Modeling and analyzing banana prices in the city of Mosul using the ARFIMA model “Predictive Market Study
Abstract
Abstract: This study examined the use of ARFIMA models to forecast imported banana prices in the city of Mosul, based on data obtained from the Directorate of Agriculture in Nineveh for the period from 2018 to 2023. Several methods were used to estimate long memory and determine the fractional differencing parameter (d), including single-stage methods such as the maximum likelihood (EML) method used in this research, and two-stage methods such as the Geweke-Porter-Hudak (GPH) estimator, the dsprio (Smoothed periodogram estimation) method, the Fracdiff method, the Rescaled Range (R/S) method, and the Whittle estimator. The model was built by verifying the presence of long memory in the time series through several tests, and then estimating the fractional differencing parameters. The single-stage ARFIMA (1,-0.06275898,0) model outperformed the other methods based on criteria such as BIC, MSE, RMSE, and MAE. The model passed diagnostic tests and was used for forecasting banana prices, with the aim of clarifying the steps for constructing an appropriate model.
References
- Akaike, H.J.B., A Bayesian extension of the minimum AIC procedure of autoregressive model fitting. 1979. 66(2): p. 237-242.
- Belmukaddam, Mustafa, and Ben, Ayaa, Wafaa, predicting unemployment in light of the presence of the Corona epidemic in Algeria using long memory models (ARFIMA) during the time period from 2008 to 2020. 2022. 8(2)
- Benguesmi, T., Using seasonal time series models to forecast electric energy sales a case study of the National Electricity and Gas Company. 2014, Mohamed Khider Biskra University.
- Berri, Adnan. Methods of statistical forecasting (2002), Part One, King Saud University.
- Box, G.E.P. and D.A. Pierce, Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models. Journal of the American Statistical Association, 1970. 65(332): p. 1509-1526.
- Brockwell, P.J. and R.A. Davis, Time series: theory and methods. 2009: Springer science & business media.
- Bryce, R. M. and Sprague, K. B. (2012). "Revisiting detrended fluctuation analysis", Scientific Reports 315(2)
- Ceballos, R.F. and F.F.J.a.p.a. Largo, On the estimation of the Hurst exponent using adjusted rescaled range analysis, detrended fluctuation analysis and variance time plot: A case of exponential distribution. 2018.
- Dickey, D. A., and Fuller, W. A. (1979).Distribution of the estimators for Autoregressive Time Series With a unit Root, Journal of the American Statistical Association, N. 74: pp .427-431
- Dickey, D.A. and W.A.J.J.o.t.A.s.a. Fuller, Distribution of the estimators for autoregressive time series with a unit root. 1979. 74(366a): p. 427-431.
- Fox, R. and M.S. Taqqu, Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series. The Annals of Statistics, 1986. 14(2): p. 517-532.
- Geweke, J. and S.J.J.o.t.s.a. PorterHudak, The estimation and application of long memory time series models. 1983. 4(4): p. 221-238. Journal of time series analysis
- Granger, C.W. and R.J.J.o.t.s.a. Joyeux, An introduction to longmemory time series models and fractional differencing. 1980. 1(1): p. 15-29
- Haslett, J. and A.E.J.J.o.t.R.S.S.S.C. Raftery, Spacetime modelling with longmemory dependence: Assessing Ireland's wind power resource. 1989. 38(1): p. 1-21. Journal of the Royal Statistical Society: Series C
- Hosking, J.R.M., Fractional Differencing. Biometrika, 1981. 68(1): p. 165-176.
- Hurst, H.E.J.T.o.t.A.s.o.c.e., Long-term storage capacity of reservoirs. 1951. 116(1): p. 770-799. Transactions of the American society of civil engineers.
- Lo, A., Long-term Memory in Stock Market Prices, Econometrica. 1991. Journal of the Econometric Society
- MacKinnon, J.J.L.-r.e.r., Critical values for cointegration tests. 1991. 13.
- MADOURI, H. and M.J.e.-B.R. MKIDICHE, A Comparative Study of ARFIMA and Artificial Neural Networks to Forecast Exchange Rate of Dinar Algerian. 2017. 17(1): p. 159-171.
- Peng, C., S. Buldyrev, and M.J.P.R. Simons, Nature and fractals. 1994. Physics Rev. 168,.
- Reisen, V.A.J.J.o.T.S.A., Estimation of the fractional difference parameter in the ARIMA (p, d, q) model using the smoothed periodogram. 1994. 15(3): p. 335-350. J Journal of Time Series Analysis
- Safitri, D. and D. Ispriyanti. Gold price modeling in Indonesia using ARFIMA method. in Journal of Physics: Conference Series. 2019. IOP Publishing.
- Shaarawy, Samir. Introduction to modern time series analysis. 2005. King Abdulaziz University.
- Shang, H.L.J.J.o.T.S.E., A comparison of Hurst exponent estimators in long-range dependent curve time series. 2020. 12(1): p. 20190009, Journal of Time Series Econometrics
- Taqqu, M.S. and V. Teverovsky, On estimating the intensity of long-range dependence in finite and infinite variance time series. A practical guide to heavy tails: statistical techniques and applications, 1998. 177: p. 218.
- Tuama, S.A.J.A.-A.U.j.o.E. and A. Sciences, Using Analysis of Time Series to Forecast numbers of The Patients Malign