Non-equidistant “Basic Form”-focused Grey Verhulst Models (NBFGVMs) for ill-structured socio-economic forecasting problems

Mohammad Hashem-Nazari, Akbar Esfahanipour, S.M.T. Fatemi Ghomi
  • Journal of Business Economics and Management, July 2017, Vilnius Gediminas Technical University
  • DOI: 10.3846/16111699.2017.1337045

This study is in the area of grey forecasting when dealing with non-equidistant and limited data.

What is it about?

Multiple uncertainties complicate socio-economic forecasting problems, especially when relying on ill-conditioned limited data. Such problems are best addressed by grey prediction models such as Grey Verhulst Model (GVM).

Why is it important?

In most of real-world forecasting problems, we deal with non-equidistant and limited data. Therefore, such study could improve the forecasting tasks in socio-economic problems. The paper does have distinct advantages adding to its research value: 1. It develops new grey Verhulst models offering impressive advantages in both in-sample and out-of-sample results over the best traditional grey Verhulst models. 2. The developed forecasting models can adapt to a variety of socio-economic time series with considerable accuracy even when they comprise ill-conditioned data, i.e. incomplete data with irregular intervals, missing values, or outliers. 3. It applies nonparametric statistical tests in its comparative analyses, robust validation techniques usually neglected in grey prediction research. Accordingly, the significance of the claimed improvements is statistically interpretable. 4. Its Table 1 gives a thorough overview of the major recent researches on grey Verhulst model to identify 11 main fields of relevant research. Facilitating further analyses of research gaps, it can provide invaluable insights at a glance. 5. Its online supplemental material involves as many as 19 time series in various socio-economic fields. For each time series, original data are provided as well as outputs of the analyzed (traditional and proposed) grey models. Obviously, it can be utilized in order to test other grey prediction models and to compare their performance with the ones analyzed herein.


Dr Akbar Esfahanipour
Amirkabir University of Technology

This paper resolves the incompatibility between GVM’s estimation and prediction by taking its basic form equation as the basis of both. The resultant “Basic Form”-focused GVM (BFGVM) is also further developed to create Direct Non-equidistant BFGVM (DNBFGVM) and, in turn, DNBFGVM with Recursive simulation (DNBFGVMR). Experimental analyses comprise 19 socio-economic time series with an emphasis on Iranian population, a low-frequency non-equidistant time series with remarkable strategic importance. Promisingly, the proposed DNBFGVM and DNBFGVMR provide accurate in-sample and out-of-sample socio-economic forecasts, show highly significant improvements over the best traditional GVM, and offer cost-effective intelligent support of decision-making. Final results suggest future trends of studied socio-economic time series. Specifically, they reveal Iranian population to grow even slower than anticipated, demanding an urgent consideration of policy-makers.

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The following have contributed to this page: Dr Akbar Esfahanipour and Dr Mohammad Hashem-Nazari