*The author of this computation has been verified*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 29 Dec 2010 14:11:07 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/29/t1293634454140pcdauav1h8p6.htm/, Retrieved Wed, 29 Dec 2010 15:54:14 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/29/t1293634454140pcdauav1h8p6.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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1203.6 1180.59 1156.85 1191.5 1191.33 1234.18 1220.33 1228.81 1207.01 1249.48 1248.29 1280.08 1280.66 1294.87 1310.61 1270.09 1270.2 1276.66 1303.82 1335.85 1377.94 1400.63 1418.3 1438.24 1406.82 1420.86 1482.37 1530.62 1503.35 1455.27 1473.99 1526.75 1549.38 1481.14 1468.36 1378.55 1330.63 1322.7 1385.59 1400.38 1280 1267.38 1282.83 1166.36 968.75 896.24 903.25 825.88 735.09 797.87 872.81 919.14 919.32 987.48 1020.62 1057.08 1036.19 1095.63 1115.1 1073.87 1104.49 1169.43 1186.69 1089.41 1030.71 1101.6 1049.33 1141.2 1183.26 1180.55 1258.51

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 0.880784068307055 beta 0.325933142551067 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 1280.66 1238.63548611111 42.0245138888886 14 1294.87 1302.99669224229 -8.12669224229035 15 1310.61 1318.73919752580 -8.12919752579592 16 1270.09 1274.04787617265 -3.95787617265250 17 1270.2 1272.56270743747 -2.36270743747036 18 1276.66 1277.86217627737 -1.20217627736838 19 1303.82 1340.40662231881 -36.5866223188066 20 1335.85 1312.43517784914 23.4148221508581 21 1377.94 1310.55806673631 67.3819332636856 22 1400.63 1432.50735429539 -31.8773542953923 23 1418.3 1417.33981311675 0.960186883245115 24 1438.24 1465.85528568432 -27.6152856843210 25 1406.82 1454.88172323066 -48.0617232306638 26 1420.86 1412.05304816230 8.80695183769808 27 1482.37 1425.70685768183 56.6631423181725 28 1530.62 1440.17797631246 90.4420236875412 29 1503.35 1550.72600984363 -47.3760098436339 30 1455.27 1532.29166657928 -77.0216665792802 31 1473.99 1517.84594697256 -43.8559469725567 32 1526.75 1482.54689457201 44.2031054279855 33 1549.38 1502.11115376134 47.2688462386632 34 1481.14 1586.62766868982 -105.487668689824 35 1468.36 1481.52408826425 -13.1640882642473 36 1378.55 1481.12171701672 -102.571717016718 37 1330.63 1347.10118082660 -16.4711808265965 38 1322.7 1293.35651147351 29.3434885264926 39 1385.59 1291.17926441455 94.410735585451 40 1400.38 1314.13676661469 86.2432333853064 41 1280 1374.56301631379 -94.5630163137935 42 1267.38 1267.49313296416 -0.113132964160968 43 1282.83 1303.28001419461 -20.4500141946085 44 1166.36 1284.35278240748 -117.992782407479 45 968.75 1100.11851537379 -131.368515373786 46 896.24 896.495992805839 -0.255992805838673 47 903.25 812.707716781773 90.5422832182269 48 825.88 840.38361559463 -14.5036155946297 49 735.09 766.873081373722 -31.7830813737218 50 797.87 673.384547949578 124.485452050422 51 872.81 758.35769732047 114.452302679530 52 919.14 799.341081717129 119.798918282871 53 919.32 878.748000075884 40.5719999241163 54 987.48 951.73727557845 35.7427244215505 55 1020.62 1076.74878504942 -56.1287850494206 56 1057.08 1064.59290438213 -7.5129043821255 57 1036.19 1057.61445030328 -21.4244503032776 58 1095.63 1079.56348868425 16.0665113157465 59 1115.1 1138.76610474689 -23.6661047468924 60 1073.87 1138.32905037208 -64.4590503720758 61 1104.49 1089.42065523164 15.0693447683632 62 1169.43 1139.94100967898 29.4889903210180 63 1186.69 1196.88772374292 -10.1977237429192 64 1089.41 1149.77567784805 -60.3656778480515 65 1030.71 1030.38724351940 0.322756480596581 66 1101.6 1025.13114344029 76.4688565597071 67 1049.33 1144.53380145161 -95.2038014516133 68 1141.2 1062.01229664913 79.1877033508651 69 1183.26 1112.88484496628 70.3751550337245 70 1180.55 1229.65752895741 -49.1075289574128 71 1258.51 1217.50767400608 41.0023259939153 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 72 1278.51972123817 1158.64773732680 1398.39170514955 73 1323.72492226307 1139.42203667217 1508.02780785396 74 1386.22347115656 1132.48129476882 1639.96564754430 75 1427.53184292444 1098.91300279457 1756.15068305431 76 1401.41487848404 992.572931141358 1810.25682582671 77 1377.75408871093 883.549967144932 1871.95821027693 78 1416.52237125285 832.042513665965 2001.00222883974 79 1461.38476746588 781.931205696032 2140.83832923573 80 1524.11669958567 745.189575881188 2303.04382329016 81 1522.06763777814 639.346785817512 2404.78848973876 82 1560.28395184179 569.611709285632 2550.95619439795 83 1613.90056957250 511.266420211566 2716.53471893344

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293634454140pcdauav1h8p6/19njy1293631863.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293634454140pcdauav1h8p6/19njy1293631863.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293634454140pcdauav1h8p6/29njy1293631863.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293634454140pcdauav1h8p6/29njy1293631863.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293634454140pcdauav1h8p6/39njy1293631863.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293634454140pcdauav1h8p6/39njy1293631863.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

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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