Accurate and reliable forecasting is a crucial task in many different domains. The selection of a forecasting algorithm that is suitable for a specific time series can be a challenging task, since the algorithms’ performance depends on the time-series properties, as well as the properties of the forecasting algorithms. The methodology and analysis presented in this paper are contributing towards understanding the performance of time-series forecasting methods. Instead of using time-series meta-features only to obtain a good meta-model that can predict the performance of a forecasting algorithm, the methodology can link which features are important for which forecasting methods. We used time-series meta-features extracted using the tsfresh and catch22 libraries. We also found that the importance of the meta-features changes depending on the meta-model that is used. There are only a few meta-features that always appear important for a given forecasting method no matter which meta-model will be used for learning, which further provides opportunities to select a model-agnostic feature portfolio. In addition, different feature importance techniques can provide different results that are related to the methodology that is used by the meta-model. By using the feature importance obtained by a meta-model and a specified feature importance technique, we can define a representation of a forecasting method behavior, which can further provide an insight into which forecasting methods have similar behavior.