ARIMA模型VIP专享

110计量经济原理课程报告ARIMADDDDDDD2013114ARIMA一、相关概念介绍1.1（一）模型1、AR（p）（p 阶自回归模型）6（1 一 QL 一 QL2一...一 QLp）x—8+u12pttARp①（L）—1—QL—QL©LP—012pARp2、MA（q）（q 阶移动平均模型）MAq210MAqqMA(q)可逆性(用自回归序列表示)可逆条件：即[0(L)]-1收敛的条件。即 O(L)每个特征根绝对值大于 1,即全部特征根在单位圆之外。3、ARMA(p,q)(自回归移动平均过程)ARMApq0L=0OL=04、ARIMA(p,d,q)(单整自回归移动平均模型)dxt~I(d)wtwtARMApqxt~ARIMApdqARMAARIMAPdqpdqxt~Iddxt~ ARppxt~MAqqP=1P=P1AR(p)1AR(p)屮<1i=1,2,,pE()=0xx=0xx+0xx+…+0 xx+xuk>0t—kt1t—kt—12t—kt—2pt—kt—pt—kt7310y=©九+0 九 H©九 k>0k1k-12k-2pk-pAR(p)p=©p+©p+…+©pk>0k1k-12k-2pk-p2kAR(k)Y0j>0p 二 1p=pYule-Walker0j-jkp1,p2,,pk1122/4kkp3k=3xtxt-3xt-1xt-2屮 k=3xt-1xt-2xtxt-3332MA(q)1MA(q)k>qpk=0xtxt+k0MA(q)q2MA(q)MA(q)ARAR3ARMApqPq1.2ARIMAARIMA4101.3ARMAARIMA自回归过程YttGDPYtYut(ut)YtAR⑴PY移动平均过程ARYYu()tYYMA(1)5101()dAEIMA(pdq)610q自回归于移动平均过程YARMAARMAYARMA(1ARMA(pq)pq自回归求积移动平均过程AEMA(pq)AEIMA(p0q)=AEMA(pq)□□□□□□□□□□□2.1 基本思路pdq()()7102.2 基本程序ADFARMAARMA□□□□□□□□□□3.1 识别ARIMA(ACF)(PACF)ARMAACFPACF810ACFPACFAR(p)qMA(q)qARMA(p,q)AR(P)ACFPACFMA(q)ACFPACFAR(p)AC()PACF()MA(q)19701991GDPd=1ACF41812(0)95%1812GDPAR(12)181218123.2 模型估计MA0d1)AR(ARARIMAY*Y3.3 诊断检查910ACFPACFAutocorrelationPartialCorrelationACPACQ-StatProb11111110.0440.0440.17500.6761□111120.1000.09S1.O0S50.5S0111130.0190.0111.12320.7711匸11匚14 -0.088-0.1011.85330.7631[11115 -0.064-0.0612.24300.0151[1116 -0.028-0.0042.31760.0081[1111 -0.040-0.0222.46960.9291匚11匚18 -0.116-0.1203.79200.0751111]190.0630.0694.18830.8991□11□1100.1250.1475.76910.S341111]1110.0900.0696.59960.0311[111112-0.026-0.0976.66980.8791□1111130.1080.0927.09270.051匚11匚114-0.178-0.15511.2580.6661匚11匚115-0.134-0.13613.2010.5S71[11[116-0.077-0.05613.0530.6101匚111117-0.119-0.04315.4310.56411111180.0050.04715.4340.632111119-0.005-0.02215.4360.6941匚1匚120-0.103-0.17716.6710.674111111210.0620.06517.1160.70411111220.001-0.03217.1160.7571[11匚123-0.051-0.11917.4290.7081[111124-0.040-0.05017.6260.021111]125-0.0020.09217.6270.858ACF25PACF