As product variety is an important feature for modern enterprises, multi-product demand forecasting is essential to support order decision-making and inventory management. However, these well-established forecasting approaches for multi-dimensional time series, such as VAR or DFM, all cannot deal very well with time series with high or ultra-high dimensionality, especially when the time series are short. Considering that besides the demand trends in historical data, that of associated products (including highly correlated ones or ones having significantly causality) can also provide rich information for prediction, we propose new forecasting approaches for multiple products in this study. The demand of associated products is treated as predictors to add in AR model to improve its prediction accuracy. If there are many time series associated with the object, we introduce two schemes to simplify variables to avoid over-fitting. Then procurement data from a grid company in China is applied to test forecasting performance of the proposed approaches. The empirical results reveal that compared with four conventional models, namely SES, AR, VAR and DFM respectively, the new approaches perform better in terms of forecasting errors and inventory simulation performance. They can provide more effective guidance for actual operational activities.