Geodesic
Algorithm of variance estimation in weighted least squares method
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 19 (2023) no. 4, pp. 484-496

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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.
Keywords: time series, piecewise-stationary process, weighted least squares method. 
@article{VSPUI_2023_19_4_a4,
     author = {A. V. Prasolov and N. G. Ivanov and N. V. Smirnov},
     title = {Algorithm of variance estimation in weighted least squares method},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {484--496},
     publisher = {mathdoc},
     volume = {19},
     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2023_19_4_a4/}
}
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A. V. Prasolov; N. G. Ivanov; N. V. Smirnov. Algorithm of variance estimation in weighted least squares method. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 19 (2023) no. 4, pp. 484-496. http://geodesic.mathdoc.fr/item/VSPUI_2023_19_4_a4/