Inducing Normality from Non-Gaussian Long Memory Time Series and its Application to Stock Return Data

Motivated by Lee and Ko ( Appl. Stochastic Models. Bus. Ind. 2007; 23 :493–502) but not limited to the study, this paper proposes a wavelet-based Bayesian power transformation procedure through the well-known Box–Cox transformation to induce normality from non-Gaussian long memory processes. We consider power transformations of non-Gaussian long memory time series under the assumption of an unknown transformation parameter, a situation that arises commonly in practice, while most research has been devoted to non-linear transformations of Gaussian long memory time series with known transformation parameter. Specially, this study is mainly focused on the simultaneous estimation of the transformation parameter and long memory parameter. To this end, posterior estimations via Markov chain Monte Carlo methods are performed in the wavelet domain. Performances are assessed on a simulation study and a German stock return data set.