On the time dependence of smoothed variables

In Meteorology one often concentrates the study not on instantaneous values of a variable, but on smoothed values, like daily, pentadic and monthly averages. When studying the time dependency of instantaneous and smoothed variables, the problem arises of fitting statistical models to observed series of data. The present paper considers which models must be applied to smoothed data when models of moving average type or autoregressive models have been introduced for the instantaneous variables. A result of the simple formulae derived is to give a warning against use of simple models for the smoothed data.