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Adaptive computing systems rely on accurate predictions of application behavior to understand and respond to the dynamically varying characteristics. In this study, we present a Statistical Metric Model (SMM) that is system- and metric-independent for predicting application behavior. SMM is a probability distribution over application patterns of varying length and it models how likely a specific behavior occurs. Maximum Likelihood Estimation (MLE) criterion is used to estimate the parameters of SMM. The parameters are further refined with a smoothing method to improve prediction robustness. We also propose an extension to SMM (i.e., SMM-Interp) to handle sudden short-term changes in application behavior. SMM learns the application patterns during runtime, and at the same time predicts the upcoming application phases based on what it has learned up to that point. We demonstrate several key features of SMM: (1) adaptation, (2) variable length sequence modeling, and (3) long-term memory. An extensive and rigorous series of prediction experiments show the superior performance of the SMM predictor over existing predictors on a wide range of benchmarks. For some of the benchmarks, SMM reduces the prediction error rate by 10X and 3X, compared to last value and table-based prediction approaches, respectively. SMM's improved prediction accuracy results in superior power-performance tradeoffs when it is applied to an adaptive dynamic power management scheme.