Predicting spatiotemporal neural activity could lead to early detection of seizures and better understanding of cognitive processes in the brain. Parallel reservoir computing, where spatiotemporal data are split into regions and one reservoir predicts each region, has been proposed as a method to predict large spatiotemporal data with high efficiency and accuracy. However, no studies have extended parallel reservoir computing to predict large-scale brain activity. As the accuracy of the prediction will drop dramatically if the hyperparameters are not properly set, the relationship between the hyperparameters of parallel reservoir computing and parameters of neuronal simulations such as connection length, axonal conduction speed, and excitatory and inhibitory synaptic conductance should be explored. In this study, we systematically investigated the relationship between the appropriate hyperparameters of parallel reservoir computing and parameters from neuronal simulations. Specifically, we first simulated spiking neural networks and evaluated their spatial features while varying the parameters. Then, for each parameter setting, we investigated the hyperparameters of parallel reservoir computing that reproduced the temporal features of traveling waves. Our findings indicated that axonal conduction speed and connection length drastically affected the appropriate hyperparameters, while excitatory and inhibitory synaptic weights did not. In addition, spatial features alone did not necessarily determine the appropriate hyperparameters to predict neural activity. Our study reveals that more studies are needed to find a way to assess the dynamics of neuronal population, thereby paving the way for the prediction of large-scale brain activity.