Nonlinear models of analysis of variance

It seems quite natural for economists to decompose a series with several indexes (time, industry, etc.) into several series with one index a piece, each of which will be analyzed separately. This operation has generally been made in a linear way in the traditional analysis of variance, possibly after some transformation of the initial series. We propose to do this in a multiplicative way which does not allow us to use the basic theorems of econometrics, and which is near factor analysis. We present several kinds of estimators, study their statistical properties and finally compare our method to more classical ones, using a series of the distribution of dividends paid by French corporations, available over 11 years for 26 industries.