oef 10.2 Thomas Simons

*Unverified author*

R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)

Title produced by software: Exponential Smoothing

Date of computation: Thu, 19 May 2011 21:52:51 +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/19/t1305841740i1fq779vxsxyjz1.htm/, Retrieved Thu, 19 May 2011 23:49:00 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

17,1 13,4 15,3 14 9,7 13,7 13,7 12,5 9,8 7 -1,9 -2,9 -6,8 -10,4 -17,2 -19,8 -16,8 -23,2 -21,7 -17,6 -13 -12,6 -4 -0,2 3,1 6,5 19,2 26,6 26,6 31,4 31,2 26,4 20,7 20,7 15 13,3 8,7 10,2 4,3 -0,1 -4,6 -3,9 -3,5 -3,4 -2,5 -1,1 0,3 -0,9 3,6 2,7 -0,2 -1 5,8 6,4 9,6 13,2 10,6 10,9 12,9 15,9 12,2 9,1 9 17,4 14,7 17 13,7 9,5 14,8 13,6 12,6 8,9 10,2 12,7 16 10,4 9,9 9,5 8,6 10 3,5 -4,2 -4,4 -1,5 -0,1 0,8 -2,4 -1,2 0,2 -1,9 -1,6 -4,2 -2,2 6,2 5,7 3,1 1,1 -0,9 0,1 -4 -4 -5,3 -8 -6,3 -3,6 -3,5 -5,1 -3,3

