The problem of estimating unknown observational variances in multivariate dynamic linear models is considered. Conjugate procedures are possible for univariate models and also for special very restrictive common components models but they are not generally applicable. However, for clarity of operation and in order to avoid numerical integration, it is desirable to have conjugacy or approximate conjugacy. Such an approximate procedure is proposed based upon a simple analytic approximation. It is exact for the sub-class of conjugate models and improves on a previous procedure based upon the Robust filter.

This paper presents short-term forecasting methods applied to electricity consumption in Brazil. The focus is on comparing the results obtained after using two distinct approaches: dynamic non-linear models and econometric models. The ®rst method, that we propose, is based on structural statistical models for multiple time series analysis and forecasting. It involves nonobservable components of locally linear trends for each individual series and a shared multiplicative seasonal component described by dynamic harmonics. The second method, adopted by the electricity power utilities in Brazil, consists of extrapolation of the past data and is based on statistical relations of simple or multiple regression type. To illustrate the proposed methodology, a numerical application is considered with real data. The data represents the monthly industrial electricity consumption in Brazil from the three main power utilities: Eletropaulo, Cemig and Light, situated at the major energy-consuming states, Sao Paulo, Rio de Janeiro and Minas Gerais, respectively, in the Brazilian Southeast region. The chosen time period, January 1990 to September 1994, corresponds to an economically unstable period just before the beginning of the Brazilian Privatization Program. Implementation of the algorithms considered in this work was made via the statistical software S-PLUS.

This paper presents short-term forecasting methods applied to electricity consumption in Brazil. The focus is on comparing the results obtained after using two distinct approaches: dynamic non-linear models and econometric models. The ®rst method, that we propose, is based on structural statistical models for multiple time series analysis and forecasting. It involves nonobservable components of locally linear trends for each individual series and a shared multiplicative seasonal component described by dynamic harmonics. The second method, adopted by the electricity power utilities in Brazil, consists of extrapolation of the past data and is based on statistical relations of simple or multiple regression type. To illustrate the proposed methodology, a numerical application is considered with real data. The data represents the monthly industrial electricity consumption in Brazil from the three main power utilities: Eletropaulo, Cemig and Light, situated at the major energy-consuming states, Sao Paulo, Rio de Janeiro and Minas Gerais, respectively, in the Brazilian Southeast region. The chosen time period, January 1990 to September 1994, corresponds to an economically unstable period just before the beginning of the Brazilian Privatization Program. Implementation of the algorithms considered in this work was made via the statistical software S-PLUS.