Abstract
An important concern in statistics is the linear combination of predictors of a random variable that are based on several sources of information. In the time-series context the technique is used, for example, to forecast or estimate missing observations. At the practical level, it is well known in the combining forecasts literature that combining is a pragmatic solution to the failure to synthesize all the information into an optimal forecast. In this paper we caution against using this procedure arbitrarily, in particular with weighted averages, to obtain an overall linear predictor of the random quantity. We illustrate the results with examples about estimating the missing observations in time series.
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