Abstract: 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.

Key words: grey operator, weighted detrended moving average, multifractal weighted detrended moving average, long memory