时间序列分析习题及答案.docx
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时间序列分析习题及答案
时间序列分析
第一题：
1、绘制时序图：
dataex1_1;
inputx@@;
time=intnx（'month','01jul2004'd,_n_-1）;
formattimedate.;
cards;
153134145117187175203178234243189149
212227214178300298295248221256220202
201237231162175165174135123124119120
10410685968587679078747563
;
procgplotdata=ex1_1;
plotx*time=1;
symbol1c=blackv=stari=join;
run;
时序图：
2、绘制自相关图：
dataex1_1;
inputx@@;
time=intnx（'month','01jul2004'd,_n_-1）;
formattimedate.;
cards;
153134145117187175203178234243189149
212227214178300298295248221256220202
201237231162175165174135123124119120
10410685968587679078747563
;
procarimadata=ex1_1;
identifyvar=x;
run;
样本自相关图：
白噪声检验输出结果：
因为P值小于α，所以该序列为非白噪声序列，根据时序图看出数据并不在一个常数值附近随机波动，后期有递减的趋势，所以不是平稳序列。
第二题：
1、选择拟合模型
方法一：
首先绘制该序列的时序图，直观检验序列平稳性。
时序图显示序列没有显著的非平稳特征。
在考察自相关图和偏自相关图，自相关图显示延迟1阶、6阶、19阶的自相关系数在2倍标准差范围之外，其他阶数的自相关系数都在2倍标准差范围内波动，根据自相关系数的这个特点可以判断该序列具有短期相关性，进一步确定序列平稳。
同时可以认为该序列自相关系数1阶截尾。
偏自相关系数可以看为拖尾，综合该序列自相关系数和偏自相关系数的性质，为拟合模型定阶为MA
（1）模型。
绘制时序图
dataex1_2;
inputx@@;
time=intnx（'month','01jul2004'd,_n_-1）;
formattimedate.;
cards;
81.989.479.081.484.885.988.080.382.683.580.285.287.283.584.382.9
84.782.981.583.487.781.879.685.877.989.785.486.380.783.890.584.5
82.486.783.081.889.379.382.788.079.687.883.679.583.388.486.684.6
79.786.084.283.084.883.681.885.988.283.587.283.787.383.090.580.7
83.186.590.077.584.784.687.280.586.182.685.484.782.881.983.686.8
84.084.282.883.082.084.784.488.982.483.085.082.281.686.285.482.1
81.485.085.884.283.586.585.080.485.786.786.782.386.482.582.079.5
86.780.591.781.683.985.684.878.489.985.086.283.085.484.484.586.2
85.683.285.783.580.182.288.682.085.085.285.384.382.389.784.883.1
80.687.486.883.586.284.182.384.886.683.578.188.881.983.380.087.2
83.386.679.584.182.290.886.579.781.087.281.684.484.482.288.980.9
85.187.184.076.582.785.183.390.481.080.379.889.083.780.987.3
81.185.686.680.086.683.383.182.386.780.2
;
procgplotdata=ex1_2;
plotx*time=1;
symbol1c=blackv=stari=join;
run;
时序图
绘制自相关图、偏自相关图
dataex1_2;
inputx@@;
time=intnx（'month','01jul2004'd,_n_-1）;
formattimedate.;
cards;
81.989.479.081.484.885.988.080.382.683.580.285.287.283.584.382.9
84.782.981.583.487.781.879.685.877.989.785.486.380.783.890.584.5
82.486.783.081.889.379.382.788.079.687.883.679.583.388.486.684.6
79.786.084.283.084.883.681.885.988.283.587.283.787.383.090.580.7
83.186.590.077.584.784.687.280.586.182.685.484.782.881.983.686.8
84.084.282.883.082.084.784.488.982.483.085.082.281.686.285.482.1
81.485.085.884.283.586.585.080.485.786.786.782.386.482.582.079.5
86.780.591.781.683.985.684.878.489.985.086.283.085.484.484.586.2
85.683.285.783.580.182.288.682.085.085.285.384.382.389.784.883.1
80.687.486.883.586.284.182.384.886.683.578.188.881.983.380.087.2
83.386.679.584.182.290.886.579.781.087.281.684.484.482.288.980.9
85.187.184.076.582.785.183.390.481.080.379.889.083.780.987.3
81.185.686.680.086.683.383.182.386.780.2
;
procarimadata=ex1_2;
identifyvar=x;
run;
自相关图
偏自相关图
方法二：
相对最优定阶
dataex1_2;
inputx@@;
time=intnx（'month','01jul2004'd,_n_-1）;
formattimedate.;
cards;
81.989.479.081.484.885.988.080.382.683.580.285.287.283.584.382.9
84.782.981.583.487.781.879.685.877.989.785.486.380.783.890.584.5
82.486.783.081.889.379.382.788.079.687.883.679.583.388.486.684.6
79.786.084.283.084.883.681.885.988.283.587.283.787.383.090.580.7
83.186.590.077.584.784.687.280.586.182.685.484.782.881.983.686.8
84.084.282.883.082.084.784.488.982.483.085.082.281.686.285.482.1
81.485.085.884.283.586.585.080.485.786.786.782.386.482.582.079.5
86.780.591.781.683.985.684.878.489.985.086.283.085.484.484.586.2
85.683.285.783.580.182.288.682.085.085.285.384.382.389.784.883.1
80.687.486.883.586.284.182.384.886.683.578.188.881.983.380.087.2
83.386.679.584.182.290.886.579.781.087.281.684.484.482.288.980.9
85.187.184.076.582.785.183.390.481.080.379.889.083.780.987.3
81.185.686.680.086.683.383.182.386.780.2
;
procarimadata=ex1_2;
identifyvar=xnlag=8minicp=（0:
5）q=（0:
5）;
run;
最后一条信息显示，在自相关延迟阶数小于等于5，移动平均延迟阶数也小于等于5的所有ARMA（p，q）模型中，BIC信息量相对最小的是ARMA（0,1）模型，即MA
（1）模型。
2、估计模型中未知参数的值，
dataex1_2;
inputx@@;
time=intnx（'month','01jul2004'd,_n_-1）;
formattimedate.;
cards;
81.989.479.081.484.885.988.080.382.683.580.285.287.283.584.382.9
84.782.981.583.487.
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