時(shí)間序列分解結(jié)果

1、在隨機(jī)時(shí)間序列分析中，為簡(jiǎn)便起見(jiàn)，我們假定時(shí)間序列主要由趨勢(shì)項(xiàng)（T）、季節(jié)項(xiàng)（S）和隨機(jī)項(xiàng)（R）構(gòu)成。#讀入數(shù)據(jù)，畫(huà)曲線圖> sales <- read.csv(file = "sales.csv",header = TRUE)> head(sales)> plot(sales$t,sales$Y,type = "l")o10203040sales St觀察這幅圖形，可以看出有明顯的長(zhǎng)期趨勢(shì)和季節(jié)變動(dòng)。利用分解法，假設(shè)這48個(gè)數(shù)據(jù)可表示為：¥ Tt Ct S It，Yt代表實(shí) 際銷(xiāo)售額度。長(zhǎng)期趨勢(shì)的分解用時(shí)間回歸法，在同

2、一圖中畫(huà)出趨勢(shì)項(xiàng)目、季節(jié)項(xiàng)和隨機(jī)項(xiàng)的數(shù)據(jù)圖，女口下：decompose。 函數(shù)主要用來(lái)做季節(jié)指數(shù)分解，figure 項(xiàng)即指季節(jié)指數(shù)。同時(shí) 也返回原始數(shù)據(jù)，以及MA算法的結(jié)果；trend 趨勢(shì)項(xiàng)使用光滑移動(dòng)平均法求得， 它包含了長(zhǎng)期趨勢(shì)T和周期變動(dòng)因素C,之前用回歸法求得長(zhǎng)期趨勢(shì)T,利用此 函數(shù)的返回值Trend即可求得周期變動(dòng)因素C； Random即為不規(guī)則變動(dòng)。 此函數(shù)的基本結(jié)構(gòu)：Additive:xtMultiplicative:=Trend + Seas onal + Ran dom xt = Trend * Seas onal * Ran dom> salesl <- ts

3、(sales,2,start = 1,freque ncy = 4)#季節(jié)變動(dòng)趨勢(shì)分解> m <- decompose(sales1,type = "multiplicative")> plot(m)> m $xQtr1 Qtr2 Qtr3 Qtr42003 3017.60 3043.54 2094.35 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

4、.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 4965.46 5026.05 3470.14 4525.942014 5258.71 5189.58 3596.76 3881.60$seasonalQtr1 Qtr2 Qt

5、r3 Qtr42003 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 1.1213967 1.0938549 0.7535947 1.03115372009 1.1213967 1.0938549 0.75

6、35947 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$trend (居中平均TC)Qtr1 Qtr2 Qtr3 Qtr42003 NA NA 2773.483 2820.600200

7、4 2838.062 2867.399 2900.825 2948.6852005 3030.662 3129.642 3232.620 3298.2892006 3311.570 3299.977 3316.641 3342.2042007 3380.191 3428.931 3473.306 3527.6702008 3576.665 3662.923 3758.539 3821.3502009 3862.541 3872.932 3860.176 3829.1502010 3805.843 3795.361 3804.049 3864.1562011 3945.921 4005.759

8、4070.469 4153.4812012 4216.496 4282.001 4360.608 4436.4262013 4493.846 4503.359 4533.554 4590.6512014 4626.920 4562.205 NA NA$ra ndom（不規(guī)則變動(dòng)）Qtr1 Qtr2 Qtr3 Qtr42003 NA NA 1.0020422 0.96608802004 1.0289720 1.0085324 0.9671844 0.99474522005 0.9790810 1.0204784 1.0015782 1.02638812006 0.9923245 1.014276

9、4 0.9515991 1.00383722007 1.0155901 0.9867832 1.0095187 0.98569102008 1.0169040 0.9751303 0.9986037 1.03783902009 1.0018860 0.9792688 1.0025581 1.03449402010 0.9940394 0.9629070 1.0049880 1.01297282011 0.9853980 0.9951643 1.0341310 0.98619672012 0.9919877 1.0022614 1.0171081 1.00065412013 0.9853307

10、1.0203063 1.0157116 0.95611712014 1.0135098 1.0399147 NA NA$figure（季節(jié)變動(dòng)指數(shù)）1 1.1213967 1.0938549 0.7535947 1.0311537$type1 "multiplicative"attr（，“class"）1 "decomposed.ts"呂口Inosm- QDQH 8S-呂呂 CMcpCMn 呂960PQJAJ2 如 qoPUW4 -e匸 OSH如 EQPUffl觀察趨勢(shì)圖，可以發(fā)現(xiàn)明顯的呈現(xiàn)直線上升的趨勢(shì)，所有采用線性回歸擬合。> Im.

