Smoothness priors analysis of quasi-periodic time series

The analysis of quasi-periodic data, that is cyclical-like but where the period and amplitude appear to change gradually is realized in a smoothness priors general state space model setting. Prior distributions, (the equivalent of stochastic perturbations), on the amplitude and phase of a nominal periodic function are parameterized by two hyperparameters. The minimization of the likelihood of the hyperparameters yields a model with a relatively complex structure and a relatively large number of implicitly inferred parameters. The analysis, in which recursive prediction, filtering and smoothing are realized by numerical integration, yields a joint posterior amplitude and phase distribution. An example of the analysis of the well known Wolfer sunspot series is shown.