A method for monitoring an operational state of a system on the basis of telemetry data, wherein the operational state is either a first state or a second state, the second state being a state different from the first state, and the telemetry data (109; 409; 509) comprises time series data of at least one parameter of the system indicating the operational state of the system over time, the method comprising: obtaining first interval data indicating time series data of a parameter of the at least one parameter of the system relating to a time interval of a predetermined duration characterized by determining a plurality of characteristic quantities of the first interval data, the plurality of characteristic quantities determined at this step forming a first set of characteristic quantities, wherein the first set of characteristic quantities is arranged as a first tuple of characteristic quantities; obtaining a plurality of second sets of characteristic quantities (110; 410; 510) formed by the plurality of characteristic quantities, wherein the plurality of second sets of characteristic (110; 410; 510) quantities relate to the parameter of the at least one parameter of the system and to a plurality of time intervals of the predetermined duration during which the system was in the first state, wherein the plurality of second sets of characteristic quantities (110; 410; 510) are arranged as a plurality of second tuples of characteristic quantities; and determining a probability of the first set of characteristic quantities being an outlier with respect to the plurality of second sets of characteristic quantities, wherein determining the probability of the first set of characteristic quantities being an outlier with respect to the plurality of second sets of characteristic quantities comprises: determining, using a distance function indicating a separation between two given tuples of characteristic quantities, a first group of second tuples comprising a predetermined number of nearest neighbors of the first tuple; determining, using the distance function, a first density measure indicating an average density of the tuples of the first group of second tuples; determining, using the distance function, for each tuple in the first group of second tuples a second group of second tuples comprising the predetermined number of nearest neighbors of the respective tuple in the first group of second tuples; determining, using the distance function, for each second group of second tuples a second density measure indicating an average density of the tuples of the respective second group of second tuples; and determining a probability of the first tuple being an outlier with respect to the plurality of second tuples based on the first density measure and the second density measures. obtaining first interval data indicating time series data of a parameter of the at least one parameter of the system relating to a time interval of a predetermined duration determining a plurality of characteristic quantities of the first interval data, the plurality of characteristic quantities determined at this step forming a first set of characteristic quantities, wherein the first set of characteristic quantities is arranged as a first tuple of characteristic quantities; obtaining a plurality of second sets of characteristic quantities (110; 410; 510) formed by the plurality of characteristic quantities, wherein the plurality of second sets of characteristic (110; 410; 510) quantities relate to the parameter of the at least one parameter of the system and to a plurality of time intervals of the predetermined duration during which the system was in the first state, wherein the plurality of second sets of characteristic quantities (110; 410; 510) are arranged as a plurality of second tuples of characteristic quantities; and determining a probability of the first set of characteristic quantities being an outlier with respect to the plurality of second sets of characteristic quantities, determining, using a distance function indicating a separation between two given tuples of characteristic quantities, a first group of second tuples comprising a predetermined number of nearest neighbors of the first tuple; determining, using the distance function, a first density measure indicating an average density of the tuples of the first group of second tuples; determining, using the distance function, for each tuple in the first group of second tuples a second group of second tuples comprising the predetermined number of nearest neighbors of the respective tuple in the first group of second tuples; determining, using the distance function, for each second group of second tuples a second density measure indicating an average density of the tuples of the respective second group of second tuples; and determining a probability of the first tuple being an outlier with respect to the plurality of second tuples based on the first density measure and the second density measures.