TESTING THE EXISTENCE OF CLUSTERING IN THE EXTREME VALUES

This paper introduces an estimator for the extremal index as the ratio of the number of elements of two point processes defined by threshold sequences un, vn and a partition of the sequence in different blocks of the same size. The first point process is defined by the sequence of the block maxima that exceed un. This paper introduces a thinning of this point process, defined by a threshold vn with vn > un, and with the appealing property that under some mild conditions the ratio of the number of elements of both point processes is a consistent estimator of the extremal index. The method supports a hypothesis test for the extremal index, and hence for testing the existence of clustering in the extreme values. Other advantages are that it allows some freedom to choose un, and it is not very sensitive to the choice of the partition. Finally, the stylized facts found in financial returns (clustering, skewness, heavy tails) are tested via the extremal index, in this case for the DaX returns

CONTAGION VERSUS FLIGHT TO QUALITY IN FINANCIAL MARKETS

None doubts that financial markets are related (interdependent). What is not so clear is whether there exists contagion among them or not, its intensity, and its causal direction. The aim of this paper is to define properly the term contagion (different from interdependence) and to present a formal test for its existence, the magnitude of its intensity, and for its direction. Our definition of contagion lies on tail dependence measures and it is made operational through its equivalence with some copula properties. In order to do that, we define a NEW copula, a variant of the Gumbel type, that is sufficiently flexible to describe different patterns of dependence, as well as being able to model asymmetric effects of the analyzed variables (something not allowed with the standard copula models). Finally, we estimate our copula model to test the intensity and the direction of the extreme causality between bonds and stocks markets (in particular, the flight to quality phenomenon) during crises periods. We find evidence of a substitution effect between Dow Jones Corporate Bonds Index with 2 years maturity and Dow Jones Stock Price Index when one of them is through distress periods. On the contrary, if both are going through crises periods a contagion effect is observed. The analysis of the corresponding 30 years maturity bonds with the stock market reflects independent effects of the shocks.

The impact of heavy tails and comovements in downside-risk diversification

This paper uncovers the factors influencing optimal asset allocation for downside-risk averse investors. These are comovements between assets, the product of marginal tail probabilities, and the tail index of the optimal portfolio. We measure these factors by using the Clayton copula to model comovements and extreme value theory to estimate shortfall probabilities. These techniques allow us to identify useless diversification strategies based on assets with different tail behaviour, and show that in case of financial distress the asset with heavier tail drives the return on the overall portfolio down. An application to financial indexes of UK and US shows that mean-variance and downside-risk averse investors construct different efficient portfolios.

Growth in a cross-section of cities: location, increasing returns or random growth?

This article analyzes empirically the main existing theories on income and population city growth: increasing returns to scale, locational fundamentals and random growth. To do this we implement a threshold nonlinearity test that extends standard linear growth regression models to a dataset on urban, climatological and macroeconomic variables on 1,175 U.S. cities. Our analysis reveals the existence of increasing returns when per-capita income levels are beyond $19; 264. Despite this, income growth is mostly explained by social and locational fundamentals. Population growth also exhibits two distinct equilibria determined by a threshold value of 116,300 inhabitants beyond which city population grows at a higher rate. Income and population growth do not go hand in hand, implying an optimal level of population beyond which income growth stagnates or deteriorates.Threshold nonlinearity test, locational fundamentals, multiple equilibria, random growth

