First-order dynamic occupancy models (FODOMs) are a class of state-space model in which the true state (occurrence) is observed imperfectly. An important assumption of FODOMs is that site dynamics only depend on the current state and that variations in dynamic processes are adequately captured with covariates or random effects. However, it is often difficult to understand and/or measure the covariates that generate ecological data, which are typically spatiotemporally correlated. Consequently, the non-independent error structure of correlated data causes underestimation of parameter uncertainty and poor ecological inference. Here, we extend the FODOM framework with a second-order Markov process to accommodate site memory when covariates are not available. Our modeling framework can be used to make reliable inference about site occupancy, colonization, extinction, turnover, and detection probabilities. We present a series of simulations to illustrate the data requirements and model performance. We then applied our modeling framework to 13 yr of data from an amphibian community in southern Arizona, USA. In this analysis, we found residual temporal autocorrelation of population processes for most species, even after accounting for long-term drought dynamics. Our approach represents a valuable advance in obtaining inference on population dynamics, especially as they relate to metapopulations.