Date: 2017-09-29

Time: 14:30-16:30

Location: BURN 1205

Abstract:

McNeil: In this talk we study a class of backtests for forecast distributions in which the test statistic is a spectral transformation that weights exceedance events by a function of the modelled probability level. The choice of the kernel function makes explicit the user’s priorities for model performance. The class of spectral backtests includes tests of unconditional coverage and tests of conditional coverage. We show how the class embeds a wide variety of backtests in the existing literature, and propose novel variants as well. We assess the size and power of the backtests in realistic sample sizes, and in particular demonstrate the tradeoff between power and specificity in validating quantile forecasts.

Jasiulis-Goldyn: We consider extremal Markovian sequences connected with the Kendall convolution called Kendall random walks. The best tool for solving problems connected with the Kendall generalized convolution is the Williamson transform, which is also generator of Archimedean copula. We prove that one dimensional distributions of Kendall random walks are regularly varying. The Central Limit Theorem in the Kendall convolution algebra will be showed using the Williamsom transform. We notice that obtained stable distributions belong to maximal domain of attraction of the Fréchet distribution. We prove convergence of finite dimensional distributions for continuous time stochastic processes constructed by Kendall random walks. We also construct renewal processes for extremal Markovian sequences of the Kendall type and present significant connections with the limit distribution of Kendall random walks.

Speaker

Alexander McNeil is Professor of Actuarial Science at the University of York, England.

Barbara Jasiulis-Goldyn is an Assistant Professor in the Mathematical Institute, University of Wrocław, Poland.