11、fit <- lm(Y t,data = sales)> summary(lm.fit)Call:lm(formula = Y t, data = sales)Residuals:Min 1Q Media n3Q Max-1062.7 -724.4 241.7 384.8 769.7Coefficie nts:Estimate Std. Error t value Pr(>|t|)(In tercept) 2736.101168.642 16.224 < 2e-16 *t38.9545.992 6.501 5.11e-08 *Signif. codes: 0'

12、* ' 0.001' * ' 0.01' *' 0.05'. ' 0.1' '1Residual sta ndard error: 575.1 on 46 degrees of freedomMultiple R-squared: 0.4789,Adjusted R-squared: 0.4675F-statistic: 42.27 on 1 and 46 DF, p-value: 5.115e-08由此，長(zhǎng)期趨勢(shì)方程為：T=2736.10+38.95t，利用此方程即可求得每個(gè)季度的趨勢(shì)值。#長(zhǎng)期趨勢(shì)預(yù)測(cè)> Im.p

13、redict <- predict(lm.fit,n ewdata = data.frame(t = seq(1:48)> Im.predict> pre15 <- predict(lm.fit, newdata = data.frame(t = 49)> pre1514644.865周期變動(dòng)因素c：采取百分比率，其值大于100的表明該季度經(jīng)濟(jì)活動(dòng)水平高于所有季度的平 均值，而小于100的循環(huán)指數(shù)所表明的情況則剛好相反。#周期變動(dòng)C> c <- m$tre nd/lm.predict> write.csv(rou nd(c,4),file = &

14、quot;sales2.csv")decompose()函數(shù)主要用來(lái)做季節(jié)指數(shù)分解，figure項(xiàng)即指季節(jié)指數(shù)。同時(shí)也返回原始數(shù)據(jù)，以及MA算法的結(jié)果；trend趨勢(shì)項(xiàng)使用光滑移動(dòng)平均法求得，它包含了長(zhǎng)期趨勢(shì)T和周期變動(dòng)因素C,之前用回歸法求得長(zhǎng)期趨勢(shì)T,利用此 函數(shù)的返回值Trend即可求得周期變動(dòng)因素C； Random即為不規(guī)則變動(dòng)。 此函數(shù)的基本結(jié)構(gòu)：Additive:xt = Trend + Seas onal + Ran domMultiplicative:xt = Trend * Seas onal * Ran dom> salesl <- ts(sales,

15、2,start = 1,freque ncy = 4)#季節(jié)變動(dòng)趨勢(shì)分解> m <- decompose(sales1,type = "multiplicative")> plot(m)> m $xQtr1 Qtr2 Qtr3 Qtr42003 3017.60 3043.54 2094.35 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 3849.63 370

16、1.18 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 4965.46 5026.05 3470.14 4525.94 2014 5258.71 5189.58 3596.76 3881.60$seasonalQtr1 Qtr2 Qtr3 Qtr

17、42003 1.1213967 1.0938549 0.7535947 1.0311537 2004 1.1213967 1.0938549 0.7535947 1.0311537 2005 1.1213967 1.0938549 0.7535947 1.0311537 2006 1.1213967 1.0938549 0.7535947 1.0311537 2007 1.1213967 1.0938549 0.7535947 1.0311537 2008 1.1213967 1.0938549 0.7535947 1.0311537 2009 1.1213967 1.0938549 0.75

18、35947 1.0311537 2010 1.1213967 1.0938549 0.7535947 1.0311537 2011 1.1213967 1.0938549 0.7535947 1.0311537 2012 1.1213967 1.0938549 0.7535947 1.0311537 2013 1.1213967 1.0938549 0.7535947 1.0311537 2014 1.1213967 1.0938549 0.7535947 1.0311537$trend （居中平均 TC ）Qtr1 Qtr2 Qtr3 Qtr42003 NA NA 2773.483 2820

19、.6002004 2838.062 2867.399 2900.825 2948.685 2005 3030.662 3129.642 3232.620 3298.289 2006 3311.570 3299.977 3316.641 3342.204 2007 3380.191 3428.931 3473.306 3527.670 2008 3576.665 3662.923 3758.539 3821.350 2009 3862.541 3872.932 3860.176 3829.150 2010 3805.843 3795.361 3804.049 3864.156 2011 3945.921 4005.759 4070.469 4153.481 2012 4216.496 4282.001 4360.608 4436.426 2013 4493.846 4503.359 4533.554 4590.651 2014 4626.920 4562.205 NA NA $random （不規(guī)則變動(dòng)）Qtr1 Qtr2 Qtr3 Q