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.0129118310986201 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 -6.8 5.29011904502332 -12.0901190450233 14 -10.4 -8.84171324014721 -1.55828675985279 15 -17.2 -15.9777490065531 -1.22225099344691 16 -19.8 -19.2767864574917 -0.523213542508337 17 -16.8 -17.4447550613783 0.644755061378326 18 -23.2 -25.6515712032783 2.45157120327834 19 -21.7 -22.7216106860833 1.02161068608327 20 -17.6 -27.7644764890422 10.1644764890422 21 -13 -23.2666467148864 10.2666467148864 22 -12.6 -26.3010044782941 13.7010044782941 23 -4 -18.9086575698116 14.9086575698116 24 -0.2 -2.02357903063458 1.82357903063458 25 3.1 -1.49201857893718 4.59201857893718 26 6.5 2.01844508797077 4.48155491202923 27 19.2 7.01265005348185 12.1873499465182 28 26.6 17.6315183424416 8.96848165755836 29 26.6 20.0432882620052 6.55671173799476 30 31.4 35.4760470482716 -4.07604704827165 31 31.2 26.6707282575723 4.52927174242769 32 26.4 35.0400343978482 -8.6400343978482 33 20.7 29.121780244723 -8.42178024472298 34 20.7 31.8724152661828 -11.1724152661828 35 15 19.698985465602 -4.69898546560196 36 13.3 2.68691920634813 10.6130807936519 37 8.7 15.0018137763925 -6.30181377639252 38 10.2 8.18633685500812 2.01366314499188 39 4.3 12.1873122352001 -7.88731223520014 40 -0.1 2.85287939834127 -2.95287939834127 41 -4.6 -1.23202195284512 -3.36797804715488 42 -3.9 -8.0189175674334 4.1189175674334 43 -3.5 -4.88744331137933 1.38744331137933 44 -3.4 -5.72230740148329 2.32230740148329 45 -2.5 -5.85143471834727 3.35143471834727 46 -1.1 -7.32300181020793 6.22300181020793 47 0.3 -4.64616789106606 4.94616789106606 48 -0.9 -0.723371722037258 -0.176628277962742 49 3.6 -2.02736684196994 5.62736684196994 50 2.7 2.88068944693305 -0.180689446933046 51 -0.2 2.33993111446629 -2.53993111446629 52 -1 -1.45894998659693 0.458949986596932 53 5.8 -1.78705521406384 7.58705521406384 54 6.4 6.78395031443612 -0.383950314436121 55 9.6 4.57927487564638 5.02072512435362 56 13.2 9.98483733517275 3.21516266482725 57 10.6 14.0490822853714 -3.44908228537135 58 10.9 15.5107002009973 -4.61070020099728 59 12.9 9.52806161767183 3.37193838232817 60 15.9 2.42119499932248 13.4788050006775 61 12.2 18.4313153693455 -6.23131536934553 62 9.1 12.235734114758 -3.135734114758 63 9 11.0968677546165 -2.09686775461647 64 17.4 7.95731408297065 9.44268591702935 65 14.7 13.1140651690469 1.58593483095308 66 17 19.4266947755849 -2.42669477558491 67 13.7 14.265274203766 -0.565274203766021 68 9.5 14.9983918972925 -5.49839189729249 69 14.8 9.8646200732908 4.9353799267092 70 13.6 23.018654100887 -9.41865410088695 71 12.6 12.9705529867879 -0.37055298678793 72 8.9 2.43308277596981 6.46691722403019 73 10.2 10.0597855698704 0.140214430129612 74 12.7 10.1958385383712 2.50416146162881 75 16 16.0653780776154 -0.0653780776153816 76 10.4 15.1310834436457 -4.73108344364572 77 9.9 7.5980102770202 2.3019897229798 78 9.5 12.8440215409794 -3.34402154097945 79 8.6 7.6437147267147 0.956285273285293 80 10 9.11933041423105 0.880669585768947 81 3.5 10.6275335375779 -7.1275335375779 82 -4.2 3.97518243477542 -8.17518243477542 83 -4.4 -7.03640718058249 2.63640718058249 84 -1.5 -1.58532966425595 0.0853296642559509 85 -0.1 -2.43471972696672 2.33471972696672 86 0.8 -0.75450079413503 1.55450079413503 87 -2.4 0.227130211188902 -2.6271302111889 88 -1.2 -3.24300742534464 2.04300742534464 89 0.2 -1.61223726725314 1.81223726725314 90 -1.9 -0.605446798773695 -1.29455320122631 91 -1.6 -2.48633153195007 0.88633153195007 92 -4.2 -2.78478623755605 -1.41521376244395 93 -2.2 -6.00017033176583 3.80017033176583 94 6.2 -5.47963543102029 11.6796354310203 95 5.7 5.17096964284982 0.529030357150184 96 3.1 0.924394713266959 2.17560528673304 97 1.1 3.22217617686705 -2.12217617686705 98 -0.9 0.626064053175678 -1.52606405317568 99 0.1 -1.93194385717674 2.03194385717674 100 -4 -0.609061691802807 -3.39093830819719 101 -4 -3.7668836166656 -0.233116383334405 102 -5.3 -6.36284721069496 1.06284721069496 103 -8 -5.43241262096231 -2.56758737903769 104 -6.3 -10.2165708515616 3.91657085156157 105 -3.6 -8.33243326213262 4.73243326213262 106 -3.5 -7.61940988647601 4.11940988647601 107 -5.1 -5.62254278041096 0.522542780410958 108 -3.3 -1.60974105661271 -1.69025894338729 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 109 -4.44284851504703 -15.1026372020344 6.21694017194033 110 -5.23428871886869 -20.8659350488255 10.3973576110881 111 -7.63572478088411 -31.1619943847527 15.8905448229845 112 -8.27753317344292 -34.2222250606486 17.6671587137628 113 -7.11374296291278 -30.5085123965361 16.2810264707105 114 -10.6058132489667 -45.068046409191 23.8564199112576 115 -10.1003986641228 -42.8773584730367 22.6765611447911 116 -12.5753399888747 -52.7271861864918 27.5765062087423 117 -15.6150514136752 -64.2753883226724 33.0452854953221 118 -27.9316081905319 -111.783414649533 55.9201982684687 119 -33.2535434044915 -129.522151514782 63.015064705799 120 -8.326146148085 -32.4065436990005 15.7542514028305

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/19/t1305841740i1fq779vxsxyjz1/1elpw1305841967.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305841740i1fq779vxsxyjz1/1elpw1305841967.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305841740i1fq779vxsxyjz1/2lsjq1305841967.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305841740i1fq779vxsxyjz1/2lsjq1305841967.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305841740i1fq779vxsxyjz1/3b2ro1305841967.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305841740i1fq779vxsxyjz1/3b2ro1305841967.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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