经验模式分解算法分析和应用
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摘要
时间序列分析在经济学、信息科学、地理科学等各个领域研究中都是重要的研究工具。而传统的时间序列方法是用随机过程来描述的,它被看作是离散时间的随机过程。这种思路的起点是基于时间域,但是在仅仅在时间域中研究序列并不能得到复杂的频率信息。
时频分析是自动控制领域进行信号分析非常有效的工具,但在传统的时间序列分析上鲜被关注。在时频分析中有一个非常重要的序列分析工具.经验模式分解算法(Empirical Mode Decomposition Algorithm),它是一种数据驱动自适应分解序列的算法,不但适用于线性和稳定序列,也适用于非线性非稳定序列。传统时间序列分析对序列的线性和稳定性有很高的要求,而经济管理领域中的时间序列大多不具备这种性质。本文拟对经验模式分解算法进行研究和改进,使之成为经济管理领域中一种有效的时间序列分析工具。
迄今为止,经验模式分解算法的理论基础仍不够完善。本文通过对经验模式分解中若干本质的深入探讨,提出了两种新的经验模式分解算法。实验模拟表明,新算法较之已有的算法具有优越性。我们将这些算法应用到经济管理领域中时间序列分析和预测,结果显示它们在经济管理领域时间序列分析应用中颇具潜力。
本文主要工作与创新点有:
一.对经验模式算法的过程-筛过程(Sifting Process)以往的研究主要集中于经验模式分解的应用,对于筛过程特征的研究比较缺乏。本文采用矩阵形式研究了筛过程,揭示了筛过程本质的特征。同时应用得到的结果,结合假设条件探讨了经验模式分解算法的收敛性。
二.提出了带宽经验模式分解算法。本文从瞬时频率出发,分析经验模式分解算法及常用的衍生经验模式分解算法优缺点,通过推导,提出了带宽经验模式分解算法。并应用实际例子验证了带宽经验模式分解算法的优越性。
三.提出了加细经验模式分解算法。本文分析了经验模式分解算法的基础-本质模式函数(Intrinsic Mode Decomposition),探讨了它的本质。在此基础上提出了加细经验模式分解算法,部分地解决了经验模式分解算法的尺度混迭问题。
四.采用经验模式分解算法提取序列的趋势项。本文在探讨传统的提取序列趋势项方法缺点的基础上,采用经验模式分解算法来提取序列的趋势项,并以实际例子证明它的有效性。
五.应用经验模式分解算法作为时间序列分析中一种新的季节性调整方法。本文应用带宽经验模式分解算法分解电力消费量数据,得到了电费量的各个周期性波动,与实际相符。
六.此外,本文在经验模式分解算法有效分解序列的基础上,提出了一种结合经验模式分解算法和支撑向量机的预测方法。
理论分析和实验说明,本论文算法在理论性、创新性和适用性上有着优势。本文试图在经济领域引入序列自适应分解的思路做了一定的工作和尝试。
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.
时频分析是自动控制领域进行信号分析非常有效的工具,但在传统的时间序列分析上鲜被关注。在时频分析中有一个非常重要的序列分析工具.经验模式分解算法(Empirical Mode Decomposition Algorithm),它是一种数据驱动自适应分解序列的算法,不但适用于线性和稳定序列,也适用于非线性非稳定序列。传统时间序列分析对序列的线性和稳定性有很高的要求,而经济管理领域中的时间序列大多不具备这种性质。本文拟对经验模式分解算法进行研究和改进,使之成为经济管理领域中一种有效的时间序列分析工具。
迄今为止,经验模式分解算法的理论基础仍不够完善。本文通过对经验模式分解中若干本质的深入探讨,提出了两种新的经验模式分解算法。实验模拟表明,新算法较之已有的算法具有优越性。我们将这些算法应用到经济管理领域中时间序列分析和预测,结果显示它们在经济管理领域时间序列分析应用中颇具潜力。
本文主要工作与创新点有:
一.对经验模式算法的过程-筛过程(Sifting Process)以往的研究主要集中于经验模式分解的应用,对于筛过程特征的研究比较缺乏。本文采用矩阵形式研究了筛过程,揭示了筛过程本质的特征。同时应用得到的结果,结合假设条件探讨了经验模式分解算法的收敛性。
二.提出了带宽经验模式分解算法。本文从瞬时频率出发,分析经验模式分解算法及常用的衍生经验模式分解算法优缺点,通过推导,提出了带宽经验模式分解算法。并应用实际例子验证了带宽经验模式分解算法的优越性。
三.提出了加细经验模式分解算法。本文分析了经验模式分解算法的基础-本质模式函数(Intrinsic Mode Decomposition),探讨了它的本质。在此基础上提出了加细经验模式分解算法,部分地解决了经验模式分解算法的尺度混迭问题。
四.采用经验模式分解算法提取序列的趋势项。本文在探讨传统的提取序列趋势项方法缺点的基础上,采用经验模式分解算法来提取序列的趋势项,并以实际例子证明它的有效性。
五.应用经验模式分解算法作为时间序列分析中一种新的季节性调整方法。本文应用带宽经验模式分解算法分解电力消费量数据,得到了电费量的各个周期性波动,与实际相符。
六.此外,本文在经验模式分解算法有效分解序列的基础上,提出了一种结合经验模式分解算法和支撑向量机的预测方法。
理论分析和实验说明,本论文算法在理论性、创新性和适用性上有着优势。本文试图在经济领域引入序列自适应分解的思路做了一定的工作和尝试。
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.
引文
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