In recent months, a global surge in inflation rates has been attributed to numerous factors, including the Russian invasion of Ukraine and the impact of the COVID-19 pandemic. The dynamic and unforeseeable nature of these events poses a significant challenge to predictive models. Consequently, a persistent need arises to develop forecasting techniques capable of adapting to evolving conditions in price formation, enhancing informed decision-making. To address this imperative, we undertake the training, validation, and comparative assessment of multiple models that integrate machine learning techniques with quantile regression methodologies. Specifically, we analyze the predictive performance of quantile transformer networks (QTN) and benchmark them against quantile autoregressive integrated moving average models (QARIMA), quantile convolutional neural networks (QCNN), and quantile long short-term memory networks (QLSTM). The evaluation employs monthly data spanning 1970 to 2022 from three developed economies (France, Germany, and the United States) and three developing economies (India, South Africa, and Mexico). Our findings indicate that predictive accuracy varies by forecast quantile. For the 0.1 quantile, QARIMA achieved the lowest pinball losses in four out of six countries. For the 0.5 quantile, QTN performed better with the lowest pinball losses in four out of six countries. Finally, at the 0.9 quantile, QLSTM was the best-performing model in three out of six countries, followed closely by QCNN.