Long memory in the Hybrid Time Series

Masad Awdh Alrasheedi

Masad Awdh Alrasheedi Faculty of Business, Taibah University, Saudi Arabia.

Keywords: Hybrid systems; hybrid time series; structural breaks; Markov process

Abstract

In this paper, consideration is given to the assessment of the availability of long-term memory in a time series with variable coefficients that depend on the Markov chain or the continuous Markov process. In the work we succeeded in establishing sufficient conditions for the present of a long-term memory based on a multifractal detrended fluctuation analysis and a Geweke – Porter-Hudak method. A real example is analysed of the Erste Group in the period 07.01.2000 – 23.10.2017, as a result of which it was possible to prove that this company.

Downloads

Download data is not yet available.

References

Aladag, C, Egrioglub, E, Kadilar C. (2009). Forecasting Nonlinear Time Series with A Hybrid Methodology. Applied Mathematics Letters, 22(9), 1467-1470.

Andrews, D. (2003). Tests for Parameter Instability and Structural Change with Unknown Change Point: A Corrigendum. Econometrica. 71 (1), 395–397.

Bai, J, Perron, P. (2003). Computation and Analysis of Multiple Structural Change Models. Journal of Applied Econometrics. 18 (1), 1–22.

Baillic, RT. (1996). Long memory processes and fractional integration in econometrics, Journal of Econometrics 73(59), 5-59.

Box, EPB, Jenkince, GM, Reinsel, GS, Ljung, GM. 2015 Time series analysis: forecasting and control (5th Edition), Wiley.

Brockwell, PJ, Davis, RA. 2016 Introduction to Time Series and Forecasting (3rd Edition), Springer International Publishing Switzerland.

Calvet, L, Adlai F. (2004). How to Forecast Long-Run Volatility: RegimeSwitching and the Estimation of Multifractal Processes. Journal of Financial Econometrics 2, 49-83.

Durrett, R. 2013 Probability: Theory and Examples (4th Edition), Cambridge University Press.

Einstein, A. 1926 Investigations on the Theory of the Brownian Movement. Methuen & Co.

Ferreira, C. 2006 Gene Expression Programming: Mathematical Modeling By An Artificial Intelligence, Springer-Verlag.

Francq, C, Zakoian JM. (2001). Stationarity of Multivariate Markov-Switching ARMA Models. Journal of Econometrics, 102, 339-364.

Geweke, J, Porter-Hudak, S. (1983). The Estimation and Application of Long Memory Time Series Models. Journal of Time Series Analysis, 4, 221-237.

Hauser, MA. (1999). Maximum likelihood estimators for ARMA and ARFIMA models: A Monte Carlo study. J. Statist. Planning Inference, 80, 229–255.

Henry, OT. (2002). Long memory in stock international evidence. Applied Financial Economics, 12 , 725-729.

Hurst, HE. (1951). Long-Term Storage Capacity of Reservoirs.

Transactions of the American Society of Civil Engineers, 116(1), 770-799.

Kantelhardt, JW, Zschiegner, SA, Koscielny-Bunde, E, Havlin, S, Bunde, A, Stanley, HE (2002). Multifractal detrended fluctuation analysis of non stationary time series. Physica A, 316, 87–114.

Kolmogorov, AN (1940). The Wiener spiral and some other interesting curves in Hilbert space. Dokl. Akad. Nauk SSSR, 26, 115–118.

Plikynas, D. (2005). Explaining International Investment Patterns: A Neural Network Approach. Information Technology and Control, 34(1), 42-50.

Zhang, G. (2003). Time Series Forecasting Using A Hybrid ARMA and Neural Network Model. Journal of Neurocomputing, 50, 159-175.

Wilfredo, P. 2007 Long-memory time series: Theory and Methods. Wiley.