Applying (ARFIMA) Model for Forecast the Saudi Stock Market Prices
DOI:
https://doi.org/10.59992/IJSR.2024.v3n8p1Keywords:
Time Series Models, Forecasting, Fractionally Difference, ARFIMA models, Stock Market pricesAbstract
The interest in the topic of time series forecasting has increased during the recent years and thus appeared specific modern methods, for example Autoregressive Fractional Integrated Moving Average model (ARFIMA), or what is called long memory model, which use fractionally difference (d) instead of integer which used in ARIMA models. In this study we displayed long memory feature and its tests.
Our discussion supported by analysing the real time series (daily closing index of the Saudi Arabia Stock Market prices) over period 1/1/2018 to 19/12/2022, including 1240 observations, to make a good model to giving forecast results for future, using statistical tests and statistical software (R- 4.2.2 program).
Firstly we checked that the data series was unstable by testing unit root, using Dickey fuller and Philips Perron tests ; and confirmed the presence of a long memory pattern in it by calculating the Hurst exponent (H), then calculated the fractional differential coefficient (d), determined the appropriate models for analysis and prediction, then the best model was chosen among them based on the comparison criteria, then predicted the values for the next 5 days, R - 4.2.2 software was used in all of these tests and predictions Statistical results indicated that the optimal model to represent the data series is ARFIMA (3,0.383,2) which used to predict future values.
References
- Abdalgader, S., & Mohammad, M., (2014), Using ARFIMA Model for Predict cruel oil prices, Journal of Economic And financial researches (JEFR), no (1), 62-76.
- Adhikari R., (2008), An Introductory Study on Time Series Modeling and Forecasting, Master Thesis, Faculty of SC & SS.
- Akaike, H., (1973), Maximum Likelihood Identification of Gaussian Autoregressive Moving Average Models, Biometrika, vol.60 no. (2), 255-265.
- Bharatpur, A. S., (2022), A literature Review on Time Series Forecasting Methods, Bournemouth University- UK.
- Bourbonnais, R. & Maftei, M. M., (2017), ARFIMA Process: Tests and Applications at a White Noise Process A Random Walk Process and the Stock Exchange Index CAC 40, Journal of Economic Computation and Economic Cybernetics Studies and Research, vol. 46,no(1), https://hal.archives-ouvertes.fr/hal-01491880
- Box G. E. P., Jenkins, G. M, Reinsel, G. C., & Ljung, G. M., (2016), Time Series Analysis: Forecasting and Control (5th edition), New Jersey, John Wiley & Sons.
- Box, G. E. P. and Price, D. A., (1970), Distribution of residual autocorrelations in autoregressive-integrated moving average time series models, J. American Statistical Association, vol. 65, 1509-1526.
- Burnecki, K., Sikora, G., (2017), Identification and validation of stable ARFIMA processes with application to UMTS data, Solitons & Fractals, vol 102, no. 10, 456-466, doi.org/10.1016/j.chaos.2017.03.059.
- Dickey, D. A., & Fuller, W. A., (1979), Distributions of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, vol.74 no. (366), 427–481.
- Eltelbany, S.& Elsoase, M., (2016), Using ARFIMA Models in Forecasting Indicator of the Food and Agriculture Organization, IUGJEBS, ISSN 2410-5198, vol. 24 no (1), 168-187.
- Geweke, J., & Hudak, S. P., (1983), The Estimation and Application of Long Memory Time Series Models, Journal of Time series Analysis, vol.4 no (4), 221-231.
- Granger, C.W.J. and Joyeux, R., (1980), An introduction to long-memory time series models and fractional differencing, Time Series Analysis journal, vol.1, no. (1), 15–29.
- Hosking, J.R.M.,(1981), “Fractional Differencing”, Biometrika, vol.68 no.(1), 165-176 http://links.jstor.org/sici?sici=0006-3444%28198104%2968%3A1%3C165%3AFD%3E2.0.CO%3B2-B .
- Hurst, H. E., (1951), Long Term Storage Capacity of Reservoirs, Transactions of the American Society of Civil Engineers, vol.116, 770-799.
- José, M., Belbuteab, Alfredo M. Pereirac,(2015), An Alternative Reference Scenario for Global CO2 Emissions From Fuel Consumption: An ARFIMA approach, Economics Letters, vol.136, no.(10), 108-111, doi.org/10.1016/j.econlet.2015.09.001.
- Kartikasari, P. Yasin, H. & Maruddani, D. A., (2020), ARFIMA Model for Short Term Forecasting of New Death Cases COVID19, ICENIS, 202, 13007, doi.org/10.1051/e3sconf/202020213007.
- Kartikasari, P., (2020), Bank Negara Indonesia Dengan Menggunakan, Autoregressive Fractional Integrated Moving Average Model (ARFIMA), Jurnal Statistika Universitas Muhammadiyah Semarang, vol. 8, no. (1), 1- 7.
- Lo, A. W., (1991), Long-term memory in stock market prices, Econometrica, vol.59, no. (5), 1279-1313.
- Mandelbrot B., Wallis J., (1968) Noah, Joseph, and Operational Hydrology, Water resources research,4, 909-918.
- Monge, M. 1 & Infante, J., (2022), A Fractional ARIMA (ARFIMA) Model in the Analysis of Historical Crude Oil Prices, Energy Reserch Letters, 3(Issue Early View), 1-3, doi.org/10.46557/001c.36578
- Monge, M., & Gil-Alana, L. A., (2021), Spatial crude oil production divergence and crude oil price behaviour in the United States, Energy, vol. 232, doi.org/10.1016/j.energy.2021.121034
- Ocker, R. M., (2014), A Stochastic Parameter Regression Model for Long Memory Time Series”, Master of Science in Mathematics, Boise State University.
- Phillips, P. C. B., & Perron, P., (1988), Testing for a unit root in time series regression, Biometrika, vol.75, no. (2), 335–346.
- Raicharoen, T., Lursinsap, C. and Sanguanbhokai, P. (2003), Application of critical support vector machine to time series prediction, Circuits and Systems, ISCAS'03, Proceedings of the 2003 International Symposium, vol. 5(25 May 2003), 741-744.
- Saber, A. M., & Saleh, R. A., (2022), A Comparative Study for Estimate Fractional Parameter of ARFIMA Model, Journal of Economics and Administrative Sciences, vol.28, no. (133), 131-148, http://jeasiq.uobaghdad.edu.iq
- Salman, S. A. & Aboudia, E. H., (2022), A hybrid ARFIMA-fuzzy time series (FTS) model for forecasting daily cases of Covid-19 in Iraq, IJNAA, vol.13 no. (1), 627-641, doi.org/10.22075/ijnaa.2022.5553
- Sowell, F., (1992b) Modelling Long-Run Behavior with the Fractional ARIMA-Model, Journal of Monetary Econometrics, vol.29, 277-302.
