news-based measures of economic policy and equity market uncertainty in causing and predicting the conditional quantiles of crude oil returns and risk. For this purpose, we studied both the causality relationships in quantiles through a non-parametric testing method and, building on a collection of quantiles forecasts, we estimated the conditional density of oil returns and volatility, the out-of-sample performance of which was evaluated by using suitable tests. A dynamic analysis shows that the uncertainty indexes are not always relevant in causing and forecasting oil movements. Nevertheless, the informative content of the uncertainty indexes turns out to be relevant during periods of market distress, when the role of oil risk is the predominant interest, with heterogeneous eects over the dierent quantiles levels.

This paper applies the Fractional Frequency Flexible Fourier Form (FFFFF) Dickey-Fuller (DF)-type unit root test on the natural logarithm of US real GNP over the quarterly period of 1875:1-2015:2, to determine whether the same is trend-or difference-stationary. While, standard and Integer Frequency Flexible Fourier Form (IFFFF) DF-type test fails to reject the null of unit root, the relatively more powerful FFFFF DF-type test provides strong evidence of the real GNP as being trend-stationary, i.e., US output returns to a deterministic log-nonlinear trend in the long run.

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 ℓ 1 -norm penalty on the assets weights.

We introduce the Conditional Autoregressive Quantile-Located VaR (QL-CoCaViaR), that extends the Conditional Value-at-Risk (Adrian and Brunnermeier, 2016) by using an estimation process capturing the state of joint distress of the financial system and of individual companies. Furthermore, we include autoregressive components of conditional quantiles to explicitly model volatility clustering and heteroskedasticity. We support our model with a large empirical analysis, in which we use both classical and novel backtesting methods. Our results show that the quantilelocated relationships lead to relevant improvements in terms of predictive accuracy during stressed periods, providing a valuable tool for regulators to assess systemic events.

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