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

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

What works in primary schools?

Olmo Silva reviews the evidence on the effectiveness of increasing resources, modifying teaching methods and introducing choice and competition. Policies to improve primary education can involve increasing the resources available to schools, modifying teaching methods or introducing elements of accountability, choice and competition into education 'markets'. Olmo Silva reviews the latest evidence on the effectiveness of these three broad areas of intervention.

Early Detection Techniques for Market Risk Failure

The implementation of appropriate statistical techniques for monitoring conditional VaR models, i.e, backtesting, reported by institutions is fundamental to determine their exposure to market risk. Backtesting techniques are important since the severity of the departures of the VaR model from market results determine the penalties imposed for inadequate VaR models. In this paper we make six contributions to backtesting techniques. In particular, we show that the Kupiec test can be viewed as a combination of CUSUM change point tests; we detail the lack of power of CUSUM methods in detecting violations of VaR as soon as these occur; we develop an alternative technique based on weighted U-statistic type processes that have power against wrong specifications of the risk measure and early detection; we show these new backtesting techniques are robust to the presence of estimation risk; we construct a new class of weight functions that can be used to weight our processes; and our methods are applicable both under conditional and unconditional VaR settings

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

A Nonlinear Threshold Model for the Dependence of Extremes of Stationary Sequences

One of the main implications of the effcient market hypothesis (EMH) is that expected future returns on financial assets are not predictable if investors are risk neutral. In this paper we argue that financial time series offer more information than that this hypothesis seems to supply. In particular we postulate that runs of very large returns can be predictable for small time periods. In order to prove this we propose a TAR(3,1)-GARCH(1,1) model that is able to describe two different types of extreme events: a first type generated by large uncertainty regimes where runs of extremes are not predictable and a second type where extremes come from isolated dread/joy events. This model is new in the literature in nonlinear processes. Its novelty resides on two features of the model that make it different from previous TAR methodologies. The regimes are motivated by the occurrence of extreme values and the threshold variable is defined by the shock affecting the process in the preceding period. In this way this model is able to uncover dependence and clustering of extremes in high as well as in low volatility periods. This model is tested with data from General Motors stock prices corresponding to two crises that had a substantial impact in financial markets worldwide; the Black Monday of October 1987 and September 11th, 2001. By analyzing the periods around these crises we find evidence of statistical significance of our model and thereby of predictability of extremes for September 11th but not for Black Monday. These findings support the hypotheses of a big negative event producing runs of negative returns in the first case, and of the burst of a worldwide stock market bubble in the second example

Black holes in extended gravity theories in Palatini formalism

We consider several physical scenarios where black holes within classical gravity theories including $R^2$ and Ricci-squared corrections and formulated \`a la Palatini can be analytically studied.Comment: 4 pages, contribution to the "Spanish Relativity Meeting in Portugal 2012 (Progress in Mathematical Relativity, Gravitation and Cosmology)", Springer Proceedings in Mathematics (to appear

Prediction of Housing Location Price by a Multivariate Spatial Method: Cokriging

Cokriging is a multivariate spatial method to estimate spatial correlated variables. This method allows spatial estimations to be made and interpolated maps of house price to be created. These maps are interesting for appraisers, real estate companies, and bureaus because they provide an overview of location prices. Kriging uses one variable of interest (house price) to make estimates at unsampled locations, and cokriging uses the variable of interest and auxiliary correlated variables. In this paper, housing location price is estimated using kriging methods, isotopic data cokriging, and heterotopic data cokriging methods. The results of these methods are then compared.