The article is devoted to a new indicator for forecasting critical points of financial time series based on modified Hölder indicators. The indicator was developed to predict large movements of financial instruments in the stock market. The analysis of the indicator's performance was conducted on the US and Russian stock markets using time series with a minute sampling frequency. It is shown that this indicator is able to predict large movements of financial time series with good enough statistics. The corresponding calculations, tables and statistics are presented. The paper shows that the developed predictor on average in 80% of cases in the US market and on average in 60% of cases on the Russian market correctly predicts large movements in the market. These results were obtained by statistical processing of all predictions of critical points in the markets of the USA and Russia. Also, a significant difference was found between the parameters of the developed indicator for the US and Russian markets.