时间序列AR模型建立全过程

clc;clear; series=[10.93 9.34 11.00 10.98 11.29 11.84... 10.62 10.90 12.77 12.15 12.24 12.30... 9.91 10.24 10.41 10.47 11.51 12.45... 11.32 11.73 12.61 13.04 13.14 14.15... 10.85 10.30 12.74 12.73 13.08 14.27... 13.18 13.75 14.42 13.95 14.53 14.91... 12.94 11.43 14.36 14.57 14.25 15.86... 15.18 15.94 16.54 16.90 16.88 18.10... 13.70 10.88 15.79 16.36 17.22 17.75... 16.62 16.96 17.69 16.40 17.51 19.73... 13.73 12.85 15.68 16.79 17.59 18.51... 16.80 17.27 20.83 19.18 21.40 23.76... 15.73 13.14 17.24 17.93 18.82 19.12... 17.70 19.87 21.17 21.44 22.14 22.45... 17.88 16.00 20.29 21.03 21.78 22.51... 21.55 22.01 22.68 23.02 24.55 24.67... 19.61 17.15 22.46 23.19 23.40 26.26... 22.91 24.03 23.94 24.12 25.87 28.25]; t=1:numel(series)-12; %plot(t,series);%可见数据有明显的周期性，做一次差分Y(t)=Z(t)-Z(t-12)及均值化 series1=series(13:numel(series)); series1=series1-series(1:numel(series)-12); ma=mean(series1); series1=series1-ma; Series=iddata(series1');%转换为matlab数据类型iddata %%%%%%%%%%%%%%%%Box-Jenkins方法建模过程%%%%%%%%%%%%%%%%%%%%%%% %subplot(2,2,1); %plot(t,series1);%从图中可以看出周期性明显被消除掉且均值为0 %%%%%%%%%%%%%%%%Box-Jenkins方法建模过程%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%Pandit-Wu方法建模过程%%%%%%%%%%%%%%%%%%%%%%% %%%%一、模型定阶（残差图定阶法） for n=1:6 m=armax(Series,[2*n,2*n-1]); e=resid(m,Series); residual(n)=sum((e.outputdata).^2);%模型残差 estx(n)=sum((e.outputdata).^2)/((96-2*n)-(2*n+2*n-1));sum((e.outputdata).^2);%每种AR(k)模型残差方差 end;residual(1:2) %subplot(2,2,2); %plot(estx);%残差方差图 %xlabel('n');ylabel('残差方差'); %%%%很明显可以看出ARMA（4,3）及ARMA(2,1)残差方差差别很小 %%%%模型定阶F检验法 F=((residual(1)-residual(2))/4)/(residual(2)/(96-2*2-2*2+1)); if F<finv(1-0.05,4,120) %disp('ARMA(2,1)与ARMA(4,3)无显著差异!'); else %disp('ARMA(2,1)与ARMA(4,3)有显著差异!') end; m1=armax(Series,[2*1,2*1-1]);p=predict(m1,Series,1);p.outputdata m2=armax(Series,[2*2,2*2-1]); %%%%输出适合的AR(2)模型 m=ar(Series,2,'ls'); e=resid(m,Series); estx=sum((e.outputdata).^2)/(96-2*2); %%%%%%%%%%%%%%%%Pandit-Wu方法建模过程%%%%%%%%%%%%%%%%%%%%%%%