在灰色缓冲算子和灰色调整系数的框架下，构造灰色算子，提出了权重可调的加权移动平均去趋势法，进一步将其拓广为多重分形加权移动平均去趋势法。算法表明原有的移动平均去趋势法及其多重分形形式分别是加权移动平均去趋势法及其多重分形的特例。用带波动和线性趋势的分形高斯噪声与二项式多重分形进行数值模拟，表明权重为6的中心加权移动平均去趋势法及其多重分形能有效地去除序列趋势，计算出的Hurst值和多重分形谱f（α）比原有算法更接近真值。将权重为6的中心加权移动平均去趋势法及其多重分形分析南京市气温序列的长记忆性与多重分形性，结果表明从1951-2008年，七月份气温增速要明显小于一月份的增速，一月份和七月份气温都存在长记忆性，但七月份气温序列的长记忆性要高于一月份，表明一月份和七月份气温序列均可预测，七月份的可预测性更高些，这为通过预测对气温灾害风险防范提供了可行性；此外，一月份、七月份的气温序列均有多重分形性，说明可从多标度角度对其建模分析。
Under the framework of grey buffer operator and grey adjustment coefficients, the grey operation is constructed, and the weighted detrended moving average with adjustable weighted coefficients and its multifractal form called as multifractal weighted detrended moving average are put forward. The original detrended moving average is a special of the modified fractal method. Numerical simulation on fractal Gauss noise and binomial multifractal with fluctuation and linear trend shows that the centered detrended weighted moving algorithm whose weight is 6 can effectively remove the sequence trend, and the accuracy of Hurst and f(α) calculated by weighted detrended moving average and multifractal weighted detrended moving average are more close to analytics value compared with original algorithm. In empirical part, the long term memory and multifractality of daily temperature series in Nanjing from 1951 to 2008 by modified methods are investigated. The results show that the growth rate of temperature in July is significantly smaller than that of January; compared to the original methods, the conclusions from modified fractal methods are more close to reality; all temperature sequences have the long term memory feature, but the long term memory of daily temperature series in contained the highest, the lowest and the average temperature are stronger than that in January, which indicates that predictability of temperature in July is higher than that in January. The prediction of temperature series gives a way to manage the temperature disaster risk. Besides, temperature series of Nanjing in January and July possess multifractality, which suggest that the temperature series can be studied from multi scale. Through the shape of multifractal spectrum, it is found that the internal structure of the highest and average temperature sequences are more complex than the lowest temperature sequences whether for January or July.
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