Http://blog.sina.com.cn/s/blog_55954cfb0102e9y2.html
a signal analysis method presented by Dr. Simplicity, an American engineering Fellow, in 1998:The focus is on Dr. Hwang's innovative empirical mode decomposition (empirical mode decomposition), or EMD, which is an adaptive data processing or mining method that is well suited for nonlinear, non-stationary time series processing, is essentially the smoothing of data sequences or signals.
1: General understanding of the stationarity of time series :the so-called time series smoothness, generally refers to the width of smooth, that is, time series mean and variance is a time-independent constant, its covariance is related to time interval and is also independent of time. Simply put, a stationary time series refers to the sample time series that the thinking back can obtain in the future, and we can conclude that the mean, variance, and covariance must be equal to the sample time series that is now available.
Conversely, if the essential characteristics of the sample time series exist only in the current period, and do not continue to the future, that is, the sample time series of mean, variance, covariance is very few, then such a time series is not enough to reveal the future, we call this sample time series is non-stationary.
Image understanding, smoothness is required through the sample time series obtained by the fitting curve in the future period can still follow the existing form of "inertia" to continue to continue; If the data is not stable, then the pattern of the sample fitting curve does not have the characteristics of "inertia" continuation, That is, the curve that is fitted out based on the sample time series to be obtained will be different from the current sample fitting curve.
In fact, there is virtually no ideal "stationary" time series in the world. "The stationary sequence eliminates the small probability event", said Ouyang first professor. In the view of Professor Ouyang's theory of collapse, the EMD method is also problematic. However, this approach does extend the scope of the traditional idea of smoothing, which extends to the processing of any type of time series, and is a remarkable new development.
2:emd Method:
The EMD method can theoretically be applied to the decomposition of any kind of time series (signal), so it is more advantageous than the previous stationary method to deal with nonstationary and nonlinear data. Therefore, the EMD method has been applied rapidly and effectively in different engineering fields, such as ocean, atmosphere, celestial observation data and geophysical record analysis. The key of this method is that it can decompose complex signals into finite eigen-mode functions (intrinsic mode function, referred to as IMF), and the decomposed IMF components contain local characteristic signals of different time scales of the original signal. The EMD decomposition method is based on the following hypothetical conditions:⑴ data has at least two extrema, a maximum value and a minimum value;The local time domain characteristic of ⑵ data is determined only by the time scale between extreme points;⑶ If the data has no extremum points but has a inflection point, the extremum can be obtained once or multiple times by the derivative of the data, and then the decomposition result is obtained by integral.
The basic idea of empirical mode decomposition is to convert one frequency irregular wave into multiple single-frequency wave + residual wave. Original waveform =∑imfs + fallout.
The essence of this method is to obtain the eigen-fluctuation pattern by the characteristic time scale of the data, then decompose the data. This decomposition process can be visually referred to as the "screening (sifting)" process. The decomposition process is to find out all the maximal points of the original data sequence X (t) and to fit the upper envelope of the original data with the three spline interpolation function; Similarly, find all the minimum points and fit all the minimum points through three spline interpolation functions to form the lower envelope of the data. The mean value of the upper envelope line and the lower envelope is recorded as ML (in fact, some scholars use the mean value instead of the median, possibly more reasonable, because the non-stationary time series), the original data series X (t) minus the average envelope ml, to get a new data sequence HL,:X (t)-ml=hlThe new data minus the envelope average after the original data, if there are negative local maxima and positive local minima, indicates that this is not an intrinsic modulus function, and needs to continue to "filter". As indicated:
3: Brief analysis:I am exposed to this method, which is learned from the empirical mode decomposition of the oilfield logging signal sequence. Then read a lot of EMD method in different fields of application, especially in the processing of financial signal data series, aroused my great interest and resonance. The empirical modal decomposition is based on the time-scale characteristics of the data itself for signal decomposition, that is, local smoothing, without pre-setting any basis functions. This is fundamentally different from the Fourier decomposition and wavelet decomposition methods based on the priori hypothesis, the harmonic basis function (or the base frequency) and the wavelets function. This is in common with the floating frequency method that I use, which is one of the resonance. Weng Wenbo has pointed out that Fourier's basic frequency hypothesis in the case of limited data, the signal sequence (data) of the characteristic frequency and the harmonic frequency of the basic frequency inconsistent, will lead to serious distortion of the signal, therefore, a floating frequency method is proposed. Dr Huang seems to have seen this, from his name, "Empirical modal decomposition", that the word "empirical" is relative to "transzendental (transcendental)", which is equal to the difference between the transcendental Fourier and wavelet decomposition methods. Both Weng and Huang have proposed their own innovative concepts and methods from the point where they are triggered. This IMF sequence, from what I read, including Dr Huang's many literatures, is called a function, which is actually represented as the processing of filtered data sequences, which can be expressed graphically, without being summed up as functional equations. Typical figures of the IMF, such as the prev IMF, are just the last 4 low-frequency IMF function sequences:
in the IMF1---IMF3 fold together, you can basically reconstruct the prev trend: The basic and the stock index, similar to a moving average.
from the decomposition of the above to the process of reconstruction: in fact, is a subtraction to the addition of the process, subtraction, stripping out the frequency (period) roughly the same IMF, and the addition to seek the same, back to the original waveform. The fallout is actually a trend line, a very low (long-term) wave that can be seen as a base, and other IMF buildings are built on it.
Interestingly, the filtered intrinsic modulus function The IMF (including the fallout) can represent the physical meaning that its vibrational patterns necessarily correspond to physical causes. The IMF, which is divided by the index, should correspond to the macroeconomic causes. For example, the IMF2 in the first picture is almost identical to the CPI or PPI movement, and the cycle is the same, while the IMF1 is basically consistent with a smooth post-quarter GDP growth rate, which is broadly in line with the megatrends of power generation or industrial value added. In other words, this new technical analysis also concluded: The stock index is a reflection of macro-fundamentals. Benbow has recommended a way to follow the CPI trend as a stock market, and this EMD method has proved to be feasible. China's CPI this 10几 year has been following the circular law of about 42 months, can use a sine wave image. The IMF is the composite result of several sine waves. In contrast to the floating frequency method, the floating frequency method only finds the actual frequency in the signal sequence, while the positive mode function (IMF) is to find both the floating frequency and the vibration modal sequence of the complex signal sequence including different amplitude. The IMF is closer to the actual time series. Most of the authors I see applying this method may not understand the floating frequency method. If this method only stays at the stage of extracting the IMF and analyzing the average period on this basis, it may still cause the periodic signal to be distorted. Therefore, trying to combine them is a possible path. Of course, the analysis of macro-fundamentals is the basis, can be combined with technical analysis. As shown in the following:in the macroscopic data of different weights after the superposition of composite results, and the index of the direction of operation of the first is consistent, the direction is also information, even more important than the amount of information. The disadvantage is that more specific and accurate points of time are not easy to determine. The method used in fact is simple addition, the addition of the principle of the same, so that the direction of prominence, and so that we get the intuitive directional information. human beings are always approaching reality through different paths, but there is always imperfection!! 1
Analysis of empirical modal decomposition method (turn)
