| Exonential Smoothing - Verkoop australische rosewijn- Sophie Rousseau | | *Unverified author* | | R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values) | | Title produced by software: Exponential Smoothing | | Date of computation: Fri, 20 May 2011 05:27:09 +0000 | | | | Cite this page as follows: | | Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/20/t13058690932ond23u942xt926.htm/, Retrieved Fri, 20 May 2011 07:24:56 +0200 | | | | Original text written by user: | | | | | IsPrivate? | | No (this computation is public) | | | | User-defined keywords: | | KDGP2W102 | | | | Dataseries X: | | » Textbox « » Textfile « » CSV « | | 112
118
129
99
116
168
118
129
205
147
150
267
126
129
124
97
102
127
222
214
118
141
154
226
89
77
82
97
127
121
117
117
106
112
134
169
75
108
115
85
101
108
109
124
105
95
135
164
88
85
112
87
91
87
87
142
95
108
139
159
61
82
124
93
108
75
87
103
90
108
123
129
57
65
67
71
76
67
110
118
99
85
107
141
58
65
70
86
93
74
87
73
101
100
96
157
63
115
70
66
67
83
79
77
102
116
100
135
71
60
89
74
73
91
86
74
87
87
109
137
43
69
73
77
69
76
78
70
83
65
110
132
54
55
66
65
60
65
96
55
71
63
74
106
34
47
56
53
53
55
67
52
46
51
58
91
33
40
46
45
41
55
57
54
46
52
48
77
30
35
42
48
44
45
0
0
46
51
63
84
30
39
45
52
28
40
62 | | | | Output produced by software: |
| Estimated Parameters of Exponential Smoothing | | Parameter | Value | | alpha | 0.155095379150641 | | beta | 0.13725398518357 | | gamma | FALSE |
| Interpolation Forecasts of Exponential Smoothing | | t | Observed | Fitted | Residuals | | 3 | 129 | 124 | 5 | | 4 | 99 | 130.881914190113 | -31.8819141901131 | | 5 | 116 | 131.364928978027 | -15.3649289780271 | | 6 | 168 | 134.082571556144 | 33.9174284438556 | | 7 | 118 | 145.165695907088 | -27.1656959070881 | | 8 | 129 | 146.196821292765 | -17.1968212927654 | | 9 | 205 | 148.407996440458 | 56.5920035595423 | | 10 | 147 | 163.268177303956 | -16.2681773039558 | | 11 | 150 | 166.481772636165 | -16.4817726361653 | | 12 | 267 | 169.311385262211 | 97.6886147377888 | | 13 | 126 | 191.927839774288 | -65.9278397742877 | | 14 | 129 | 187.764702060816 | -58.7647020608163 | | 15 | 124 | 183.46158272868 | -59.46158272868 | | 16 | 97 | 177.784594428339 | -80.784594428339 | | 17 | 102 | 167.080806812423 | -65.0808068124227 | | 18 | 127 | 157.427199092523 | -30.4271990925232 | | 19 | 222 | 152.500488051607 | 69.4995119483926 | | 20 | 214 | 164.551416149083 | 49.4485838509167 | | 21 | 118 | 174.545172645963 | -56.545172645963 | | 22 | 141 | 166.896084254248 | -25.8960842542484 | | 23 | 154 | 163.449266018761 | -9.44926601876057 | | 24 | 226 | 162.352122431583 | 63.6478775684174 | | 25 | 89 | 173.946909619913 | -84.9469096199135 | | 26 | 77 | 160.687028104626 | -83.6870281046255 | | 27 | 82 | 145.84106422174 | -63.8410642217403 | | 28 | 97 | 132.714103602917 | -35.7141036029173 | | 29 | 127 | 123.189242094029 | 3.81075790597107 | | 30 | 121 | 119.875625318933 | 1.12437468106735 | | 31 | 117 | 116.169297998806 | 0.83070200119407 | | 32 | 117 | 112.435106937733 | 4.56489306226665 | | 33 | 106 | 109.377246628417 | -3.37724662841678 | | 34 | 112 | 105.015704153803 | 6.98429584619664 | | 35 | 134 | 102.409866948451 | 31.5901330515488 | | 36 | 169 | 104.292755051877 | 64.7072449481226 | | 37 | 75 | 112.689406996829 | -37.6894069968294 | | 38 | 108 | 104.402499683268 | 3.59750031673163 | | 39 | 115 | 102.595582553496 | 12.4044174465042 | | 40 | 85 | 102.418636101337 | -17.418636101337 | | 41 | 101 | 97.2454733521327 | 3.75452664786731 | | 42 | 108 | 95.4360946389346 | 12.5639053610654 | | 43 | 109 | 95.2604634759868 | 13.7395365240132 | | 44 | 124 | 95.5596470926727 | 28.4403529073273 | | 45 | 105 | 98.744282242972 | 6.25571775702798 | | 46 | 95 | 98.6213513277845 | -3.6213513277845 | | 47 | 135 | 96.8894432705397 | 38.1105567294603 | | 48 | 164 | 102.44123822508 | 61.5587617749203 | | 49 | 88 | 112.940171041041 | -24.9401710410411 | | 50 | 85 | 109.492606210489 | -24.4926062104887 | | 51 | 112 | 105.593071269652 | 6.40692873034806 | | 52 | 87 | 106.622298647886 | -19.6222986478857 | | 53 | 91 | 103.196804261453 | -12.1968042614535 | | 54 | 87 | 100.663330773181 | -13.6633307731806 | | 55 | 87 | 97.6115482076485 | -10.6115482076485 | | 56 | 142 | 94.8071901201646 | 47.1928098798354 | | 57 | 95 | 101.972635866189 | -6.97263586618871 | | 58 | 108 | 100.588841568139 | 7.41115843186108 | | 59 | 139 | 101.593672030682 | 37.406327969318 | | 60 | 159 | 108.046900353523 | 50.9530996464766 | | 61 | 61 | 117.685832379025 | -56.6858323790253 | | 62 | 82 | 109.423766105269 | -27.4237661052693 | | 63 | 124 | 105.116328801892 | 18.8836711981081 | | 64 | 93 | 108.392946418558 | -15.3929464185582 | | 65 | 108 | 106.025742316162 | 1.97425768383771 | | 66 | 75 | 106.394138248061 | -31.3941382480615 | | 67 | 87 | 100.918948734477 | -13.9189487344771 | | 68 | 103 | 97.857781315505 | 5.14221868449495 | | 69 | 90 | 97.8623776531892 | -7.86237765318921 | | 70 | 108 | 95.682651150251 | 12.3173488497491 | | 71 | 123 | 96.894912037493 | 26.105087962507 | | 72 | 129 | 100.80129853641 | 28.1987014635903 | | 73 | 57 | 105.632673512721 | -48.6326735127214 | | 74 | 65 | 97.5125912191803 | -32.5125912191803 | | 75 | 67 | 91.2005487524956 | -24.2005487524956 | | 76 | 71 | 85.6624974774495 | -14.6624974774495 | | 77 | 76 | 81.2916265692531 | -5.29162656925311 | | 78 | 67 | 78.2614891545763 | -11.2614891545763 | | 79 | 110 | 74.0657251515363 | 35.9342748484637 | | 80 | 118 | 77.9547554587831 | 40.0452445412169 | | 81 | 99 | 83.3338396653939 | 15.6661603346061 | | 82 | 85 | 85.2653333074398 | -0.265333307439761 | | 83 | 107 | 84.720277630767 | 22.279722369233 | | 84 | 141 | 88.1461345858544 | 52.8538654141456 | | 85 | 58 | 97.4390243349273 | -39.4390243349273 | | 86 | 65 | 91.5781567469786 | -26.5781567469786 | | 87 | 70 | 87.1461688751446 | -17.1461688751446 | | 88 | 86 | 83.8120403736952 | 2.18795962630483 | | 89 | 93 | 83.5231219632838 | 9.47687803671619 | | 90 | 74 | 84.5664197687747 | -10.5664197687747 | | 91 | 87 | 82.2761624754418 | 4.72383752455816 | | 92 | 73 | 82.4579119313513 | -9.45791193135126 | | 93 | 101 | 80.2388026671235 | 20.7611973328765 | | 94 | 100 | 83.1484907461826 | 16.8515092538174 | | 95 | 96 | 85.8105300804307 | 10.1894699195693 | | 96 | 157 | 87.6562258200573 | 69.3437741799427 | | 97 | 63 | 100.152633548222 | -37.1526335482224 | | 98 | 115 | 95.3410553829629 | 19.6589446170371 | | 99 | 70 | 99.7591794483923 | -29.7591794483923 | | 100 | 66 | 95.879283516409 | -29.8792835164089 | | 101 | 67 | 91.3447059794791 | -24.3447059794791 | | 102 | 83 | 87.1502789167894 | -4.15027891678942 | | 103 | 79 | 85.9995652843691 | -6.99956528436913 | | 104 | 77 | 84.2579375443475 | -7.25793754434754 | | 105 | 102 | 82.3217344137319 | 19.6782655862681 | | 106 | 116 | 84.9821121898774 | 31.0178878101226 | | 107 | 100 | 90.0615049853103 | 9.93849501468965 | | 108 | 135 | 92.083146666745 | 42.916853333255 | | 109 | 71 | 100.13317008561 | -29.1331700856098 | | 110 | 60 | 96.3883966445052 | -36.3883966445052 | | 111 | 89 | 90.7437545924378 | -1.74375459243777 | | 112 | 74 | 90.4352163308046 | -16.4352163308046 | | 113 | 73 | 87.4982362488881 | -14.4982362488881 | | 114 | 91 | 84.5530422193192 | 6.44695778068076 | | 115 | 86 | 84.9935903477557 | 1.00640965224426 | | 116 | 74 | 84.6117585055056 | -10.6117585055056 | | 117 | 87 | 82.202105095048 | 4.79789490495205 | | 118 | 87 | 82.2845527133265 | 4.71544728667352 | | 119 | 109 | 82.454592977166 | 26.5454070228339 | | 120 | 137 | 86.5754433833673 | 50.4245566166327 | | 121 | 43 | 95.4732502247282 | -52.4732502247282 | | 122 | 69 | 87.2950605442206 | -18.2950605442206 | | 123 | 73 | 84.0282948019983 | -11.0282948019983 | | 124 | 77 | 81.6538064757393 | -4.65380647573929 | | 125 | 69 | 80.1689041193823 | -11.1689041193823 | | 126 | 76 | 77.4357826366945 | -1.43578263669451 | | 127 | 78 | 76.1816591568557 | 1.81834084314427 | | 128 | 70 | 75.4709430478392 | -5.47094304783924 | | 129 | 83 | 73.5132302148922 | 9.48676978510784 | | 130 | 65 | 74.0773387466259 | -9.07733874662586 | | 131 | 110 | 71.5690063518008 | 38.4309936481992 | | 132 | 132 | 77.2470949792613 | 54.7529050207387 | | 133 | 54 | 86.6221868532595 | -32.6221868532595 | | 134 | 55 | 81.751362263785 | -26.751362263785 | | 135 | 66 | 77.221606915982 | -11.2216069159821 | | 136 | 65 | 74.8615653662618 | -9.8615653662618 | | 137 | 60 | 72.5025323092084 | -12.5025323092084 | | 138 | 65 | 69.4677503404864 | -4.46775034048645 | | 139 | 96 | 67.5840188759728 | 28.4159811240272 | | 140 | 55 | 71.4053062403205 | -16.4053062403205 | | 141 | 71 | 67.9257917650018 | 3.07420823499822 | | 142 | 63 | 67.5329020542694 | -4.53290205426944 | | 143 | 74 | 65.8636907229314 | 8.1363092770686 | | 144 | 106 | 66.3326168756722 | 39.6673831243278 | | 145 | 34 | 72.5362846685988 | -38.5362846685988 | | 146 | 47 | 65.7905853792488 | -18.7905853792488 | | 147 | 56 | 61.7073489943339 | -5.70734899433391 | | 148 | 53 | 59.5317671600699 | -6.53176716006992 | | 149 | 53 | 57.0892771530311 | -4.08927715303106 | | 150 | 55 | 54.9385557404943 | 0.0614442595057341 | | 151 | 67 | 53.4329000313307 | 13.5670999686693 | | 152 | 52 | 54.310718197653 | -2.310718197653 | | 153 | 46 | 52.6767708167873 | -6.67677081678733 | | 154 | 51 | 50.2235373654054 | 0.776462634594637 | | 155 | 58 | 48.9427948984633 | 9.05720510153672 | | 156 | 91 | 49.1391622051745 | 41.8608377948255 | | 157 | 33 | 55.3143322248737 | -22.3143322248737 | | 158 | 40 | 51.0612144888181 | -11.0612144888181 | | 159 | 46 | 48.317938166158 | -2.31793816615794 | | 160 | 45 | 46.8813605863997 | -1.88136058639971 | | 161 | 41 | 45.4724447857964 | -4.4724447857964 | | 162 | 55 | 43.5664568144416 | 11.4335431855584 | | 163 | 57 | 44.3708051585932 | 12.6291948414068 | | 