Turbot,a flatfish of deep water species,is a highnutrition and economic valued species and currently cultured widely in China.In recent years,however,serious germ plasm degeneration has come into being due to the lack of the long-term and effective broodstock management programmes,production of farmed turbot became highly unstable and total output declined gradually.Therefore,the genetic improvement of turbot will be necessary to sustain the industry development.Within a breeding program in aquaculture,growth rate which determines the total harvest yield is a highly desirable economic trait.However,the growth rate at different development is variational because genes are expressed selectively at different growth stages following a certain sequence of time and place.It is necessary,obviously,to determine a good selection time during selective breeding for obtaining maximal genetic gain.In present study,according to Box-Jenkins theory and ARIMA(p,d,q)model,the time series of growth rate of body weight of five selected families of turbot selective breeding F₁ were identified,simulated and predicted.SPSS 15.0 software was used to construct the ARIMA model.Raw data for model establishment and validation were from 3 to 27 months.The results showed that family E♂1×E♀2,F♂4×N♀3,F♂2×E♀4,E♂2×F♀1 and F♂1×F♀4 adapt to ARIMA(2,0,0),ARIMA(1,0,0),ARIMA(2,0,0),ARIMA(1,0,0)and ARIMA(1,0,0)model,respectively(Constants were not included in all five models).The residual errors of five models were all the white noise series(P>0.05).Relative precisions of the forecasting for growth rate of body weight of five families during months 27-27.5,27.5-28 were comparatively high,which indicated those ARIMA models are able to well-describe the temporal and spatial changes in growth rate of body weight of turbot.The development changes of growth rate of body weight would be analysed through past observed values and forecast values,which can provide theoretic basis for determining optimal selection time during selective breeding of turbot.