Adjusting the errors of the GM(1, 2) grey model in the financial data series using an adaptive fuzzy controller

Purpose The purpose of this paper is to focus on the adjustment of the GM(1, 2) errors for financial data series that measures changes in the public sector financial indicators, taking into account that the errors in grey models remain a key problem in reconstructing the original data series. Design/methodology/approach Adjusting the errors in grey models must follow some rules that most often cannot be determined based on the chaotic trends they register in reconstructing data series. In order to ensure the adjustment of these errors, for improving the robustness of GM(1, 2), was constructed an adaptive fuzzy controller which is based on two input variables and one output variable. The input variables in the adaptive fuzzy controller are: the absolute error <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msubsup> <m:mrow> <m:mi>ε</m:mi> </m:mrow> <m:mrow> <m:mi>i</m:mi> </m:mrow> <m:mrow> <m:mn>0</m:mn> </m:mrow> </m:msubsup> <m:mrow> <m:mo stretchy="true">(</m:mo> <m:mi>k</m:mi> <m:mo stretchy="true">)</m:mo> </m:mrow> <m:mrow> <m:mo stretchy="true">[</m:mo> <m:mo>%</m:mo> <m:mo stretchy="true">]</m:mo> </m:mrow> </m:math> of GM(1, 2), and the distance between two values <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msubsup> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>i</m:mi> </m:mrow> <m:mrow> <m:mn>0</m:mn> </m:mrow> </m:msubsup> <m:mrow> <m:mo stretchy="true">(</m:mo> <m:mi>k</m:mi> <m:mo stretchy="true">)</m:mo> </m:mrow> <m:mrow> <m:mo stretchy="true">[</m:mo> <m:mo>%</m:mo> <m:mo stretchy="true">]</m:mo> </m:mrow> </m:math> , while the output variable is the error adjustment <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>A</m:mi> <m:msubsup> <m:mrow> <m:mi>ε</m:mi> </m:mrow> <m:mrow> <m:mi>i</m:mi> </m:mrow> <m:mrow> <m:mn>0</m:mn> </m:mrow> </m:msubsup> <m:mrow> <m:mo stretchy="true">(</m:mo> <m:mi>k</m:mi> <m:mo stretchy="true">)</m:mo> </m:mrow> <m:mrow> <m:mo stretchy="true">[</m:mo> <m:mo>%</m:mo> <m:mo stretchy="true">]</m:mo> </m:mrow> </m:math> determined with the help of the above-mentioned input variables. Findings The adaptive fuzzy controller has the advantage that sets the values for error adjustments by the intensity (size) of the errors, in this way being possible to determine the value adjustments for each element of the reconstructed financial data series. Originality/value To ensure a robust process of planning the financial resources, the available financial data are used for long periods of time, in order to notice the trend of the financial indicators that need to be planned. In this context, the financial data series could be reconstituted using grey models that are based on sequences of financial data that best describe the status of the analyzed indicators and the status of the relevant factors of influence. In this context, the present study proposes the construction of a fuzzy adaptive controller that with the help of the output variable will ensure the error’s adjustment in the reconstituted data series with GM(1, 2).

Topic: Grey System Theory Applications
Subfield: Management Science and Operations Research
Field: Decision Sciences
Domain: Social Sciences