Forecasting contemporal aggregates of multiple time series

The paper considers forecasting a contemporal linear aggregate yt of a vector time series Z't =(Z1t,...,Zkt). We first disciss the case where Zt follows a stationary multiple moving average process and propose a measure of the efficiency of aggregation. A necessary and sufficient condition is given for the case of no gain by employing the component series. Extension of the results to stationary multiple autoregressive process and some non-stationarity processes is discussed, and an illustrative example is given.