In this paper several univariate and multivariate (more specifically dimensionality reduction techniques, such as the Dynamic Factor Model, DFM) time series approaches and different training strategies for these models are proposed in order to compute forecasts for the number of cases per 100,000 inhabitants of Acute Respiratory Infections (AcRI) in several countries of the European Union (EU) whose historical datasets are available from RespiCast. All the proposals are used to compute weekly forecasts from 2020 up to spring 2025 and carefully compared using an adequate Analysis of Variance (ANOVA). Here, the forecasting horizon is extended up to 22 weeks, although in RespiCast the models provided by all the participants are 4 weeks maximum. As a summary, it can be stated that univariate ARIMA models accounting for seasonality are better for the short-term, and DFM produces more accurate forecasts in the long run. Additionally, the combination of forecasts here built with our best reduces the forecasting error of the baseline provided by RespiCast about 50% for the short-term. In some recent periods (first two months in 2025) our approach beats (in accuracy terms) most forecasts submitted by other teams (ranking 1, 2 or 3 out of 10 teams). For the rest of the span of time considered the average ranking is 4. It should be taken into account that just our DFM approach is capable of computing relatively accurate forecasts for longer forecasting horizons (up to 22 weeks) than those considered in RespiCast (just up to 4 weeks).