The Model of Time Series as a Piecewise-Stationary Process

This work is devoted to determining the space-time area that contains a time-series trend to address mathematical expectations. A time series trajectory represents the realization of a stochastic process in discrete time; thus, its approximation is random and cannot be considered a trend valuation. We offer to interpret an arbitrary time series as a trajectory of a piecewise-stationary process. This allows for us to describe an algorithm that constructs the area where the trend is located.