Inferencing trigonometric time series model

I dont think that is the correct intuition. Think of the MCMC sampling as trying to take an integral, all these small local peaks adds up to a lot of volumes that NUTS is desperately trying to compensate, while Metropolis wrongly stuck in one mode. Notice also that since we are estimating an expectation using MCMC samples, it will not converge to anything meaningful if the expectation does not exist - which I suspect it is what the NUTS sampler is showing here.