Many financial crises have occurred in recent decades, such as the International Debt Crisis of 1982, the East Asian Economic Crisis of 1997–2001, the Russian economic crisis of 1992–1997, the Latin American debt Crisis of 1994–2002, the Global Economic Recession of 2007–2009, which had a strong impact on international relations. The aim of this article is to create an econometric model of the indicator for identifying crisis situations arising in stock markets. The approach under consideration includes data for preprocessing and assessing the stability of the trend of time series using higher-order moments. The results obtained are compared with specific practical situations. To test the proposed indicator, real data of the stock indices of the USA, Germany and Hong Kong in the period World Financial Crisis are used. The scientific novelty of the results of the article consists in the analysis of the initial and given initial moments of high order, as well as the central and reduced central moments of high order. The econometric model of the indicator for identifying crisis situations arising considered in the work, based on high-order moments plays a pivotal role in crisis detection in stock markets, influencing financial innovations in managing the national economy. The findings contribute to the resilience and adaptability of the financial system, ultimately shaping the trajectory of the national economy. By facilitating timely crisis detection, the model supports efforts to maintain economic stability, thereby fostering sustainable growth and resilience in the face of financial disruptions. The model’s insights can shape the national innovation ecosystem by guiding the development and adoption of monetary and financial innovations that are aligned with the economy’s specific needs and challenges.