Sains Malaysiana 54(11)(2025): 2797-2808

http://doi.org/10.17576/jsm-2025-5411-18

 

An Innovative Approach to Financial Market Analysis: Hybrid ARFIMA with Sieve and Moving Block Bootstrap

(Pendekatan Inovatif untuk Analisis Pasaran Kewangan: Hibrid ARFIMA dengan Saringan dan Butstrap Blok Bergerak)

 

ALSHAIMAA ELWASIFY1,2 & ZAIDI ISA1,2*

 

1School of Mathematical Sciences, Faculty of Sciences & Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia

2Applied Statistics Department, Faculty of Commerce, Damietta University, 34511 Damietta, Egypt

 

Received: 14 April 2025/Accepted: 24 October 2025

 

Abstract

This paper aims to develop the field of financial time series analysis by focusing on the Egyptian stock market, EGX 30 in particular, using innovative modeling and forecasting techniques. Our study explores the application of ARFIMA models either independently or in combination with advanced bootstrap techniques to improve the accuracy of parameter estimation and forecasting. The study includes four main methodologies: the traditional ARFIMA model, ARFIMA with Sieve Bootstrap (SB), ARFIMA with Moving Block Bootstrap (MBB), and the proposed model that combines the two bootstrap techniques with the ARFIMA model. The proposed model aims to address the time complexities in the financial series, including long term and short-term dependencies. The results show that the proposed model significantly outperforms other traditional and combined models in terms of forecasting accuracy and estimation reliability. This improved performance underscores the importance of integrating advanced bootstrap techniques with traditional models to better understand the complex characteristics of financial data. Our paper contributes to scientific literature by introducing a new approach that has not been applied before in financial markets. It also offers practical applications for investors and financial analysts by providing a robust framework for forecasting and supporting decision-making in dynamic and volatile market environments, with a focus on the Egyptian market. This study represents a basis for applying similar methodologies in other emerging markets.

Keywords: ARFIMA; bootstrap; MBB; Reisen method; sieve bootstrap

 

Abstrak

Kertas ini bertujuan untuk membangunkan bidang analisis siri masa kewangan dengan memberi tumpuan kepada pasaran saham Mesir, khususnya EGX 30, menggunakan teknik pemodelan dan ramalan yang inovatif. Penyelidikan kami meneroka penggunaan model ARFIMA sama ada secara bebas atau digabungkan dengan teknik butstrap lanjutan untuk meningkatkan ketepatan anggaran dan ramalan parameter. Kajian ini merangkumi empat metod utama: model ARFIMA tradisional, ARFIMA dengan Butstrap Saringan (SB), ARFIMA dengan Butstrap Blok Bergerak (MBB) dan model yang dicadangkan yang menggabungkan dua teknik butstrap dengan model ARFIMA. Model yang dicadangkan bertujuan untuk menangani kerumitan masa dalam siri kewangan, termasuk kebergantungan jangka panjang dan jangka pendek. Keputusan menunjukkan bahawa model yang dicadangkan mengatasi model tradisional dan gabungan lain dengan ketara dari segi ketepatan ramalan dan kebolehpercayaan anggaran. Prestasi yang dipertingkatkan ini menggariskan kepentingan mengintegrasikan teknik butstrap lanjutan dengan model tradisional untuk lebih memahami ciri kompleks data kewangan. Kertas kami ini menyumbang kepada kepustakaan saintifik dengan memperkenalkan pendekatan baharu yang belum pernah digunakan sebelum ini dalam pasaran kewangan. Ia juga menawarkan aplikasi praktikal untuk pelabur dan penganalisis kewangan dengan menyediakan rangka kerja yang mantap untuk membuat ramalan dan menyokong proses membuat keputusan dalam persekitaran pasaran yang dinamik dan tidak menentu dengan tumpuan kepada pasaran Mesir. Kajian ini merupakan asas untuk mengaplikasikan metod yang serupa dalam pasaran baharu lain yang muncul.

Kata kunci: ARFIMA; butstrap; butstrap saringan; kaedah Reisen; MBB

 

REFERENCES

Aladag, C.H., Egrioglu, E. & Kadilar, C. 2012. Improvement in forecasting accuracy using the hybrid model of ARFIMA and feed forward neural network. American Journal of Intelligent Systems 2(2): 12-17.

Brockwell, P.J. & Davis, R.A. 1990. Time Series: Theory and Methods. 2nd ed. Springer Series in Statistics - Springer.

Bühlmann, P. 1997. Sieve bootstrap for time series. Bernoulli 3(2): 123-148.

Carlstein, E. 1986. The use of subseries values for estimating the variance of a general statistic from a stationary sequence. The Annals of Statistics 14(3): 1171-1179.

Dingari, M., Reddy, D.M. & Sumalatha, V. 2019. Time series analysis for long memory process of air traffic using ARFIMA. International Journal of Scientific and Technology Research 8(10): 395-400.

Efron, B. 1979. Bootstrap methods: Another look at the jackknife. The Annals of Statistics 7(1): 1-26.

