Bayesian spectral density estimation using P-splines with quantile-based knot placement

This article proposes a Bayesian approach to estimating the spectral density of stationary time series using prior based on mixture P-spline distributions. Our proposal is motivated by B-spline Dirichlet process Edwards et al. (Stat Comput 29(1):67–78, 2019. https://doi.org/10.1007/s11222-017-9796-9 ) in combination with Whittle’s likelihood and aims at reducing high computational complexity its posterior computations. The strength over Bernstein–Dirichlet Choudhuri (J Am Stat Assoc 99(468):1050–1059, 2004. https://doi.org/10.1198/016214504000000557 lies ability estimate densities sharp peaks abrupt changes due flexibility B-splines variable number location knots. Here, we suggest use P-splines Eilers Marx Sci 11(2):89–121, 1996. https://doi.org/10.1214/ss/1038425655 that combine basis discrete penalty coefficients. In addition equidistant knots, novel strategy for more expedient placement knots proposed makes information provided periodogram about steepness power distribution. We demonstrate simulation study two real case studies this retains B-splines, achieves similar accurately new data-driven knot allocation scheme but significantly reduces costs.