CAJ | 학술논문

引入分形原理分析时间序列问题．运用数组存储代替重复计算的方式改进饱和关联维数法，当时间序列样本数据为100时，改进饱和关联维数法的运行时间比改进前缩短了61倍，程序的运算步骤有效简化，且计算出的关联维为1．4156，证明该时间序列具有分形特征．用变标度极差分析法求时间序列的Hurst指数，结果为0．9074，说明该序列具有持续效应．用累加和变换法建立短时间序列的分形预测模型，建立的模型预测后一期数据的残差最大绝对值都小于1 mm．实验结果表明：使用分形原理可有效描述时间序列的有关特征，且分形预测模型为短时间序列的预测问题提供了一种新方法．
인입분형원리분석시간서렬문제．운용수조존저대체중복계산적방식개진포화관련유수법，당시간서렬양본수거위100시，개진포화관련유수법적운행시간비개진전축단료61배，정서적운산보취유효간화，차계산출적관련유위1．4156，증명해시간서렬구유분형특정．용변표도겁차분석법구시간서렬적Hurst지수，결과위0．9074，설명해서렬구유지속효응．용루가화변환법건립단시간서렬적분형예측모형，건립적모형예측후일기수거적잔차최대절대치도소우1 mm．실험결과표명：사용분형원리가유효묘술시간서렬적유관특정，차분형예측모형위단시간서렬적예측문제제공료일충신방법．
The fractal theory is introduced to analyze time series problem.Saturation correlation di-mension is improved by the method of storing the data into an array, instead of calculating repeated-ly.Specifically, when the sample data of time series is 100, the running time of the new algorithm shortens 61 times than that of the original one, and the calculation steps are effectively simplified. Moreover, the correlation dimension is 1.415 6, which proves that the time series have fractal fea-ture.Then the Hurst exponent obtained by the rescaled-range analysis is 0.907 4, which indicates its continuous effect.Based on the fractal forecast model of short time series established by the accumu-lative transform method, the maximum absolute residuals of the data collected from the next observa-tion period is 1 mm.Experimental results show that some characteristics of time series can be de-scribed by the fractal theory, and the fractal forecast model provides a new approach to solve the pre-diction problem of short time series.