The Analysis And Application Of Empirical Mode Decomposition Algorithm

Time-series analysis is an important tool for many fields, such as economics, information science and geography. Classical time-series method is characterized by discrete time stochastic process. The method is based on time domain, but we could not find the complex frequency component just in time domain.This paper presents time-frequency analysis, which is an important tool for signal analysis in the Automatic control domain. Empirical Mode Decomposition (EMD) algorithm is an important time-frequency analysis tool. It is a fully data-driven and self-adaptive algorithm. EMD algorithm breaks through limitation of the linear and stationary behavior. It not only could process the linear and stationary series, but also process the nonlinear and nonstationary series. Classical time series analysis is based on the stability and linearity, but the most economic series do not have this nature. The paper plans to improve the EMD algorithm so that it will become effective in the field of time series analysis.So far the foundation of EMD algorithm is not perfectly. Based on the investigation of the nature of EMD algorithm, this paper proposes two kinds of empirical mode decomposition. Simulated experiments indicate that the new algorithms are superior than the existing algorithms. We apply the algorithm to the time-series analysis and forecasting. The results show that they have the potential in the economic time series analysis.The main innovation and work are:Firstly, because previously investivagation focused on the application of the EMD, the research on the characteristic of Sifting Process is quite deficient. This paper has been studying the Sifting Process and present nature characteristic of Sifting Process, which we use matrix form to rewrite the Sifting Process. Unified assumption and obtained the results, we investigate the convergence of the EMD.Secondly, we propose the Bandwidth Empirical Mode Decomposition algorithm. We analyze advantages and disadvantages of the EMD and its derivatives based on the discussion about instantaneous frequency. We obtain bandwidth EMD algorithm through derivation and confirm that the superiority through some examples.Thirdly, we propose the refinable Empirical Mode Decomposition algorithm. We analyze the nature of the Intrinsic Mode Function(IMF), which is the EMD basis. On the elements, we propose the Refinable Empirical Mode Decomposition algorithm, which could solve the scale mixture problem partially.Fourthly, we deem that the EMD could be applied to trend extraction based on the analysis the disadvantages of the classical methods of trend extraction. At last, we use practical example to prove its effectiveness.Fifthly, Empirical mode decomposition algorithm can be used as a new seasonal adjustment method. The thesis applies the Bandwidth EMD to decompose the power consumption series and obtains the various cyclical fluctuations which is matched the fact.Sixthly, based on the effectiveness of the EMD, we propose the new methodology which is combined with the EMD and the support vector machine(SVM) to forcast time-series.Theory analysis and experiment results indicates that the proposed algorithms of the thesis have advantages in theory, innovative and simplicity. To introduce the adaptive decomposition methodology in economics, the thesis has done some work and attempt.