1、非平稳时间序列分析非平稳时间序列分析1、 首先画出时序图如下:t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:difx1401301201101009080706050403020100-10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:dif2x9080706050403020100-10-20-30-40-50-60-70-80-90-100-110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:AutocorrelationsLagCova
2、rianceCorrelation-1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1Std Error0577.3331.00000 |*|01-209.345-.36261| *| .| 0.0712472-52.915660-.09166| .*| .| 0.08006939.1391950.01583 |. | .| 0.080600415.3758920.02663. |* .| 0.0806155-59.441547-.10296.*| .| 0.0806606-23.834489-.04128| . *| .| 0.0813247100.2850.
3、17370 |. |*| 0.0814318-146.329-.25346| *| .| 0.083290952.2286580.09047| . |*.| 0.0871181021.0085750.03639| . |* .| 0.08759311134.0180.23213 |. |*| 0.08767012-181.531-.31443| *| .| 0.0907361323.2684700.04030| . |* .| 0.0961081471.1121950.12317 |. |* .| 0.09619415-105.621-.18295| *| .| 0.0969911637.59
4、19960.06511. |* .| 0.0987271723.0315060.03989| . |* .| 0.0989451845.6547450.07908| . |* .| 0.09902719-101.320-.17550| *| .| 0.09934720127.6070.22103| . |*| 0.10090821-61.519663-.10656| . *| .| 0.1033372235.8253170.06205| . |* .| 0.10389323-93.627333-.16217| .*| .| 0.1040812455.4512080.09605| . |* .|
5、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 630.706.0001-0.363-0.0920.0160.027-0.103-0.0411284.5412.00010.174-0.2530.0900.0360.232-0.3141897.9818.00010.0400.123-0.1830.0650.0400.07924126.9924 |t| Lag
6、MU0.402860.169002.380.0181 0MA1,10.890630.0326627.27LagSquareDF ChiSq Autocorrelations 624.6960.0004-0.1380.1890.0220.0610.0110.05212121.0812.0001-0.0820.043-0.013-0.1280.068-0.45418128.8718.00010.041-0.041-0.081-0.0580.034-0.06624134.7224 |t|LagMU0.279795.676720.050.96070MA1,11.037220.0274537.78.00011MA1,2-1.965780.02662-73.86.00012MA1,31.012210.0281635.94.00013MA1,4-0.933380.02327-40.11.00014AR1,10.887070.0578315.34.00011AR1,2-1.561090.07112-21.95.00012AR1,3
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