This paper offers for the first time a novel method for creating Predictive Associative Memories of Time series (PAMeT), where a full set of time series variables is used to create a machine learning predictive model (global learning), and afterward, only a few temporal variables are used at a shorter time to recall the model on new data (local recall). Inspired by human brain processes, PAMeT-SNN leverages the brain-inspired SNN NeuCube and the concept of spatio-temporal associative memories (STAM). PAMeT-SNN is a 4-dimensional spatio-temporal structure. First, it encodes time series data into spike sequences that reflects on the changes in the data over time and then maps the temporal variables into the SNN using temporal similarity to define the spatial locations of the variables in the SNN. It then learns temporal associations between a full set of time series variables, thereby memorizing these temporal associations as spatio-temporal connections between neurons. These connections are activated when only part of the time series data is used to recall the model on new data. The proposed groundbreaking method is exemplified with PAMeT-SNN for predictive modeling on two distinct case study time series data sets: trade dynamics and commodity prices. In these case studies, the method effectively captures the intricate data dynamics, enabling accurate forecasting of future values using a minimal set of variables. The method has the potential to be applied in diverse domains.