164 | 54 | 45.6294370154134 | 8.37056298458665 | | 165 | 46 | 46.4057627650067 | -0.405762765006742 | | 166 | 52 | 45.8122832867456 | 6.18771671325445 | | 167 | 48 | 46.3731427731321 | 1.62685722686787 | | 168 | 77 | 46.2612656845323 | 30.7387343154677 | | 169 | 30 | 51.3188557532931 | -21.3188557532931 | | 170 | 35 | 47.8487298876248 | -12.8487298876248 | | 171 | 42 | 45.4187645955059 | -3.41876459550591 | | 172 | 48 | 44.3785665350258 | 3.6214334649742 | | 173 | 44 | 44.5073617779747 | -0.507361777974722 | | 174 | 45 | 43.9849995143013 | 1.01500048569874 | | 175 | 0 | 43.7203553842112 | -43.7203553842112 | | 176 | 0 | 35.5867690069288 | -35.5867690069288 | | 177 | 46 | 27.9571124110637 | 18.0428875889363 | | 178 | 51 | 29.0292549661343 | 21.9707450338657 | | 179 | 63 | 31.1782913921711 | 31.8217086078289 | | 180 | 84 | 35.5325700619363 | 48.4674299380637 | | 181 | 30 | 43.5002716140874 | -13.5002716140874 | | 182 | 39 | 41.5696825221683 | -2.56968252216831 | | 183 | 45 | 41.2796752787956 | 3.72032472120442 | | 184 | 52 | 42.0444153531871 | 9.95558464681292 | | 185 | 28 | 43.9881445285592 | -15.9881445285592 | | 186 | 40 | 41.5677742218044 | -1.56777422180443 | | 187 | 62 | 41.3505627860012 | 20.6494372139988 |
| Extrapolation Forecasts of Exponential Smoothing | | t | Forecast | 95% Lower Bound | 95% Upper Bound | | 188 | 45.0187122269264 | -13.6151969793061 | 103.652621433159 | | 189 | 45.4842293738992 | -14.054771201188 | 105.023229948986 | | 190 | 45.9497465208719 | -14.7068682367719 | 106.606361278516 | | 191 | 46.4152636678446 | -15.5851244221473 | 108.415651757837 | | 192 | 46.8807808148173 | -16.699704078044 | 110.461265707679 | | 193 | 47.3462979617901 | -18.0572995152328 | 112.749895438813 | | 194 | 47.8118151087628 | -19.6613015812104 | 115.284931798736 | | 195 | 48.2773322557355 | -21.5121127868512 | 118.066777298322 | | 196 | 48.7428494027083 | -23.6075610646198 | 121.093259870036 | | 197 | 49.208366549681 | -25.9433671864647 | 124.360100285827 | | 198 | 49.6738836966537 | -28.5136219995843 | 127.861389392892 | | 199 | 50.1394008436264 | -31.311238359003 | 131.590040046256 |
| | | | Charts produced by software: |  | | http://www.freestatistics.org/blog/date/2011/May/20/t13058690932ond23u942xt926/1631w1305869226.png (open in new window) | | http://www.freestatistics.org/blog/date/2011/May/20/t13058690932ond23u942xt926/1631w1305869226.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2011/May/20/t13058690932ond23u942xt926/24feq1305869226.png (open in new window) | | http://www.freestatistics.org/blog/date/2011/May/20/t13058690932ond23u942xt926/24feq1305869226.ps (open in new window) |
 | | http://www.freestatistics.org/blog/date/2011/May/20/t13058690932ond23u942xt926/3b6c11305869226.png (open in new window) | | http://www.freestatistics.org/blog/date/2011/May/20/t13058690932ond23u942xt926/3b6c11305869226.ps (open in new window) |
| | | | Parameters (Session): | | par1 = 12 ; par2 = Double ; par3 = multiplicative ; | | | | Parameters (R input): | | par1 = 12 ; par2 = Double ; par3 = multiplicative ; | | | | R code (references can be found in the software module): | par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
| | |
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