### Book chapter

## Rejection Graph for Multiple Testing of Elliptical Model for Market Network

Market network analysis attracts a growing attention last decade. Important component of the market network is a model of stock returns distribution. Elliptically contoured distributions are popular as probability model of stock returns. The question of adequacy of this model to real market data is open. There are known results that reject such model and at the same time there are results that approve such model. Obtained results are concerned to testing some properties of elliptical model. In the paper another property of elliptical model namely property of symmetry condition of tails of 2-dimentional distribution is considered. Multiple statistical procedure for testing elliptical model for stock returns distribution is proposed. Sign symmetry conditions of tails distribution are chosen as individual hypotheses for multiple testing. Uniformly most powerful tests of Neyman structure are constructed for individual hypotheses testing. Associated stepwise multiple testing procedure is applied for the real market data. To visualize the results a rejection graph is constructed. The main result is that under some conditions tail symmetry hypothesis is not rejected if one remove a few number of hubs from the rejection graph.