The Flexible Transmuted Record Type-Scale Mixture of Normal Family and its AR(1) Extension

In the present paper, a flexible skew version of the scale mixture of normal family is introduced based on the transmuted record type, called TRT-SMN, which seems suitable for handling any skewness and kurtosis in real data sets. Several properties of the TRT-SMN family are provided, including the moment generating function and r-th moments. The parameters of the new family are estimated through the ECME algorithm. Further to the elegant properties of the proposed family, the paper considers, in the time series context, a first-order autoregressive process with TRT-SMN distributed innovations. Some Monte Carlo simulation experiments are executed to assess the consistency of the ECME estimates. To further motivate its purpose, the proposed process is applied to analyze the series of COVID-19 incidence in Bavaria. The proposed AR(1) with TRT-SMN innovations yields superior fitting criteria compared to AR(1) process with Gaussian innovations.