Time-series data offer wide-ranging opportunities to test hypotheses about the physical and biological factors that influence species abundances. Although sophisticated models have been developed and applied to analyze abundance time series, they require information about species detectability that is often unavailable. We propose that in many cases, simpler models are adequate for testing hypotheses. We consider three relatively simple regression models for time series, using simulated and empirical (fish and mammal) datasets. Model A is a conventional generalized linear model of abundance, model B adds a temporal autoregressive term, and model C uses an estimate of population growth rate as a response variable, with the option of including a term for density dependence. All models can be fit using Bayesian and non-Bayesian methods. Simulation results demonstrated that model C tended to have greater support for long-lived, lower-fecundity organisms (K life-history strategists), while model A, the simplest, tended to be supported for shorter-lived, high-fecundity organisms (r life-history strategists). Analysis of real-world fish and mammal datasets found that models A, B, and C each enjoyed support for at least some species, but sometimes yielded different insights. In particular, model C indicated effects of predictor variables that were not evident in analyses with models A and B. Bayesian and frequentist models yielded similar parameter estimates and performance. We conclude that relatively simple models are useful for testing hypotheses about the factors that influence abundance in time-series data, and can be appropriate choices for datasets that lack the information needed to fit more complicated models. When feasible, we advise fitting datasets with multiple models because they can provide complementary information.