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1、0009 ooo寸 00010203040在随机时间序列分析中，为简便起见，我们假定时间序列主要由趋势项（T）、 季节项（S）和随机项（R）构成。#读入数据，画曲线图 sales head(sales) plot(sales$t,sales$Y,type = l)o o OCMsales$t观察这幅图形，可以看出有明显的长期趋势和季节变动。Y = T x C x S x I利用分解法，假设这48个数据可表示为： 厂t t t ，Yt代表实 际销售额度。长期趋势的分解用时间回归法，在同一图中画出趋势项目、季节项和随机项的数据图，如 下：decompose （）函数主要用来做季节指数分解figur
2、e项即指季节指数。同时 也返回原始数据，以及MA算法的结果；trend趋势项使用光滑移动平均法求得, 它包含了长期趋势T和周期变动因素C,之前用回归法求得长期趋势T,利用此 函数的返回值Trend即可求得周期变动因素C； Random即为不规则变动。 此函数的基本结构：Additive: xt 二 Trend + Seasonal + RandomMultiplicative: xt 二 Trend * Seasonal * Random salesl m plot(m) m$xQtr1Qtr2Qtr3Qtr420033017.603043.542094.352809.8420043274.8
3、03163.282114.313024.5720053327.483493.482439.933490.7920063685.083661.232378.433459.5520073849.633701.182642.383585.5220084078.663907.062828.464089.5020094339.614148.602916.454084.6420104242.423997.582881.014036.2320114360.334360.533172.184223.7620124690.484694.483342.354577.6320134965.465026.053470
4、.144525.9420145258.715189.583596.763881.60$seasonalQtr1Qtr2Qtr3Qtr42003 1.1213967 1.0938549 0.7535947 1.03115372004 1.1213967 1.0938549 0.7535947 1.03115372005 1.1213967 1.0938549 0.7535947 1.03115372006 1.1213967 1.0938549 0.7535947 1.03115372007 1.1213967 1.0938549 0.7535947 1.03115372008 1.121396
5、7 1.0938549 0.7535947 1.03115372009 1.1213967 1.0938549 0.7535947 1.03115372010 1.1213967 1.0938549 0.7535947 1.03115372011 1.1213967 1.0938549 0.7535947 1.03115372012 1.1213967 1.0938549 0.7535947 1.03115372013 1.1213967 1.0938549 0.7535947 1.03115372014 1.1213967 1.0938549 0.7535947 1.0311537$tren
6、d (居中平均TC)Qtr1 Qtr2 Qtr3 Qtr42003 NANA2773.4832820.6002004 2838.062 2867.399 2900.825 2948.6852005 3030.6623129.6423232.6203298.2892006 3311.5703299.9773316.6413342.2042007 3380.1913428.9313473.3063527.6702008 3576.6653662.9233758.5393821.3502009 3862.5413872.9323860.1763829.1502010 3805.8433795.361
7、3804.0493864.1562011 3945.9214005.7594070.4694153.4812012 4216.4964282.0014360.6084436.4262013 4493.8464503.3594533.5544590.6512014 4626.9204562.205NANA$random （不规则变动）Qtr1Qtr2Qtr3Qtr42003NANA1.00204220.966088020041.02897201.00853240.96718440.994745220050.97908101.02047841.00157821.026388120060.99232
8、451.01427640.95159911.003837220071.01559010.98678321.00951870.985691020081.01690400.97513030.99860371.037839020091.00188600.97926881.00255811.034494020100.99403940.96290701.00498801.012972820110.98539800.99516431.03413100.986196720120.99198771.00226141.01710811.000654120130.98533071.02030631.0157116
9、0.956117120141.01350981.0399147NANA$figure （季节变动指数）1 1.1213967 1.0938549 0.7535947 1.0311537$type1 multiplicative attr（,class）1 decomposed.tsDecomposition of multiplicative time seriesymwwm000 00 000 000寸 口口启QLCDCMr L 00 - so PD亡(Dsqo PU lm.fit summary(lm.fit)Call:lm(formula = Y t, data = sales)Resi
10、duals:Min1Q Media n3QMax-1062.7-724.4241.7384.8769.7Coefficients:Estimate Std.Error tvaluePr(|t|)(Intercept) 2736.101168.64216.224 lm.predict lm.predict pre15 pre151 4644.865采取百分比率，其值大于100的表明该季度经济活动水平高于所有季度的平 均值，而小于100的循环指数所表明的情况则刚好相反。 #周期变动C c write.csv(round(c,4),file = sales2.csv)decompose ()函数主要
11、用来做季节指数分解figure项即指季节指数。同时 也返回原始数据，以及MA算法的结果；trend趋势项使用光滑移动平均法求得， 它包含了长期趋势T和周期变动因素C,之前用回归法求得长期趋势T,利用此 函数的返回值Trend即可求得周期变动因素C； Random即为不规则变动。 此函数的基本结构：Additive: xt 二 Trend + Seasonal + RandomMultiplicative: xt 二 Trend * Seasonal * Random sales1 m plot(m) m$xQtr1 Qtr2 Qtr3 Qtr42003 3017.60 3043.54 2094
12、.35 2809.842004 3274.80 3163.28 2114.31 3024.572005 3327.48 3493.48 2439.93 3490.792006 3685.08 3661.23 2378.43 3459.552007 3849.63 3701.18 2642.38 3585.522008 4078.66 3907.06 2828.46 4089.502009 4339.61 4148.60 2916.45 4084.642010 4242.42 3997.58 2881.01 4036.232011 4360.33 4360.53 3172.18 4223.762012 4690.48 4694.48 3342.35 4577.632013 4
