The Application of Morlet Wavelet Transform Method in Research of the Impact of Credit Financing on .doc

1、1The Application of Morlet Wavelet Transform Method in Research of the Impact of Credit Financing on Abstract. In this article, technique of dynamic analysis based on wavelet transform will be applied into investigation of the impact of credit financing on composite material industry development in

2、China. At first, we will introduce the principle and calculation method of Morlet wavelet transform. Then, it is used to reveal the dynamic change characteristics in both time domain and frequency domain. The result of computer simulation demonstrates that credit financing has significantly positive

3、 impact on composite material industry. The conclusion indicates that there should be more increased financial support for composite material industry to boost its future development. Key words: Morlet wavelet transform, credit financing, composite material industry Introduction With the development

4、 of science and technology, composite materials, for their superior performance characteristics, are more and more widely used in each field of social production 2and social living, such as the aerospace, automobile and construction industries and so on. In this paper, we will discuss financial fact

5、ors for promoting the development of composite material industry, in other words, we will explore the effect of credit financing to this industry in China. As characterized by high technology and high input, composite material industry requires huge capital support. So, in theory, adequate credit fi

6、nancing will promote the development of the industry, and this needs to be verified. However, the traditional time series analysis methods could only analyze the dependency of data between different time sequences but not provide any information about data frequency. In order to make a more comprehe

7、nsive research, we will introduce technique of wavelet transformation to analyze relevant data. Wavelet transformation, as a kind of dynamic signal-processing technology in the engineering field, is well suited to describing the characteristics of dynamic features of non-stationary signals in both t

8、ime domain and frequency domain. In this paper, we will apply it to research the effect of credit financing to composite material industry in China. The remainder of this paper is organized as follows. The basic methods of Morlet wavelet transformation analysis is 3introduced in the subsequent secti

9、on. The result of Wavelet transformation with MATLAB is analyzed in Section III, and the final conclusion is made in Section IV. Morlet Wavelet transformation analysis The principle of wavelet transforms Wavelet is defined as a function which has zero mean and can be localized both in time and frequ

10、ency domain. If and are represented respectively as mother wavelet function and wavelet base function, their relationship is: Where is called scaling parameter which is used to measure scalability of mother wavelet, while is called location parameter which is used to measure position translation of

11、mother wavelet.（ ）represents regularized factor, which can reflect different frequencies. Morlet wavelet transform In practice, wavelet transform can be divided into two basic forms: continuous wavelet transforms (CWT) and discrete wavelet transforms (DWT). CWT is generally used to extract active fe

12、atures of signals from finite signal data. Since we use quarterly data in this paper, it is more effective to analyze the relationship between two time series though continuous wavelet transforms. 4In equation (1)，if and are continues， is said to be wavelet base function and be continues mother wave

13、let function. For a time series , its continuous wavelet transform for a wavelet is: Where * implies the complex conjugation of wavelet base function , and is called as continuous wavelet transform function. In the continuous wavelet transform, mother wavelet function need to satisfy three propertie

14、s: (a) , which means its a wavelet with mean zero. (b) , which means that the function is localized in a time interval. (c) , which means that it is possible to convert between wavelet base function and mother wavelet function. As one kind of CWT, the form of Morlet wavelet is: When =6, it is pretty

15、 much guaranteed that Morlet wavelet could have good properties in both time domain and frequency domain. In addition, due to Morlet wavelet is complex wavelet, it provides valuable information such as wavelet power spectrum, correlation coefficients and phase difference. So it is perfectly suited f

16、or analysis of dynamic characteristic in a vibration system. Wavelet power spectrum, Wavelet coherency coefficient and 5phase difference In the wavelet theory, for two time series and , the cross wavelet transform is defined as: The cross wavelet power is defined as , which reflects the covariance b

17、etween two time series along both time scales and frequencies. The wavelet coherence coefficient is defined as the ratio of cross-spectrum to the product of the spectrum of each individual series. Here S represents a smoothing operator along both time and scale. We can further derive the phase diffe

18、rence between two time series which gives the relative position of two time series. The phase difference is given below: As Aguiar-Conraria and Soares (2011b), the value of can be divided into some parts, and there are some rules to interpret the phase difference, which is shown in Table 1. In addit

19、ion, phase difference can also be used for judgment on the causality relationship between and . In detail, is the cause of when leads , while is the cause of when leads . Morlet Wavelet transformation analysis Data description The quarterly data of credit financing (CF) and industry 6development (ID

20、) come from Chinese economy information databases from the first quarter in 2001 to the fourth quarter in 2012. These two variables are transformed into logarithmic forms to avoid heteroskedasticity, and they are listed in the table below. Results analysis by programming with MATLAB The test results

21、 of the wavelet coherency between LnCF and LnID with wavelet transform simulation are shown in Figure 1. Its also worth mentioning that the deeper the colour (red) in an area, the stronger the relationship. Figure 1. The relationship between LnCF and LnID through wavelet coherence: (b.1) wavelet coh

22、erency; (b.2) phase difference in 14 years frequency band; (b.3) phase difference in4-8 years band. Above all, the positive effect of credit financing to composite material industry development has been confirmed, and these cause-and-effect relationships are dynamic. From the perspective of phase di

23、fference, credit financing energize the industry of composite material at a 1-4 years frequency in China. Conclusions In this paper, we apply the technique of Morlet wavelet 7transform successfully in research of the effect of credit financing to composite material industry development in China. The

24、 positive impact of credit financing on composite material industry development has been confirmed in a relatively short frequency band. The results indicate that credit financing do play an important role in providing a boost to composite material industry. Based on the conclusion, it is suggested

25、that more financial support should be provided to composite material industry in the future. It will play a proactive steering role in the sustainable and healthy development of this industry. Reference 1. Aguiar-Conraria, L., Azeve do, N., Soares, M. J., Using Wavelets to Decompose the Time-frequen

26、cy Effects of Monetary Policy J,Physica A: Statistical Mechanics and its Applications 387, 2008, 2863-2878. 2. Bloomfield, D., McAteer, R. , Lites, B., Judge, P., Mathi oudakis. M., Keena, F., Wavelet phase coherence analysis: Application to a Quiet-Sun magnetic elementJ,The Astrophysical Journal 61

27、7, 2004, 623-632. 3. Cohen, E., Walden, A., A Statistical Study of Temporally Smoothed Wavelet Coherence J, IEEE Transactions of Signal Processing 58(6): 2010, 29642973. 84. Grossman, A., Morlet, J., Decompsotition of Hardy functions into square integrable wavelets of constant shape J, SIAM J. Math.

28、 Anal., Vol.15, No.4, 1984, 723-736. 5. Goffe, W., Wavelets in macroeonomics: An introduction, in: D. Belsley (Ed.), Computational Techniques for Econometrics and Economic Analysis J, Kluwer Academic, 1994, 137-149. 6. Grinsted, A., Moore, J. C., Jevrejeva S., 2004, Application of the Cross Wavelet

29、Transform and Wavelet Coherence to Geophysical Time Series J, Nonlinear Process Geophysics, Vol.11, 2004, 561-566. 7. Ge, Z., Significance Tests for the Wavelet Power and the Wavelet Power Spectrum J, Annals of Geophysics 25: 2007, 2259-2269. 8. Karuppiah, J., & Los, C. A. , Wavelet multire solution analysis of high-frequency Asian FX rates J. International Review of Financial Analysis, Vol.14, 2005, 211246 9. Ramsey, J., Lampart,C., Decomposition of Economic Relationships by Time Scale Using Wavelets: Money and Income J, Macroeconomic Dynamics, 1998(2), 49-71.