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Outliers in time-series data are crucial in model estimation and forecasting. Understanding the importance of false detection of outliers in various autoregressive processes, the present study aims to evaluate test statistics' performance by utilizing multiple models through robust estimation of errors. In this study, numerous data-generating techniques have been employed via simulation at different values of the estimates, location, and size of an outlier, sample sizes, and classical cutoff to access the power of the test statistics for false detection of outlier type. The findings of the simulation reveal that the location and size of outliers, parameter values, and, to some extent, the size of the series influence the behavior of test statistics in detecting the type of outliers. Overall, the estimation method of residual standard deviation influences the sampling behavior of the test statistics. Outliers also affect the forecasting performance in the model. All results are also validated empirically. [ABSTRACT FROM AUTHOR]