Statistical learning and probabilistic prediction are fundamental processes in auditory cognition. A prominent computational model of these processes is Prediction by Partial Matching (PPM), a variable-order Markov model that learns by internalizing n-grams from training sequences. However, PPM has limitations as a cognitive model: in particular, it has a perfect memory that weights all historic observations equally, which is inconsistent with memory capacity constraints and recency effects observed in human cognition. We address these limitations with PPM-Decay, a new variant of PPM that introduces a customizable memory decay kernel. In three studies—one with artificially generated sequences, one with chord sequences from Western music, and one with new behavioral data from an auditory pattern detection experiment—we show how this decay kernel improves the model’s predictive performance for sequences whose underlying statistics change over time, and enables the model to capture effects of memory constraints on auditory pattern detection. The resulting model is available in our new open-source R package, ppm (https://github.com/pmcharrison/ppm)., Author summary Humans hear a rich variety of sounds throughout everyday life, ranging from the basic (e.g. an alarm clock, a whistling kettle, an ambulance siren) to the complex (e.g. speech, music, birdsong). Understanding these sounds depends on an ability to detect and remember patterns in these sounds, patterns ranging from the two-tone oscillation of the ambulance siren to the classic four-chord progression of Western popular music. A key challenge in audition research is to develop effective computer models of these pattern-detection processes. The Prediction by Partial Matching model is one such model, originally developed for data compression, that learns statistical patterns of varying complexity from sequences of discrete symbols (e.g. ‘A, B, A, A, B, A, B’). In previous research this model has proved particularly effective for simulating listeners’ responses to music as well as other kinds of auditory sequences. However, the model is an unrealistic simulation of human cognition in that it possesses a perfect memory, unbounded in capacity, where historic events are recalled just as clearly as recent events. In this paper we therefore introduce a memory-decay component to the model, whereby the salience of historic auditory events decreases over time in line with the dynamics of human auditory memory. We present an experiment showing that this memory-decay model provides a natural account of experimental data from an auditory pattern detection task, explaining how human performance deteriorates as a function of the length of the patterns being detected and the speed at which they are played. Conversely, we also present two simulation studies showing that this memory-decay component can improve pattern detection in auditory environments whose statistical structure changes dynamically over time. These studies indicate the potential benefit of incorporating memory constraints into statistical models of auditory pattern detection, and highlight how these memory constraints can both impair and improve pattern detection, depending on the environment.