KARHUNEN-LOÈVE BASIS IN GOODNESS-OF-FIT TESTS DECOMPOSITION: AN EVALUATION

In a previous paper (Grané and Fortiana 2006) we studied a flexible class of goodness-of-fit tests associated with an orthogonal sequence, the Karhunen-Loève decomposition of a stochastic process derived from the null hypothesis. Generally speaking, these tests outperform Kolmogorov-Smirnov and Cramér-von Mises, but we registered several exceptions. In this work we investigate the cause of these anomalies and, more precisely, whether and when such poor behaviour may be attributed to the orthogonal sequence itself, by replacing it with the Legendre polynomials, a commonly used basis for smooth tests. We find an easily computable formula for the Bahadur asymptotic relative efficiency, a helpful quantity in choosing an adequate basis.

Volatility modelling and accurate minimun capital risk requirements : a comparison among several approaches

In this paper we estimate, for several investment horizons, minimum capital risk requirements for short and long positions, using the unconditional distribution of three daily indexes futures returns and a set of GARCH-type and stochastic volatility models. We consider the possibility that errors follow a t-Student distribution in order to capture the kurtosis of the returns distributions. The results suggest that an accurate modeling of extreme returns obtained for long and short trading investment positions is possible with a simple autoregressive stochastic volatility model. Moreover, modeling volatility as a fractional integrated process produces, in general, excessive volatility persistence and consequently leads to large minimum capital risk requirement estimates. The performance of models is assessed with the help of out-of-sample tests and p-values of them are reported.

Asymptotic properties of a goodness-of-fit test based on maximum correlations

We study the efficiency properties of the goodness-of-fit test based on the Qn statistic introduced in Fortiana and Grané (2003) using the concepts of Bahadur asymptotic relative efficiency and Bahadur asymptotic optimality. We compare the test based on this statistic with those based on the Kolmogorov-Smirnov, the Cramér-von Mises and the Anderson-Darling statistics. We also describe the distribution families for which the test based on Qn is asymptotically optimal in the Bahadur sense and, as an application, we use this test to detect the presence of hidden periodicities in a stationary time series.Bahadur asymptotic relative efficiency, Goodness-of-fit, Local asymptotic optimality, L-statistics, Maximum correlation

The effect of realised volatility on stock returns risk estimates

In this paper, we estimate minimum capital risk requirements for short, long positions and three investment horizons, using the traditional GARCH model and two other GARCH-type models that incorporate the possibility of asymmetric responses of volatility to price changes; and, most importantly, we analyse the models performance when realised volatility is included as an explanatory variable into the models' variance equations. The results suggest that the inclusion of realised volatility improves the models forecastability and their capacity to calculate accurate measures of minimum capital risk requirements.

The Effect of Parental Bone Marrow & Spleen Cells in the Induction of the Graft-Versus-Host Reaction

Variously aged (C57BL X C3H)F1 hybrid mice were used as recipients in experiments to determine if spleen or bone marrow cells from normal C57BL or C3H donors, spleen or bone marrow cells from C57BL donors previously treated with cortisone, or C57BL bone marrow cells previously incubated with serum from X-irradiated C57BL mice could induce a graft-versus-host reaction (GVHR). The mice were assayed for GVHR by mortality or splenomegaly as detected by the discriminant spleen assay developed by Simonsen. Results show that spleen cells from normal C57BL, normal C3H, or cortisone-treated C57BL mice are capable of inducing a GVHR in F1 hybrids, resulting in death or splenomegaly, whereas bone marrow cells from normal C3H, normal C57BL, or cortisone-treated C57BL mice were unable to induce a GVHR in F1 hybrids. It was also found that sera from lethally irradiated C57BL mice did not cause C57BL bone marrow to induce a GVHR in F1 hybrids