Cause of failure of the non-centered-in-location KSC parameterisation

Identify the specific reasons why the non-centered-in-location parameterisation of the Gaussian off-set mixture stochastic volatility model performed poorly under the Kim–Shephard–Chib MCMC algorithm with Kalman filter and simulation smoother in the Simulation Based Calibration experiments, and assess whether alternative parameterisations, software implementations, or sampling strategies can rectify the calibration issues.

Background

The paper finds that the KSC algorithm applied to a non-centered-in-location parameterisation exhibits poor calibration under SBC, with large deviations from uniform rank statistics.

The authors suggest potential causes, such as software implementation constraints of the Kalman filter and simulation smoother or incompatibility of this parameterisation with the KSC approach, but defer a definitive diagnosis and exploration of alternatives.