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Summary This paper reviews and extends several aspects of the analysis of linear combinations of time series. Special cases are temporal and contemporaneous aggregations and systematic sampling. We present some simple examples, a unified notation, references to the literature, and some general results for linear combinations of scalar and vector time series. For basic time series following ARIMA models in scalar cases we derive the ARIMA models of the linear combinations as functions of those of the basic series in both the nonseasonal and seasonal cases. For vector time series we compare the forecast efficiencies of two alternative approaches: first model and forecast and then form the linear combination, and first form the linear combination and then model and forecast; for this analysis we use the moving average representation of a stationary time series. A final section contains an application to monthly data on milk production and milk productivity series for the State of Siio Paulo, Brazil.