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- W4285195714 abstract "Abstract The article uses spline-based phase analysis to study the dynamics of a time series of low-frequency data on the values of a certain economic indicator. The approach includes two stages. At the first stage, the original series is approximated by a smooth twice-differentiable function. Natural cubic splines are used as an approximating function <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>y</m:mi> </m:math> y . Such splines have the smallest curvature over the observation interval compared to other possible functions that satisfy the choice criterion. At the second stage, a phase trajectory is constructed in <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>t</m:mi> <m:mo>,</m:mo> <m:mi>y</m:mi> <m:mo>,</m:mo> <m:mi>y</m:mi> <m:mo accent=false>′</m:mo> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> left(t,y,y^{prime} ) -space, corresponding to the original time series, and a phase shadow as a projection of the phase trajectory onto the <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mrow> <m:mo>(</m:mo> </m:mrow> <m:mrow> <m:mi>y</m:mi> <m:mo>,</m:mo> <m:mi>y</m:mi> <m:mo accent=false>′</m:mo> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> (y,y^{prime} ) -plane. The approach is applied to the values of GDP indicators for the G7 countries. The interrelation between phase shadow loops and cycles of economic indicators evolution is shown. The study also discusses the features, limitations and prospects for the use of spline-based phase analysis." @default.
- W4285195714 created "2022-07-14" @default.
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- W4285195714 date "2022-01-01" @default.
- W4285195714 modified "2023-09-26" @default.
- W4285195714 title "Applying spline-based phase analysis to macroeconomic dynamics" @default.
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- W4285195714 doi "https://doi.org/10.1515/demo-2022-0113" @default.
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