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PozycjaAn approach to measuring The relation between risk and return. Bayesian analysis for WIG Data(Oficyna Wydawnicza AFM, 2007) Pipień, MateuszThe main goal of this paper is an application of Bayesian inference in testing the relation between risk and return of the financial time series. On the basis of the Intertemporal CAl’M model, proposed by Merton (1973), we built a general sampling model suitable in analysing such relationship. The most important feature of our model assumptions is that the possible skewness of conditional distribution of returns is used as an alternative source of relation between risk and return. Thus, pure statistical feature of the sampling model is equipped with economic interpretation. This general specification relates to GARCH-In-Mean model proposed by Osiewalski and Pipień (2000). In order to make conditional distribution of financial returns skewed we considered a constructive approach based on the inverse probability integral transformation. In particular, we apply the hidden truncation mechanism, two approaches based on the inverse scale factors in the positive and the negative orthant, order statistics concept, Beta distribution transformation, Bernstein density transformation and the method recently proposed by Ferreira and Steel (2006). Based on the daily excess returns of WIG index we checked the total impact of conditional skewness assumption on the relation between return and risk on the Warsaw Stock Market. Posterior inference about skewness mechanisms confirmed positive and decisively significant relationship between expected return and risk. The greatest data support, as measured by the posterior probability value, receives model with conditional skewness based on the Beta distribution transformation with two free parameters. PozycjaFolia Oeconomica Cracoviensia, Vol. LIII(Krakowska Akademia im. Andrzeja Frycza Modrzewskiego, Polska Akademia Nauk - Oddział w Krakowie - Komisja Nauk Ekonomicznych i Statystyki, 2012) Marzec, Jerzy; Osiewalski, Jacek; Pipień, Mateusz; Prędki, Artur; Wróbel-Rotter, Renata; Iwasiewicz, Andrzej PozycjaFolia Oeconomica Cracoviensia, Vol. XLVIII(Krakowska Akademia im. Andrzeja Frycza Modrzewskiego, Polska Akademia Nauk - Oddział w Krakowie - Komisja Nauk Ekonomicznych i Statystyki, 2007) Gurgul, Henryk; Majdosz, Paweł; Młodkowski, Paweł; Fiszeder, Piotr; Wróbel-Rotter, Renata; Pipień, Mateusz; Denkowska, Sabina; Broda, Zdzisław Jan; Iwasiewicz, Andrzej PozycjaOrthogonal transformation of coordinates in copula m-garch models - Bayesian analysis for wig20 spot and futures returns(Oficyna Wydawnicza AFM, 2012) Pipień, MateuszWe check the empirical importance of some generalisations of the conditional distribution in M-GARCH case. A copula M-GARCH model with coordinate free conditional distribution is considered, as a continuation of research concerning specification of the conditional distribution in multivariate volatility models, see Pipień (2007, 2010). The main advantage of the proposed family of probability distributions is that the coordinate axes, along which heavy tails and symmetry can be modelled, are subject to statistical inference. Along a set of specified coordinates both, linear and nonlinear dependence can be expressed in a decomposed form. In the empirical part of the paper w e considered a problem of modelling the dynamics of the returns on the spot and future quotations of the WIG20 index from the Warsaw Stock Exchange. On the basis of the posterior odds ratio we checked the data support of considered generalisation, comparing it with BEKK model with the conditional distribution simply constructed as a product of the univariate skewed components. Our example clearly showed the empirical importance of the proposed class of the coordinate free conditional distributions.