The Study On The Wavelet Theory And Their Applications Of Time Series In Economy And Finance

Wavelet analysis has been greatly valued by numerous scientists and engineers for its Time-Frequency localized features and been widely applied in Image Processing, Identification of Pattern, Geological Exploration, Medical Imaging diagnosis, and Numerical Calculation. It has begun to be used in the field of economy and finance to deal with the data of time series. But according to the domestic and foreign literatures, compared with other fields its application in the study and analysis of economic and financial phenomenon to fully collect their internal information is obviously too little. On the basis of the discussion of principle of wave structure and comparison of the appropriate wavelet basal function and Algorithms, the present thesis intends to research into the wave analysis of Time-Frequency data of economy and finance, while combining their characteristics, so as to widen the application of wavelet analysis in the field.Wave analysis has great potential as far as its application in the natural science is concerned. Its use of the field of economy and finance is relatively late and therefore a lot of work needs to be furthered. The innovations of the present thesis are:(1) In theory, the present thesis will research into algorithms of wavelet transformation and wavelet basal function. Algorithms of wavelet transformation is the key to realize wavelet transformation, so the present thesis, aiming at the discrete characteristics of economic and financial time series, also analyzes and compares the quick algorithms of several discrete wavelets with examples in order to provide methodology for the application of wavelet transformation in economy and finance. Wavelet basal function is not only an important part of wavelet analysis but also the premise and condition of time series analysis. Wavelet basal function could be chosen from the existent wavelet function, and the existent wavelet function could be properly modified or new wavelet function could be constructed. Based on the theory of wavelet construction, the present thesis analyzes and compares the performances and indexes of various wavelet functions and then tries to find out one or several wavelet functions which could be used to calculate and predict economic and financial time series analysis.(2) In application, the present thesis also researches into the application of multi-resolution Analysis (MRA) in economy and finance. (1)In economy and finance, the development and change of economic phenomenon could not exist independently. They must be under the influence of factors and such influences are usually reflected by different periods. The traditional analysis through single measurement of time tends to cause the loss of data and therefore the result is not accurate. The present thesis extends Multi-resolution Analysis, which has been widely applied in engineering, hydrology and meteorology, to the multi-time scale analysis of economic time series in order to find out the regulations of the influence of various factors. (2)In finance, various accidental factors' influence effects lots of noises in financial time data, or minor irregular interference. The noises seriously affect the further analysis and management of the data. The present thesis compares the shortcomings of traditional Filtering Methods in noises removal from financial data and discusses, while combining the characteristics of financial time series, the validity of wavelet analysis in noises removal with data from the Shanghai Composite index. (3)The present thesis extends the application of wavelet in financial data to High Frequency Data collected with the alternation of hour, minute and second, analyzing and researching into their special Calendar Effect with the multi-resolution of wavelet analysis and predicting High Frequency Data in combination with ARMA model.