This study is based on time-series data taken from the combined cycle heavy-duty utility gas turbines. For analysis, first a multistage vector autoregressive model is constructed for the nominal operation of the powerplant assuming sparsity in the association among variables and this is used as a basis for anomaly detection and prediction. This prediction is compared with the time-series data of the plant-operation containing anomalies. The comparative advantage based on prediction accuracy and applicability of the algorithms is discussed for the postprocessing. Next, the long-memory behavior of residuals is modeled, and heterogeneous variances are observed from the residuals of the generalized additive model. Autoregressive fractionally integrated moving average (ARFIMA) and generalized autoregressive conditional heteroskedasticity (GARCH) models are employed to fit the residual process, which significantly improve the prediction. Rolling one-step-ahead forecast is studied. Numerical experiments of abrupt changes and trend in the blade-path temperature are performed to evaluate the specificity and sensitivity of the prediction. The prediction is sensitive given reasonable signal-to-noise ratio and has lower false positive rate. The control chart is able to detect the simulated abrupt jump quickly.