Abstract
Two-piece location-scale models are used for modeling data presenting departures from symmetry. In this paper, we propose an objective Bayesian methodology for the tail parameter of two particular distributions of the above family: the skewed exponential power distribution and the skewed generalised logistic distribution. We apply the proposed objective approach to time series models and linear regression models where the error terms follow the distributions object of study. The performance of the proposed approach is illustrated through simulation experiments and real data analysis. The methodology yields improvements in density forecasts, as shown by the analysis we carry out on the electricity prices in Nordpool markets.
Highlights
Two-piece location-scale models have been mainly used for modeling data exhibiting departures from symmetry
We propose an objective Bayesian methodology for the tail parameter of two particular distributions of the above family: the skewed exponential power distribution and the skewed generalised logistic distribution
We assume σ1 = σ2 = σ and we focus on three particular two-piece location-scale models: the skewed Student-t distribution (SST), the skewed exponential power distribution (SEPD) and the skewed generalized logistic distribution (SGLD)
Summary
Two-piece location-scale models have been mainly used for modeling data exhibiting departures from symmetry. Rubio and Steel (2014) derived the Jeffreys rule prior and the independence Jeffreys priors for different families of skewed distributions. We introduce a novel objective prior for some distributions of the class of two-piece location-scale models, such as the skewed exponential power distribution (SEPD) and the skewed generalized logistic distribution (SGLD). Following Leisen et al (2017), we introduce a Bayesian approach obtained by applying the loss-based prior discussed in Villa and Walker (2015). We derive the loss-based prior for the parameter that controls heaviness of the tails of the distribution. The application of the SEPD and SGLD to represent the errors of time series and regression models, has received limited attention in the context of objective Bayesian analysis.
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