The temporal trajectories of the spectral energy in auditory critical bands over 250~ms segments are approximated by an all-pole model, the time-domain dual of conventional linear prediction. This quarter-second auditory spectro-temporal pattern is further smoothed by iterative alternation of spectral and temporal all-pole modeling. Just as Perceptual Linear Prediction (PLP) uses an autoregressive model in the frequency domain to estimate peaks in an auditory-like short-term spectral slice, PLP$^2$ uses all-pole modeling in both time and frequency domains to estimate peaks of a two-dimensional spectro-temporal pattern, motivated by considerations of the auditory system.