Algorithm of variance estimation in weighted least squares method

The representation of a time series model as a piecewise-stationary process is provided, wherein it is regarded as a collection of successive stationary intervals. An algorithm has been developed for identifying the domain containing the trend within this model. It is recognized that applying the least squares method directly for trend determination is not commonly employed in statistical analysis and econometric software packages. Typically, the weighted least squares method is utilized to ideally eliminate non-stationarity. The authors presents an algorithm for estimating the weight coefficients for this method through piecewise-stationary modeling. The algorithm has been tested on time series of various natures.