Exponential smoothing with credibility weighted observations

Our interest is in time series data smoothing. We view this process as an aggregation of previously observed values. We first discuss the features desired of a good smoothing operator. We particularly note the conflict that exists between our desire for minimal variance and desire to use the freshest data. We describe a number of commonly used smoothing techniques, moving average and exponential smoothing. We then consider the extension of these methods to the case where the observations can have different credibility or importances. Specifically we develop an extension of the exponential smoothing method to the case where the observations can have different importance weights in the smoothing process.