International Journal of Nonlinear Analysis and Applications

A hybrid ARFIMA-fuzzy time series (FTS) model for forecasting daily cases of Covid-19 in Iraq

Document Type : Research Paper

Authors

Department of Statistics, College of Management and Economics, Baghdad University, Baghdad, Iraq

Abstract

Most time series are characterized in practice that they consist of two components, linear and non-linear, and when making predictions, the single models are not sufficient to model these series. Recently several linear, non-linear and hybrid models have been proposed for prediction, In this research, a new hybrid model was proposed based on the combination of the linear model Auto-Regressive Fractionally Integrated Moving Average (ARFIMA) with the non-linear model fuzzy time series model (FTS). The proposed hybrid model analyzes the linear component of the specified time series using the ARFIMA model, calculates the estimated values, and then calculates the residuals for this model by subtracting the estimated values from the original time series. The nonlinear component is analyzed using the (FTS) model for the computed residuals, which inherently contain the nonlinear patterns of the time series. The final values for the prediction by applying the} {hybrid model (ARFIMA-FTS) are obtained by combining the predictions of the (ARFIMA) model of the original series with the predictions of the model (FTS) for the residual series. The new hybrid model was used to predict those infected with the Covid-19 virus in Iraq for the period from 24/2/2020 to 11/8/2021. The proposed model was more efficient in the prediction process than the single (ARFIMA) model using a number of comparison criteria, including (RMSE), (MAPE) and (MAE). The final results showed that the proposed model has the ability to predict time series that contain linear and nonlinear components

Keywords

[1] C.H. Aladag, U. Yolcu and E. Egrioglu, A high order fuzzy time series forecasting model based on adaptive expectation and artificial neural networks, Math. Comput. Simul. 81 (2020) 875–882.
[2] JC. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press, NY., 1981.
[3] G.E.P. Box and G.M. Jenkins, Time Series Analysis; Forecasting and Control, 2nd ed., Holden-Day, San Francisco, 1976.
[4] P.J. Brockwell and R.A. Davis,Time Series Theory and Method, Springer, 1995.
[5] W.A. Broock, J.A. Scheinkman, W.D. Dechert and B. LeBaron, A test for independence based on the correlation dimension, Econom. Rev. 15 (1996) 197–235.
[6] P.H. Franses, D.J.C. van Dijk and A. Opschoor, Time Series Models for Business and Economic Forecasting, 2nd Edition, Cambridge University Press, 2014.
[7] J. Geweke and S. Porter-Hudak, The estimation and application of long memory Time series models, J. Time Ser. Anal. 4 (1983) 221–238.
[8] C. W. J. Granger and R. Joyeux, An Introduction to Long Memory Time Series Models and Fractional Differencing, J. Time Ser. Anal. 1 (1980) 15–29.
[9] J. Hosking,Fractional differencing, Biomet. 68 (1981) 165–176.
[10] H.R. Hurst,Long-term storage in reservoirs, Trans. Amer. Soc. Civil Eng. 116 (1951) 770–799.
[11] S. Kumar, Neural Networks: A Classroom Approach, Tata McGraw-Hill Publishing Company Limited, New Delhi, 2004.
[12] A.W. Lo, Long-term memory in stock market prices, Econom. 59 (1991) 1279–1313.
[13] B.B. Mandelbrot and J.R. Wallis, Noah, Joseph and operational hydrology, Water Resources Res. 4 (1968) 909–918.
[14] F. Sowell, Maximum Likelihood Estimation of Stationary Univariate Fractionally Integrated Time Series Models, J. Econom. 53 (1992) 165–188.
[15] L.A. Zadeh, Fuzzy sets, Inf. Cont. 8(1965) 338–353.
[16] G.P. Zhang, Time series forecasting using a hybrid ARIMA and neural network model, Neurocomput 50 (2003) 159–175.
International Journal of Nonlinear Analysis and Applications
Volume 13, Issue 1
March 2022
Pages 627-641
  • Receive Date: 07 August 2021
  • Accept Date: 25 September 2021