In thispaper Innovations Space State Models (SSM) are used to fit series with: 1) asingle seasonal period and 2) multiple seasonal periods. Sales data of 1) axlesand 2) suspensions of a metallurgical company from Alvear (Santa Fe, Argentina)are analyzed as series with a single seasonal pattern. To analyze series withcomplex seasonal patterns, the series of a) daily vehicles passing through thetoll booth on the Rosario- Buenos Aires (Argentina) highway and b) Las Rosas(Santa Fe, Argentina) daily average gas consumption per customer measured in m3.The main purpose of these comparisons is to obtain predicted values with anacceptable error and a controllable level of uncertainty. Another reason forthese comparisons is that Argentinean series show more variability than those withmore stable development countries. In serieswith a single seasonal pattern, ETS models have a good post-sample forecastingperformance. The out-of-sample average forecast error five-step-ahead are 9.4%and 6.9%, for axles and suspensions, respectively, with a controllable level ofuncertainty. BATS (Exponential Smoothing State Space model with Box-Coxtransformation, ARMA errors, Trend and Seasonal Components) and TBATS(Trigonometric Exponential Smoothing State Space model with Box-Coxtransformation, ARMA errors, Trend and Seasonal Components) are introduced toforecast complex seasonal time series. The resultsshow that both types of models are suitable to describe and predict the timeseries of daily vehicles. The TBATS modelhas some advantages over the BATS model such as: i) better goodness of fit(lower AIC), ii) lower out-sample forecast percentage for different horizons(measured by MAPE); reduction in computation time to estimate the model, giventhe smaller number of seed values. However, for the gas demand data, the performance of the proposed models isnot as good, the BATS model does not show a good fit, and although the TBATS modelfits the data well, it provides forecasts with more error than a MEE with Spline. A possible explanation for the lower qualityforecasts of the TBATS, is that in this application TBATS models do not includeexplanatory variables that are included in the SSM, and it is known thatclimatic variables have much influence on utilities demand series. However, given the simplicity these models, they cannot becompletely discarded.