拟合ARMA模型偏自相关图Partial AutocorrelationsLagCorrelation98758916-***********10.53778-2**-0.11474..--3*0.03912.4*****！-0.27003.50.16219***.--6-0.17787****.7*0.03051:80.21004****9*0.02902.10-0.25795*****！:11I*0.04421:*120.04346:13-*i-0.03857.--14***-0.15591.:15****0.21892---160.00855:.....17I*0.05496-..---180.01825
拟合ARMA模型 ◼ 偏自相关图
建模定阶ARIMA(0,1,1)参数估计(1 - B)x, = 4.99661 +(1 +0.70766B)Var(ε) = 56.487631模型检验■模型显著■参数显著
建模 ◼ 定阶 ◼ ARIMA(0,1,1) ◼ 参数估计 ◼ 模型检验 ◼ 模型显著 ◼ 参数显著 t B t (1− B)x = 4.99661+ (1+ 0.70766 ) Var( t ) = 56.48763
ARIMA模型预测原则■最小均方误差预测原理Green函数递推公式V1= d-02=i+-02?Y, = dy j-- +...+Φp+dy j-p-d -0
ARIMA模型预测 ◼ 原则 ◼ 最小均方误差预测原理 ◼ Green函数递推公式 = + + − = + − = − j j− p+d j− p−d j 1 1 2 1 1 2 2 1 1 1
预测值X+ =(+++ +V+-+ +...+i&)+(e, +i&-- +..e.()文,(1)E[e,(U)] = 0Var[e,(l=(1+y? +...+yi)o
预测值 ( ) ( ) xt+l = t+l + 1 t+l−1 ++ l−1 t+1 + l t + l+1 t−1 + e (l) t x ˆ (l) t 2 2 1 2 1 [ ( )] (1 ) [ ( )] 0 = + + + − = t l t Var e l E e l
例5.7已知ARIMA(1,1,1)模型为车(1-0.8B)(1 - B)x, = (1 - 0.6B)8x, = 5.36, = 0.8q?=1且 x-1 = 4.51求xt+3的95%的置信区间
例5.7 ◼ 已知ARIMA(1,1,1)模型为 且 ◼ 求 的95％的置信区间 t B t (1− 0.8B)(1− B)x = (1− 0.6 ) xt−1 = 4.5 xt = 5.3 t = 0.8 1 2 = t+3 x