In this paper marginal and conditional skewness of financial return time series is studied, by means of testing procedures and suitable models, for nine major international stock indexes. To analyze time-varying conditional skewness a new GARCH-type model with dynamic skewness and kurtosis is proposed. Results indicate that there are no evidences of marginal asymmetry in the nine series, but there are clear findings of significant time-varying conditional skewness. The economic significance of conditional skewness is analyzed and compared by considering Value-at-Risk, Expected Shortfall and Market Risk Capital Requirements set by the Basel Accord.
The study of extreme values is of crucial interest in many contexts. The concentration of pollutants, the sea-level and the closing prices of stock indexes are only a few examples in which the occurrence of extreme values may lead to important consequences. In the present paper we are interested in detecting trend in sample extremes. A common statistical approach used to identify trend in extremes is based on the generalized extreme value distribution, which constitutes a building block for parametric models. However, semiparametric procedures imply several advantages when exploring data and checking the model. This paper outlines a semiparametric approach for smoothing sample extremes, based on nonlinear dynamic modelling of the generalized extreme value distribution. The relative merits of this approach are illustrated through two real examples.
In this article, we propose a spatial model for analyzing extreme rainfall values over the Triveneto region (Italy). We assess the existence of a long-term trend in the extremes. To integrate data coming from the different stations, we propose a hierarchical model. At the first level, for each monitoring station we model data by making use of a generalized extreme value distribution; at the second level, we combine results from the first stage by exploiting recent advances in modeling nonstationary spatial random fields
We propose a method for fitting semiparametric models such as the proportional hazards (PH), additive risks (AR), and proportional odds (PO) models. Each of these semiparametric models implies that some transformation of the conditional cumulative hazard function (at each t) depends linearly on the covariates. The proposed method is based on nonparametric estimation of the conditional cumulative hazard function, forming a weighted average over a range of t-values, and subsequent use of least squares to estimate the parameters suggested by each model. An approximation to the optimal weight function is given. This allows semiparametric models to be fitted even in incomplete data cases where the partial likelihood fails (e.g., left censoring, right truncation). However, the main advantage of this method rests in the fact that neither the interpretation of the parameters nor the validity of the analysis depend on the appropriateness of the PH or any of the other semiparametric models. In fact, we propose an integrated method for data analysis where the role of the various semiparametric models is to suggest the best fitting transformation. A single continuous covariate and several categorical covariates (factors) are allowed. Simulation studies indicate that the test statistics and confidence intervals have good small-sample performance. A real data set is analyzed.
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