非平稳时间序列分析.docx

此文档收集于网络，如有侵权请联系网站删除非平稳时间序列分析1、 首先画出时序图如下：从时序图中看出有明显的递增趋势，而该序列是一直递增，不随季节波动，所以认为该序列不存在季节特征。故对原序列做一阶差分，画出一阶差分后的时序图如下：从中可以看到一阶差分后序列仍然带有明显的增长趋势，再做二阶差分：做完二阶差分可以看到，数据的趋势已经消除，接下来对二阶差分后的序列进行检验： AutocorrelationsLag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1 Std Error0 577.333 1.00000 | |*| 01 -209.345 -.36261 | *| . | 0.0712472 -52.915660 -.09166 | .*| . | 0.0800693 9.139195 0.01583 | . | . | 0.0806004 15.375892 0.02663 | . |* . | 0.0806155 -59.441547 -.10296 | .*| . | 0.0806606 -23.834489 -.04128 | . *| . | 0.0813247 100.285 0.17370 | . |* | 0.0814318 -146.329 -.25346 | *| . | 0.0832909 52.228658 0.09047 | . |*. | 0.08711810 21.008575 0.03639 | . |* . | 0.08759311 134.018 0.23213 | . |* | 0.08767012 -181.531 -.31443 | *| . | 0.09073613 23.268470 0.04030 | . |* . | 0.09610814 71.112195 0.12317 | . |* . | 0.09619415 -105.621 -.18295 | *| . | 0.09699116 37.591996 0.06511 | . |* . | 0.09872717 23.031506 0.03989 | . |* . | 0.09894518 45.654745 0.07908 | . |* . | 0.09902719 -101.320 -.17550 | *| . | 0.09934720 127.607 0.22103 | . |* | 0.10090821 -61.519663 -.10656 | . *| . | 0.10333722 35.825317 0.06205 | . |* . | 0.10389323 -93.627333 -.16217 | .*| . | 0.10408124 55.451208 0.09605 | . |* . |从其自相关图中可以看出二阶差分后的序列自相关系数很快衰减为零，且都在两倍标准差范围之内，所以认为平稳，白噪声检验结果： Autocorrelation Check for White NoiseTo Chi- Pr Lag Square DF ChiSq -Autocorrelations-6 30.70 6 .0001 -0.363 -0.092 0.016 0.027 -0.103 -0.04112 84.54 12 .0001 0.174 -0.253 0.090 0.036 0.232 -0.31418 97.98 18 .0001 0.040 0.123 -0.183 0.065 0.040 0.07924 126.99 24 |t| LagMU 0.40286 0.16900 2.38 0.0181 0MA1,1 0.89063 0.03266 27.27 Lag Square DF ChiSq -Autocorrelations-6 24.69 6 0.0004 -0.138 0.189 0.022 0.061 0.011 0.05212 121.08 12 .0001 -0.082 0.043 -0.013 -0.128 0.068 -0.45418 128.87 18 .0001 0.041 -0.041 -0.081 -0.058 0.034 -0.06624 134.72 24 |t| LagMU 0.27979 5.67672 0.05 0.9607 0MA1,1 1.03722 0.02745 37.78 .0001 1MA1,2 -1.96578 0.02662 -73.86 .0001 2MA1,3 1.01221 0.02816 35.94 .0001 3MA1,4 -0.93338 0.02327 -40.11 .0001 4AR1,1 0.88707 0.05783 15.34 .0001 1AR1,2 -1.56109 0.07112 -21.95 .0001 2AR1,3 0.58435 0.09887 5.91 .0001 3AR1,4 -0.51306 0.07146 -7.18 |t| LagMA1,1 1.03708 0.02754 37.66 .0001 1MA1,2 -1.96564 0.02672 -73.57 .0001 2MA1,3 1.01208 0.02827 35.80 .0001 3MA1,4 -0.93333 0.02335 -39.97 .0001 4AR1,1 0.88696 0.05780 15.35 .0001 1AR1,2 -1.56094 0.07109 -21.96 .0001 2AR1,3 0.58434 0.09874 5.92 .0001 3AR1,4 -0.51307 0.07142 -7.18 .0001 4AR1,5 -0.11463 0.05462 -2.10 0.0365 5此时显然参数检验都显著所以最终模型为：xt=1-0.88696B+1.56094B2-0.58434B3+0.51307B4+0.11463B5*t接下来利用此模型对未来一年6个月进行预测：Forecasts for variable x时间 Forecast Std Error 95% Confidence Limits1982-1 3312.4933 107.6398 3101.5232 3523.46351982-2 3215.3428 145.0773 2930.9965 3499.68911982-3 3124.3113 187.5394 2756.7408 3491.88181982-4 2963.5109 221.5959 2529.1910 3397.83081982-5 3123.0553 254.8111 2623.6347 3622.47591982-6 3233.5793 284.3133 2676.3354 3790.8232预测图为：本题代码：data aa;input x;difx=dif(x);dif12x=dif12(difx);t=intnx(month,01jan1948d,_n_-1);format t year4.;cards;44665059256149159260463558051055355462870862972482086510071025955889965878110310929788238279288387207566588386847797547946816586446225887206707466166466785525605785145415765225305644425204845384544044244324585565066337081013103111011061104810059871006107585410087779828947957997817767618398428118437538487568488288578389868478017398657679418467687097988318337988067719517991156133212761373132513261314134312251133107510231266123711801046101010101046985971103710269471097101810549789551067113210921019111012621174139115331479141113701486145113091316131912331113136312451205108410481131113812711244113912051030130013191198114711401216120012711254120312721073137514001322121410961198113211931163112011649661154130611231033940115110131105101196310408381012963888840880939868100195696689684311801103104497289711031056105512871231107692911051127988903845102099410361050977956818103110619649678671058987111912021097994840108612381264117112061303139314631601149515611404170517391667159915161625162918091831166516591457170716071616152215851657171717891814169814811330164615961496138613021524154716321668142114751396170617151586147715001648174518562067185621042061280927832748264226282714269927762795267325582394278427512521237222022469268628152831266125902383267027712628238122242556251226902726249325442232249423152217210021162319249124322470219122412117237023922255207720472255223325392394234122312171248724492300238724742667279129042737284927232613295028252717259327032836293829753064309230632991;proc gplot;plot x*t difx*t dif12x*t;symbol c=black i=join v=star;run;proc arima;spot vt. 发现；认出identify var=x(1);run;survey n. 调查；测验proc arima;innocent adj. 清白的；无罪的；天真的identify var=x(1,12) nlag=8 minic p=(0:5) q=(0:5);paperwork n. 文书工作estimate p=5 q=4 noint;forecast lead=6 id=t interval=month out=results;arrangement n. 安排；排列run;