We discuss the various sources of error in numerical computations with the use of examples from the literature relevant to time series analysis. We also submit a case where, by manual verication, we were able to discover a plausible forecast to be erroneous due to a number of software aws in the XLSTAT addin for Microsoft Excel. Furthermore, after discussing the alternative techniques for implementing on a computer the ARIMA (AutoRegressive, Integrated, Moving Average) methodology, we show that dierent approaches can cause considerable discrepancies in the results across dierent programs and even within a single software system.