Multiplicative Exponential Models For Stationary Time Series

. A class of models for one dimensional time series is presented. The spectrum of such a model is obtained by raising the spectrum of a known parameterized model to an exponent, allowed to attain arbitrary real values. For a moving average model this for example means that the roots of the moving average operator are allowed to have any real order. This method adds a further flexibility to the model which for example allows us to model long memory time series using only a few parameters. The exponent is parameterized in a special way to make the estimation of the parameter determining the exponent asymptotically independent of the estimation of the other model‐parameters. The asymptotic distribution of the estimators is derived. The idea is also used for multiplicative models with an exponent for each seasonal factor. In this case the estimators are only approximately independent for a large season length. Finally an application of the model is given using the Beveridge wheat price index.