Comparative analysis of properties of weakening buffer operators in time series prediction models

Abstract Reducing the negative influence of stochastic disturbances in sample data has always been a difficult problem in time series analysis. In this paper, three new fractional weakening buffer operators are proposed, and then some desirable properties of these proposed sequence operators are investigated. Their potential effect in smoothing unexpected disturbances while maintaining the normal trend in sample series is analyzed and compared with other widely used sequence operators in time series modeling. Results of theoretical and empirical research show that the proposed novel fractional weakening buffer operators are effective in improving the development pattern analysis of time series in disturbance scenarios, while also avoid too subjectively weighting experimental data from collected samples. The robust of the proposed operator-based prediction algorithm against noise effect is tested in five different types of noise scenarios. Result of empirical study demonstrates that the proposed method improves the series prediction performance and it also improves the robustness of corresponding forecasting algorithms. These unique properties of the proposed weakening buffer operators make them more attractive in time series analysis.

[1]  Sifeng Liu,et al.  A Gray Model With a Time Varying Weighted Generating Operator , 2016, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[2]  José António Tenreiro Machado,et al.  Some pioneers of the applications of fractional calculus , 2013 .

[3]  Sifeng Liu,et al.  Multi-variable weakening buffer operator and its application , 2016, Inf. Sci..

[4]  António M. Lopes,et al.  Fractional State Space Analysis of Temperature Time Series , 2015 .

[5]  Mehmet Zeki Sarikaya,et al.  Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities , 2013, Math. Comput. Model..

[6]  J. A. Tenreiro Machado,et al.  Pseudo Phase Plane and Fractional Calculus modeling of western global economic downturn , 2015, Commun. Nonlinear Sci. Numer. Simul..

[7]  Yi Lin,et al.  Grey Systems: Theory and Applications , 2010 .

[8]  Tang Xue-wen,et al.  Study on the Buffer Weakening Operator , 2004 .

[9]  N. Laskin.  Fractional market dynamics , 2000 .

[10]  Xinping Xiao,et al.  A novel fractional grey system model and its application , 2016 .

[11]  U. Diwekar,et al.  A fractional calculus approach to the dynamic optimization of biological reactive systems. Part I: Fractional models for biological reactions , 2014 .

[12]  Dong Wang,et al.  Wavelet Method for Nonlinear Partial Differential Equations of Fractional Order , 2011, Comput. Inf. Sci..

[13]  Huan Guo,et al.  The modeling mechanism, extension and optimization of grey GM (1, 1) model , 2014 .

[14]  F. Mainardi,et al.  Recent history of fractional calculus , 2011 .

[15]  Xinxiu Li,et al.  Numerical solution of fractional differential equations using cubic B-spline wavelet collocation method , 2012 .

[16]  Sergio Adriani David,et al.  Dynamics of Commodities Prices: Integer and Fractional Models , 2017, Fundam. Informaticae.

[17]  António M. Lopes,et al.  Dynamical Analysis of the Global Warming , 2012 .

[18]  Dang Luo,et al.  The multi-attribute grey target decision method for attribute value within three-parameter interval grey number , 2012 .

[19]  Timothy D. Sauer,et al.  Time-Scale Separation from Diffusion-Mapped Delay Coordinates , 2013, SIAM J. Appl. Dyn. Syst..

[20]  Jose L. Salmeron,et al.  Modelling grey uncertainty with Fuzzy Grey Cognitive Maps , 2010, Expert Syst. Appl..

[21]  Sifeng Liu,et al.  Grey system model with the fractional order accumulation , 2013, Commun. Nonlinear Sci. Numer. Simul..

[22]  Jeffrey Forrest,et al.  New progress of Grey System Theory in the new millennium , 2016, Grey Syst. Theory Appl..

[23]  Delfim F. M. Torres,et al.  Fractional conservation laws in optimal control theory , 2007, 0711.0609.

[24]  Miguel Angel Moreles,et al.  Mathematical modelling of fractional order circuit elements and bioimpedance applications , 2017, Commun. Nonlinear Sci. Numer. Simul..

[25]  Clara-Mihaela Ionescu,et al.  The role of fractional calculus in modeling biological phenomena: A review , 2017, Commun. Nonlinear Sci. Numer. Simul..

[26]  Wei-Ching Chen,et al.  Nonlinear dynamics and chaos in a fractional-order financial system , 2008 .

[27]  Josselin Garnier,et al.  Noise Source Localization in an Attenuating Medium , 2012, SIAM J. Appl. Math..

[28]  George Biros,et al.  Constrained H1-Regularization Schemes for Diffeomorphic Image Registration , 2015, SIAM J. Imaging Sci..

[29]  Alessandro Pisano,et al.  Sliding mode control approaches to the robust regulation of linear multivariable fractional‐order dynamics , 2010 .

[30]  Shuo-Pei Chen,et al.  Forecasting of foreign exchange rates of Taiwan’s major trading partners by novel nonlinear Grey Bernoulli model NGBM(1, 1) , 2008 .

[31]  Baogui Xin,et al.  Finite-time stabilizing a fractional-order chaotic financial system with market confidence , 2015 .

[32]  Pu Yifei.  Image denoising based on Riemann-Liouville fractional integral , 2013 .

[33]  Yang Liu,et al.  Properties of Discrete Delta Functions and Local Convergence of the Immersed Boundary Method , 2012, SIAM J. Numer. Anal..

[34]  R. Gorenflo,et al.  Fractional calculus and continuous-time finance II: the waiting-time distribution , 2000, cond-mat/0006454.

[35]  José António Tenreiro Machado,et al.  Fractional Dynamics in Financial Indices , 2012, Int. J. Bifurc. Chaos.

[36]  Alessandro Pisano,et al.  Adaptive identification of the commensurate order in fractional processes by means of variable-order operators , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).