The standard method to train the Higher Order Neural Networks (HONN) is the well-known Backpropagation (BP) algorithm. Yet, the current BP algorithm has several limitations including easily stuck into local minima, particularly when dealing with highly non-linear problems and utilise computationally intensive training algorithms. The current BP algorithm is also relying heavily on the initial weight values and other parameters picked. Therefore, in an attempt to overcome the BP drawbacks, we investigate a method called Modified Cuckoo Search-Markov chain Monté Carlo for optimising the weights in HONN and boost the learning process. This method, which lies in the Swarm Intelligence area, is notably successful in optimisation task. We compared the performance with several HONN-based network models and standard Multilayer Perceptron on four (4) time series datasets: Temperature, Ozone, Gold Close Price and Bitcoin Closing Price from various repositories. Simulation results indicate that this swarm-based algorithm outperformed or at least at par with the network models with current BP algorithm in terms of lower error rate.