Can dark energy be dynamical?

We highlight shortcomings of the dynamical dark energy (DDE) paradigm. For parametric models with equation of state (EOS), $w(z) = w_0 + w_a f(z)$ for a given function of redshift $f(z)$, we show that the errors in $w_a$ are sensitive to $f(z)$: if $f(z)$ increases quickly with redshift $z$, then errors in $w_a$ are smaller, and vice versa. As a result, parametric DDE models suffer from a degree of arbitrariness and focusing too much on one model runs the risk that DDE may be overlooked. In particular, we show the ubiquitous Chevallier-Polarski-Linder model is one of the least sensitive to DDE. We also comment on ``wiggles" in $w(z)$ uncovered in non-parametric reconstructions. Concretely, we isolate the most relevant Fourier modes in the wiggles, model them and fit them back to the original data to confirm the wiggles at $\lesssim2\sigma$. We delve into the assumptions going into the reconstruction and argue that the assumed correlations, which clearly influence the wiggles, place strong constraints on field theory models of DDE.