Matrix-assisted laser desorption/ionization Fourier transform ion cyclotron resonance mass spectrometry is a technique for high mass-resolution analysis of substances that is rapidly gaining popularity as an analytic tool. Extracting signal from the background noise, however, poses significant challenges. In this article, we model the noise part of a spectrum as an autoregressive, moving average (ARMA) time series with innovations given by a generalized gamma distribution with varying scale parameter but constant shape parameter and exponent. This enables us to classify peaks found in actual spectra as either noise or signal using a reasonable criterion that outperforms a standard threshold criterion.