Analysis And Forecast Of Chaos Of The Consumer Pirce Index

chaos is the core of the nonlinear science which has developed rapidly in the1980s, it has its own particularity that can be summarized as four points as follow:intrinsic randomness, fractal property, scale invariance, sensitivity of initialconditions. With the acquaintanceship of chaos becoming deeper and deeper, weuniversally accept its existence in nature, and also has achieved marked achievementsin the application of chaos, especially the widely application of chaos control in themechanical engineering, commucination and so on. At the same time, manyspecialists and scholars put forward all kinds of new methods to study and improvecontrol problem continually.There are many researches of CPI time series, including ARMA model, VARmodel, ARIMA model and ARCH type model. All these models are based on theresiduals that is white noise. But what we doubt about is that there are non-linearfactors that can’t be tested out by traditional theoretic methods When judging whetherthe residuals is pure white noise or not. In paper, we study and forecast the fluctuationfeature of the CPI index by chaotic methods. This paper is mainly divided into threesections as follows:In the first section, it is the theory that discusses some methods of checking ifthere are non-linear factors in economic time series. those are calculate Hurst index ofeconomic time series by R/S analysis, use G-P algorithm to reconstruct phase spaceafter figuring out latency timeτ and embedding dimension m, calcucate correlationdimension of the reconstructional phase space, calculate the BDS statistics and themaximum Lyapunov index. This part is ready for checking residuals sequence from different pespectives in the next.The second part is the positive analysis. In this part, firstly we produce two setsof white Gaussian noise sequence, in order to analyze and compare different models,we have to calculate their BDS statistics respectively based of the methods ofchecking whether the sequence is white noise or not that mentioned in the first part.Then we process CPI sequence and find that CPI sequence is not stationary series bymeans of unit root method after eliminating the seasonal effect. We also discover thatCPI_TC sequence is first order single whole series after differential treatment.DCPI_TC series is remembered as the end result of treatment. Secondly, we Choosethe best fitting effect of ARIMA (2,1,3) model from the ARIMA models, but find thatthe residuals of ARIMA (2,1,3) model is nonstationary series by means of LM test,the autocorrelation function diagram and the partial autocorrelation function diagram.Thirdly, we Choose the best matching effect of GARCH(3,1) model from the ARCHtype models after many trials. we get the conclusion that the residuals series of theGARCH(3,1) model is white noise by means of LM test, the autocorrelation functiondiagram and the partial autocorrelation function diagram; At last, we use chaosmethod to test the residuals of GARCH(3,1) model. There are non-linear factors thatcan’t be tested out by traditional theoretic methods in the residuals of GARCH(3,1)model, by calculating the BDS statistic, Hurst index, the maximum Lyapunov index,which are caused by the nonlinearity of original time series. All this show that thereare many defects and shortcomings when constructing non-linear time series modelby traditional models.This part is the main part of the paper. We use G-P algorithm to reconstructphase space after figuring out latency timeτ and embedding dimension m of thepost treatment CPI sequence, and then we respectively predict the reconstructionalphase space by means of RBF neural network and Volterra adaptive predictionmethod, and get small forecast error,what is more, its Volatility is even, so Results are ideal. But we find that Volterra adaptive prediction method can get much betterresults than RBF neural network by comparing the size of absolute error and theVolatility of forecast residuals. That is Volterra adaptive prediction method is muchfitter time series.The end is a conclusion about all above, especially the choice of models. Indifferent assumed conditions, we choose different models and get different results. Sowe must deal with the data before we choose the model to check whether it isnon-linear time series or not, if it is non-linear, we must choose a non-linear model toanalyze the data, or we will get unideal or wrong results. Generally, ecomomic timeseries is non-linear, only in this way we can get meaningful and useful results.