The Study Of Surrogate Data Algorithm Based On Dynamic Characteristics

Currently, the surrogate data testing method has become a widely usedmethod in testing nonlinearity of time series. And Thieler proposed thissurrogate data testing method in1992. Surrogate data algorithms used insurrogate data testing method are the traditional implementation method and thelimited implementation method. Traditional implementation method producesthe surrogate data which is almost consistent with the original data probabilitydistribution, but this method does not take into account surrogate data should beconsistent with the dynamic characteristics of the original data, and limitedimplementation method produces surrogate data of the original data byrearranging the original data. Because the surrogate data that limitedimplementation method produces is one of the replication original data, so thealgorithm produces the surrogate data which is almost consistent with theoriginal data probability distribution and dynamic characteristics of the originaldata, but the surrogate data is the lack of randomness.Then, this paper proposes a new surrogate data algorithm called a modernimplementation method，which overcomes faults of the current surrogate method.Modern implementation method is based on the recurrence plots（RP）. Thispaper applies reconstruction time series method based on the RP Thiel proposedto generate the surrogate data of the original data, and we study the probabilitydistribution of noise data in the method Thiel proposed, and we improve thismethod. We consider its probability distribution of the noise data in thereconstruction time series method, and fit the PDF of the original data. Thepurpose is to make the random data made by probability distribution functionconsistent with the original data probability distribution. Then the newalgorithm produces the surrogate data which is almost consistent with theoriginal data probability distribution and RP of the original data. At the sametime, we test the quality of the surrogate data by modern implementation methodproduced through the analysis of the statistic test and the distance.In this paper，the surrogate data algorithm is studied and a new surrogatealgorithms proposed and called modern implementation method. Modern implementation method is compared to the previous and proved feasible byusing several groups of ECG data.We compare the TS based on the RP and modern implementation method,and analyze the phase space diagrams of the simulated data and their surrogatedata, and the surrogate data is produced by the TS and modern implementationmethod. The analysis shows their phase space diagrams are almost unanimous.So, we compare the advantages and disadvantages of two kinds of the surrogatedata algorithms through their data waveforms. So, this paper considers thesurrogate data algorithm proposed in this paper is applied to expand the amountof sample data and enlarge the applied range of surrogate data algorithms.