第四章非平稳时间序列的确定性分析实验报告

1、第四章非平稳时间序列建模实验报告下表为1993-2000年中国社会消费品零售总额的数据。表4-11993-2000年全国社会消费品零售总额单位（亿元）199319941995199619971998199920001月977.51192.21602.21909.12288.52549.52662.12774.72月892.51162.71491.51911.22213.52306.42538.42805.03月942.31167.51533.31860.12130.92279.72403.12627.04月941.31170.41548.71854.82100.52252.72356.8257

2、2.05月962.21213.71585.41898.32108.22265.22364.02637.06月1005.71281.11639.71966.02164.72326.02428.82645.07月963.81251.51623.61888.72102.52286.12380.32597.08月959.81286.01637.11916.42104.42314.62410.92636.09月1023.31396.21756.02083.52239.62443.12604.32854.010月1051.11444.11818.02148.32348.02536.02743.93029.

3、011月1102.01553.81935.22290.12454.92652.22781.53108.012月1415.51932.22389.52848.62881.73131.43405.73680.0资料来源：国家统计局网站根据以上数据，下面用Eviewis6.0对1980-2012年我国社会消费零售品总 额的月度数据进行确定性分析，并对2001年月度数据进行预测。1. 绘制时序图年中国社会消费品零售总额时序图图4-11993-2000从时序图可以看出序列中既有长期趋势又有季节波动， 故以下对其进行季节调整2. 季节调整在数据窗口中选择 “ Proc/Seasonal Adjustmen

4、t/Moving Average Methods , 出现季节调整对话框，选择 Ratio to movi ng Average选项，季节因子命名为sa，如图4-3所示。IO Series: S Workfile: UNT1TLED:Untitled£ CJg!9s99Jcw9Gener呂by Equation. Generate by Classification,. ResampleHSeasonal AdjustmentExponential Smoothing. Hodrick-Prescott Filter, Frequency Filter. Distribution P

5、lot Data.21:49Census X12Xll (Historical).Tramo/Seats+,Moving Average M亡thod鱼“1993M081993M09959.80001023 3001993M101993M111051.1001102.000廿疤內 | 茁駅| Object| Properties | Pirt| Noee| FrtEje | | Default 5or11 Ed114S(n+/-|u11993M121415.5001994M011192.2001994M021162.7001994M031167.5001994M044rn图4-2mI<j

6、Mtmerrt图4-3季节调整方法选择对话框季节调整操作#EZICaZIS12个月的季节调整因子如下图所示:'iewProc Object | Pro per tiesPrintNameFreeze|Sample | Genr | Sheet| Graph | Stats | ldent|Series： S Workfile： UNTITLED;: Untit I edDate: 06/07/14 Time: 21:57 Sample: 1993M01 2001M12 Included observations: 96Ratio to Moving Average Original S

7、eries: SAdjusted Series: SSAScaling Factors:11 04772920 99758730 96277840.94320950.94734950.96239470 93206480.92947590 985026101.0111901111.051079121.274102图4-412个月的季节调整因子经季节调整后的序列SSA寸序图如下：3. 趋势拟合在命令栏中输入：LS SSAC TREN对经季节调整后序列进行趋势拟合。结果如下图所示:口 Equation: UNTITLED Workfile: UNTITLED:Untitled| => | QV

8、iew Proc Object| Print N曰rrpe | Estimate FoEca£t| Stats ResidsDependent Variable: SSAMethod: Least SquaresDate: 06/08/14 Time: 11:56Sample： 1993M01 2000M12Included observations: 96VariableC o effi cj e ntStd. Errort-StatisticProb.C©TREND1016.64721.1300920.9313348.570590.38062255.514620.000

9、00.0000R-squared Adjusted R-squared S.E of regression Sum squared resid Log HKeiihood F-statisticProbiF-statistic)0.9704020.970087103.3443 1003925 -580,4b193081 874 0 000000rJean dependentvar S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Durtiin-'.Vatson stat202

10、0.326597.525412.1346212.1880512.156220.193032图4-6经季节调整后序列进行趋势拟合4. 长期趋势预测将样本期改为1993.1至2001.12，在命令栏中输入 LS SSAC TREND在结果窗口中点Forecast，得到以下扩展时间区间后的长期趋势值 SSAF预测值。Forecast. SSAFActual- SSAForecast sample: 1993M01 2001M12 Included observations: 96Root Mean Squared Error 102.2621Mean Ab&alute Error89 164

11、0SMean Abs Percent Error 5.056926Ttieil In&quaiity Coefficient 0.024294Bias Proportion0.000000Variance Proporticn 0.007S11 Covariance Proportion 0 992489图4-7扩展时间区间后预测长期趋势值SSAF5将趋势拟合序列SSAF与序列SSA进行比较，如下:图4-8趋势拟合序列SSAF与序列SSA的时序图#5. 对长期趋势预测进行季节调整在主窗口选择“ Quick/Generate Series ” ,设定 sf=ssaf*sa。#Sample

12、1993M01 2Q0 IM 12OK 匸 an 匚 el#图4-9经季节调整预测2001年12个月的零售总额值#讪豐问 | Proc Object| Prop&'tics | Rrintl N曰mE |【De估uit:Sort 巨SHipl +7-| Le经季节调整后2001年12个月的零售总额预测值如下图所示:L i Series: SF Workfile: UNTlTLED:Untitled7#2000M022805.91742000M032728.3552000M042692.8282000M052724.6662000 rd062788.2722DOOM072720.

13、0942000M082732.1782000M092916.2832000M103D15.1102000 rd 113156.2582000M123852 8912001M013190.4772001M023058.866200ird032972.4782001M042931.9892001 MOS2964.8772001M063032.2982001M072956.4292001 Fd082967.8562001M093165.0472001M103271 50820D1M113422.771200ird124175.954"【一 图4-102001年12个月零售总额预测值经季节调

14、整后的1993年至2001年个月度零售总额预测值如下图所示:SF经原序列S与预测序列SF进行比较，可见经过长期趋势和季节调整处理后 序列的预测值与原序列拟合效果非常好。如下图所示：SF图4-12预测序列与原序列的时序图最终确定1993-2000年中国社会消费品零售总额序列拟合模型为:Xt 二 St TtItT? =1016.647 21.13009t(t 二 0,1,2 ,95)其中，Xt ,为原序列，St为季节指数如表4-2所示，Tt为长期趋势，It为 包含没有能够提取完的相关信息的残差。表4-2季节指数月份季节指数月份季节指数11.04772970.93206420.99758780.92947530.96277890.98502640.943209101.01119050.947349111.05107960.962394121.2741029用原序列值除以季节指数，再减去长期趋势拟合值之后的残差可以视作随机波动的影响。=1t本例残差图如下:300Io