Application Of GARCH Model Based On Wavelet Analysis Theory In Financial Time Series

Due to the complexity of modern economic management system and the influence of many factors,the information covered by financial time series is more abundant and complex,and there is a wide range of nonlinear,time-varying phenomena and uncertain relationship.Therefore,traditional econometric methods have been greatly restricted in the analysis and modeling of data.In recent years,wavelet analysis has been widely applied in engineering and other fields.Due to its good characteristics,it has been widely concerned and has been gradually introduced into the economy and finance.Because of its unique Time-Frequency localizated features,wavelet analysis can be from different time domain and frequency domain to decompose and reconstruct financial time series.therefore,wavelet analysis has unique advantages to deal with and analyze the problem of traditional time series.In order to explore the internal rules of financial time series and forecast data,In this paper,wavelet analysis theory is combined with the GARCH model in time series to build new model in order to get better predicted results.In this paper,the exploratory research is carried out from the following aspects:Wavelet basal function is not only the important part of wavelet analysis theory but also the key and premise of wavelet transformation.This paper analyzes various wavelet basal functions and tries to find out one or several wavelet basal functions which could be used to the financial time series of stock data and yield data,according to their different performance indicators.In the process of wavelet transformation,it is very important to determine the appropriate decomposition level for processing and analysis of data.In order to reduce the error of the reconstructed data signal and the original data and reasonably determine the decomposition level,this paper is based on method of white noise test and proposes a adaptive method to determine the decomposition level,the method can quickly determine the decomposition level,by comparing the root mean square error and de-noising image effect,it shows that this method is of reference significance and is feasible.Wavelet threshold denoising can effectively overcome many shortcomings of traditional de-noising method.Therefore,in this paper,the wavelet threshold denoisingmethod is used to de-noising.Based on BayesShrink threshold estimation method,this paper makes appropriate improvements and apply to the denoising of financial time series.This method considers the effect of different decomposition levels on threshold estimation,the algorithm is simple and can quickly calculate the noise threshold.The empirical results show that the method is effective and the denoising effect is better than the usual threshold calculation method.At the end of the paper,this paper makes an empirical analysis of the yield data of the selected Shanghai stock closing price through the above denoising method,and then corresponding GARCH model is set up to get root mean square error of prediction.The root mean square error is compared with the common threshold denoising method,it shows that the root mean square error of this paper is relatively small and the effectiveness of this method is illustrated.