Backtesting Parametric Value-at-Risk with Estimation Risk

One of the implications of the creation of Basel Committee on Banking Supervision was the implementation of Value-at-Risk (VaR) as the standard tool for measuring market risk. Since then, the capital requirements of commercial banks with trading activities are based on VaR estimates. Therefore, appropriately constructed tests for assessing the out-of-sample forecast accuracy of the VaR model (backtesting procedures) have become of crucial practical importance. In this paper we show that the use of the standard unconditional and independence backtesting procedures to assess VaR models in out-of-sample composite environments can be misleading. These tests do not consider the impact of estimation risk and therefore may use wrong critical values to assess market risk. The purpose of this paper is to quantify such estimation risk in a very general class of dynamic parametric VaR models and to correct standard backtesting procedures to provide valid inference in out-of-sample analyses. A Monte Carlo study illustrates our theoretical findings in finite-samples and shows that our corrected unconditional test can provide more accurately sized and more powerful tests than the uncorrected one. Finally, an application to S&P500 Index shows the importance of this correction and its impact on capital requirements as imposed by Basel Accord.Backtesting; Basel Accord; Conditional Quantile; Estimation Risk; Forecast evaluation; Fixed, rolling and recursive forecasting scheme; Risk management; Value at Risk

Growth in a Cross-Section of Cities: Location, Increasing Returns or Random Growth?

This article analyzes empirically the main existing theories on income and population city growth: increasing returns to scale, locational fundamentals and random growth. To do this we implement a threshold nonlinearity test that extends standard linear growth regression models to a dataset on urban, climatological and macroeconomic variables on 1,175 U.S. cities. Our analysis reveals the existence of increasing returns when per-capita income levels are beyond $19; 264. Despite this, income growth is mostly explained by social and locational fundamentals. Population growth also exhibits two distinct equilibria determined by a threshold value of 116,300 inhabitants beyond which city population grows at a higher rate. Income and population growth do not go hand in hand, implying an optimal level of population beyond which income growth stagnates or deterioratesthreshold nonlinearity test, locational fundamentals, multiple equilibria, random growth

A nonparametric predictive regression model using partitioning estimators based on Taylor expansions

This article proposes a nonparametric predictive regression model. The unknown function modeling the predictive relationship is approximated using polynomial Taylor expansions applied over disjoint intervals covering the support of the predictor variable. The model is estimated using the theory on partitioning estimators that is extended to a stationary time series setting. We show pointwise and uniform convergence of the proposed estimator and derive its asymptotic normality. These asymptotic results are applied to test for the presence of predictive ability. We develop an asymptotic pointwise test of predictive ability using the critical values of a Normal distribution, and a uniform test with asymptotic distribution that is approximated using a p-value transformation and Wild bootstrap methods. These theoretical insights are illustrated in an extensive simulation exercise and also in an empirical application to forecasting high-frequency based realized volatility measures. Our results provide empirical support to the presence of nonlinear autoregressive predictability of these measures for the constituents of the Dow Jones index

Infrared lessons for ultraviolet gravity: the case of massive gravity and Born-Infeld

We generalize the ultraviolet sector of gravitation via a Born-Infeld action using lessons from massive gravity. The theory contains all of the elementary symmetric polynomials and is treated in the Palatini formalism. We show how the connection can be solved algebraically to be the Levi-Civita connection of an effective metric. The non-linearity of the algebraic equations yields several branches, one of which always reduces to General Relativity at low curvatures. We explore in detail a {\it minimal} version of the theory, for which we study solutions in the presence of a perfect fluid with special attention to the cosmological evolution. In vacuum we recover Ricci-flat solutions, but also an additional physical solution corresponding to an Einstein space. The existence of two physical branches remains for non-vacuum solutions and, in addition, the branch that connects to the Einstein space in vacuum is not very sensitive to the specific value of the energy density. For the branch that connects to the General Relativity limit we generically find three behaviours for the Hubble function depending on the equation of state of the fluid, namely: either there is a maximum value for the energy density that connects continuously with vacuum, or the energy density can be arbitrarily large but the Hubble function saturates and remains constant at high energy densities, or the energy density is unbounded and the Hubble function grows faster than in General Relativity. The second case is particularly interesting because it could offer an interesting inflationary epoch even in the presence of a dust component. Finally, we discuss the possibility of avoiding certain types of singularities within the minimal model.Comment: 31 pages, 3 figures (Journal version, references added