Deep Assessment Methodology Using Fractional Calculus on Mathematical Modeling and Prediction of Gross Domestic Product per Capita of Countries

Abstract

In this study, a new approach for time series modeling and prediction, “deep assessment methodology,” is proposed and the performance is reported on modeling and prediction for upcoming years of Gross Domestic Product (GDP) per capita. The proposed methodology expresses a function with the finite summation of its previous values and derivatives combining fractional calculus and the Least Square Method to find unknown coefficients. The dataset of GDP per capita used in this study includes nine countries (Brazil, China, India, Italy, Japan, the UK, the USA, Spain and Turkey) and the European Union. The modeling performance of the proposed model is compared with the Polynomial model and the Fractional model and prediction performance is compared to a special type of neural network, Long Short-Term Memory (LSTM), that used for time series. Results show that using Deep Assessment Methodology yields promising modeling and prediction results for GDP per capita. The proposed method is outperforming Polynomial model and Fractional model by 1.538% and by 1.899% average error rates, respectively. We also show that Deep Assessment Method (DAM) is superior to plain LSTM on prediction for upcoming GDP per capita values by 1.21% average error.

Modeling of Telecommunication Revenue as a Percentage of Gross Domestic Product’s for Countries With Fractional Calculus

“…The main motivation is to model the given discrete dataset and obtained a continuous curve representing the dataset with the minimum error. To achieve this goal, the Taylor expansion is employed at the first stage of the mathematical manipulations [18][19][20][21].…”

“…(𝜖 𝑖 ) 2 = (𝑝 𝑖 − 𝑓(𝑥 𝑖 )) 2 (10) The total square of the error is defined as Equation ( 11) and according to the least-squares method, the sum of error squares 𝜖 𝑇 2 is tried to be minimized [18][19][20].…”

“…T Integer-order derivatives and integrals are well-known and studied for centuries by researchers [3][4][5][6][7][8]. Fractional Calculus is the theory of non-integer or complex-valued derivatives and integrals [9][10][11][12][13][14][15][16][17][18][19][20]. The applications of such mathematical tools in practical and engineering problems are relatively new [3][4][5][6][7][8][9][10][11].…”

Modeling macroeconomic indicators in unstable economies

“…The method of the small squares and its modifications is often applied for macroeconomic modelling of GDP dynamics, with the help of which the coefficients of the regression function reflecting the dynamics of the indicator are estimated. The group of researchers (Karaçuha et al, 2020) used the small squares method to forecast GDP per capita for the population of Brazil, China, India, Italy, Japan, the UK, the USA, Spain and Turkey. It has been shown that their proposed method is superior to the polinomial and fractional models.…”

New Results of the Time-Space Fractional Derivatives of Kortewege-De Vries Equations via Novel Analytic Method

“…In financial mathematics, FC is employed in price volatility modeling. Furthermore, Symmetric properties contribute to numerous applications that depend on TSFDEs, such as applications of physics, chemistry, and engineering, so these properties play an important role in knowing the correct way to solve these equations [1,2]. In physics, long particle jumps in anomalous diffusion and the particle motions in a heterogeneous environment were modeled with the help of it.…”