Global and local trend analysis and change-point analysis of selected financial and market indices

From the macroeconomic point of view, the stock index is the best indicator of the behavior of the stock market. Stock indices fulfill different functions. One of their most important functions is to observe developments of the stock market situation. Therefore, it is crucial to describe the long-term development of indices and also to find moments of abrupt changes. Another interesting aspect is to find those indices that have evolved in a similar way over time. In this article, using trend analysis, we will uncover the global evolution of selected indices. After evaluating the global trend in the series we compare the results with local trend analysis. Other goal is to detect the moments in which this development suddenly changed using the change-point analysis. By means of cluster analysis, we find those indices that are most similar in long-term development. In each analysis, we select the most appropriate methods and compare their results.