This paper proposed a novel first-order single-valued neutrosophic hesitant fuzzy time series (SVNHFTS) forecasting model. Our aim is to improve the previously proposed neutrosophic time series (NTS) model by incorporating the degree of the hesitancy using single-valued neutrosophic hesitant fuzzy set (SVNHFS) model instead of single-valued neutrosophic set (SVNS). Our paper's novelty is that we incorporate an algorithm that automatically converts the crisp dataset into the neutrosophic set that eliminates the need for experts' input or opinions in determining the membership in each of the partitioned neutrosophic set. We also incorporate Markov Chain algorithm in the de-neutrosophication process to include the weightage of the repeating neutrosophic logical relationships (NLRs). Our paper's significant contribution is to add to the existing body of knowledge related to fuzzy time series (FTS) by developing a new FTS model based on SVNHFS, one of the improved version of fuzzy sets, since this area of research is still relatively underdeveloped. To determine our proposed model's capability, we apply our proposed SVNHFTS model to three real datasets while also comparing the result to the other FTS models based on improved versions of fuzzy sets. Our datasets include benchmark enrollment data of University of Alabama, IDX Composite (Indonesian composite stock index), and MERVAL index (Argentinian composite stock index). The result shows that our proposed SVNHFTS model outperforms most of the other FTS models in terms of AFE and RMSE, especially the previously proposed NTS model.