Erfani, A. & Samimi, A.J. 2009. Long memory forecasting of stock price index using a fractionally differenced ARMA model. Journal of Applied Sciences Research 5(10): 1721-1731.

Fokam, C.T., Jentsch, C., Lang, M. & Pauly, M. 2024. AR-sieve bootstrap for the random forest and a simulation-based comparison with rangerts time series prediction. https://doi.org/10.48550/arXiv.2410.00942

Franco, G.C., Lana, G.C. & Reisen, V.A. 2021. Prediction intervals in the ARFIMA model using bootstrap. Financial Statistical Journal 4(1): 1-8.

Hall, P. 1985. Resampling a coverage pattern. Stochastic Processes and their Applications 20(2): 231-246.

Hassler, U. 1993. Regression of spectral estimators with fractionally integrated time series. Journal of Time Series Analysis 14(4): 369-380.

Kartikasari, P., Yasin, H. & Asih I Maruddani, D. 2020. ARFIMA model for short term forecasting of new death cases COVID-19. E3S Web of Conferences 202: 13007.

Kim, Y.M. & Kim, Y. 2017. Bootstrap methods for long-memory processes: A review. Communications for Statistical Applications and Methods 24(1): 1-13.

Kreiss, J.P. 1992. Bootstrap procedures for AR (∞) - processes. In Bootstrapping and Related Technique. Lecture Notes in Economics and Mathematical Systems, edited by Jöckel, K.H., Rothe, G. & Sendler, W. Berlin, Heidelberg: Springer. 376: 107-113.

Kreiss, J.P. 1988. Asymptotic statistical inference for a class of stochastic processes. Verlag nicht ermittelbar.

Kreiss, J.P. & Lahiri, S.N. 2012. Bootstrap methods for time series. Time Series Analysis: Methods and Applications 30: 3-26.

Künsch, H. 1987. Statistical aspects of self-similar processes. Proceedings of the First World Congress of the Bernoulli Society. Utrecht: VNU Science. 1: 67-74.

Kurita, T. 2010. A forecasting model for Japan’s unemployment rate. Eurasian Journal of Business and Economics 3(5): 127-134.

Lahiri, S.N. 2003. Resampling Methods for Dependent Data. Springer Series in Statistics - Springer.

Lola, M.S., David, A. & Zainuddin, N.H. 2016. Bootstrap approaches to autoregressive model on exchange rates currency. Open Journal of Statistics 6(6): 1010-1024.

Olatayo, T.O. & Adedotun, A.F. 2014. On the test and estimation of fractional parameter in ARFIMA model: Bootstrap approach. Applied Mathematical Sciences 8(96): 4783-4792.

Omekara, C.O., Okereke, O.E. & Ukaegeu, L.U. 2016. Forecasting liquidity ratio of commercial banks in Nigeria. Microeconomics and Macroeconomics 4(1): 28-36.

Paparoditis, E. & Politis, D.N. 2002. The local bootstrap for Markov processes. Journal of Statistical Planning and Inference 108(1-2): 301-328.

Paul, R.K. 2014. Forecasting wholesale price of pigeon pea using long memory time-series models. Agricultural Economics Research Review 27(2): 167-176.

Reisen, V.A. 1994. Estimation of the fractional difference parameter in the ARIMA (p, d, q) model using the smoothed periodogram. Journal of Time Series Analysis 15(3): 335-350.

Reisen, V., Abraham, B. & Lopes, S. 2001. Estimation of parameters in ARFIMA processes: A simulation study. Communications in Statistics - Simulation and Computation 30(4): 787-803.

Saâdaoui, F. & Rabbouch, H. 2024. Financial forecasting improvement with LSTM-ARFIMA hybrid models and non-Gaussian distributions. Technological Forecasting and Social Change 206: 123539.

Safitri, D., Mustafid, Ispriyanti, D. & Sugito. 2019. Gold price modeling in Indonesia using ARFIMA method. Journal of Physics: Conference Series 1217: 012087.

Shang, H.L. 2023. Sieve bootstrapping the memory parameter in long-range dependent stationary functional time series. AStA Advances in Statistical Analysis 107(3): 421-441.

Silva, E.M., Franco, G.C., Reisen, V.A. & Cruz, F.R.B. 2006. Local bootstrap approaches for fractional differential parameter estimation in ARFIMA models. Computational Statistics and Data Analysis 51(2): 1002-1011.

Sun, R., Chen, Y.Q. & Li, Q. 2008. The modeling and prediction of Great Salt Lake elevation time series based on ARFIMA. 2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007 5 PART B. pp. 1349-1359.

The Egyptian Exchange. 2024. EGX30. https://www.egx.com.eg/en/indexdata.aspx?type=1&nav=1 (Accessed in 2024)

Vogel, R.M. & Shallcross, A.L. 1996. The moving blocks bootstrap versus parametric time series models. Water Resources Research 32(6): 1875-1882.

 

*Corresponding author; email: zaidiisa@ukm.edu.my

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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