• 作者： 林燦隆
• 作者服務機構： 國立臺灣大學農學院農藝學系
• 中文摘要： 本研究提出迴歸與ARIMA（Autoregressive Integrated Moving Average Process）混合模式，並用以配合臺中區農業改良場預測燈收集之三種水稻害蟲資料，所得模式具有下列特點：（1）能預測半旬後的誘集害蟲數，（2）只需考慮半旬以前的氣象因子的影響，（3）氣象因子的影響隨時間而減弱，在年期開始時最強，（4）密度效應在年期開始時較弱，但隨後轉強。半旬後預測值的誤差均方，在二化螟為0.04，黑尾葉蟬為0.23，而褐飛蝨則為0.44。誘集蟲數之變異中，能用模式說明者達95％以上。
• 英文摘要： Models defined by (方程式無法摘錄)are fittd to the number of pest insects of rice, the stem borer (Chilo suppressalis), the green leaf-hopper (Nephotettix cincticeps) and the brown planthopper (Nilaparvata lugens), entrapped by a lighttrap at Taichung Agricultural Improvement Station in nearly five day interval from 1967 to 1975. Notational index to the models is given below: The number of insects trapped within the time t0 to t1 in the same year. The “t0” cor- responds to the time from the lst to 5th days of March for the stem borer, of April for the green Ieafhopper and of May for the brown planthopper. The natural logarithmic transformation of the accumulated amount of precipitation from the beginning of the year up to the time t-b with added 0.1. The natural logarithmic transformation of the accumulated daily maximum temperature from the beginning of the year up to the time t-b. The natural logarithmic transformation of the accumulated daily mean temperature from the beginning of the year up to the time t-b. The natural transformation of the accumulated daily minimum temperature from the be- ginning of the year up to time t-b.α0, α1, α2, α3, α4, α5: The unknown regression coefficients.φ: The vector of unknown autoregressive parameters.θ: The vector of unknown moving average parameters. The unknown parameters, α's, φ and θ, are estimated by a nonlinear least squares method byminimizing(方程式無法摘錄)whrer (方程式無法摘錄)with a=0 for t≦0. The parameters of the transformation tride are γ=0　(＝natural logarithmic transformation),0.25, 1/3, and 0.5. The transformation which minimize the Akaike's information criterion definedby(方程式無法摘錄) (NO. of parameters fitted+1)is γ=0.25. The notations in the formula are N for the length of the series and for the residualmean square divided by 2/Nth power of the Jacobian of the transformation. The d, D and S appearin the difference operation of ut, (1-B)(1-B)ut in order to obtain stationary series. The initialvalues of the regression coefficients in the nonlinear least square iteration and the initial estimatesof ut series are obtained by assuming A(B︱φ)=C(B︱θ)=0 for γ=0.0, 0.25, 1/3, 0.5 and for b=1,2,3, ...,18. The value of b which corresponds to the minimum residual mean squares as varying bfrom 1 to 18 with a specific value of γ is chosen. The initial values of ut are obtained by:(方程式無法摘錄)and are used in the model identification of A(B︱φ) and C(B︱θ). The correlation coefficients between the initial estimates of ut and the final ones are all greaterthan 0.9. The ratios as given by (the sum of squares due to the model with A(B)=C(B)=0)/(the sum of squares about mean) are 0.46, 0.63 and 0.40 for the rice stem borer, the green leafhopperand the brown planthopper respectively, while the ratios for the full models wiht appropriate ARIMA components are 0.98, 0.98 and respectively. The models fittde are able to give emphasis to the effects of environmental factors to thepopulation growth at the early season of the year. But the effects decrease gradually as time pro-ceeds and the density effects represented by ARIMA components may become strong owing to the form of the C (B︱θ) and the x's taken.
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