*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 17 Jan 2011 00:36:45 +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/Jan/17/t12952244751yji5ybo7rbcwfb.htm/, Retrieved Mon, 17 Jan 2011 01:34:38 +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/2011/Jan/17/t12952244751yji5ybo7rbcwfb.htm/}, year = {2011}, } @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 = {2011}, 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:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

1590 1798 1935 1887 2027 2080 1556 1682 1785 1869 1781 2082 2571 1862 1938 1505 1767 1607 1578 1495 1615 1700 1337 1531 1623 1543 1640 1524 1429 1827 1603 1351 1267 1742 1384 1392 1649 1665 1526 1717 1391 1790 1472 1350 1704 1391 1190 1351 1160 1236 1444 1257 1193 1701 1428 1611 1431 1472 1240 1276

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 1 seconds R Server 'Gwilym Jenkins' @ www.wessa.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.164888600957893 beta 0 gamma 0.935831558446131 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 2571 2727.36765770059 -156.367657700595 14 1862 1947.59613217641 -85.5961321764082 15 1938 2011.76874730217 -73.7687473021747 16 1505 1551.61727961216 -46.617279612163 17 1767 1822.83793193396 -55.8379319339645 18 1607 1674.0136952126 -67.0136952125954 19 1578 1469.81426637944 108.185733620563 20 1495 1557.69931261097 -62.6993126109683 21 1615 1624.878224738 -9.87822473800361 22 1700 1697.99840673963 2.00159326036805 23 1337 1626.18292959689 -289.182929596887 24 1531 1857.66913594275 -326.66913594275 25 1623 2127.0337177642 -504.033717764204 26 1543 1486.62386340662 56.3761365933808 27 1640 1562.48061526506 77.519384734936 28 1524 1226.45824506152 297.541754938476 29 1429 1502.8230712347 -73.8230712347004 30 1827 1363.14446839862 463.855531601378 31 1603 1386.97522905345 216.024770946554 32 1351 1363.54571120616 -12.5457112061647 33 1267 1468.06451244961 -201.064512449613 34 1742 1507.79397411524 234.20602588476 35 1384 1266.37601317584 117.623986824156 36 1392 1515.30572956633 -123.305729566333 37 1649 1657.14366050572 -8.1436605057172 38 1665 1535.83739880696 129.162601193041 39 1526 1640.84089407702 -114.840894077023 40 1717 1437.5603679682 279.4396320318 41 1391 1421.02264991676 -30.0226499167643 42 1790 1686.08073425484 103.919265745155 43 1472 1465.54261688229 6.45738311770879 44 1350 1246.49527240177 103.504727598233 45 1704 1221.22122338486 482.778776615138 46 1391 1716.99787093542 -325.997870935421 47 1190 1304.43857637212 -114.438576372124 48 1351 1321.86323092729 29.1367690727109 49 1160 1564.97571868442 -404.975718684415 50 1236 1483.86560344915 -247.865603449155 51 1444 1346.85478673098 97.1452132690233 52 1257 1464.99408187112 -207.994081871118 53 1193 1172.34902459801 20.6509754019937 54 1701 1488.4625351671 212.537464832899 55 1428 1253.250997642 174.749002357998 56 1611 1153.58382086826 457.41617913174 57 1431 1438.69522909813 -7.69522909813213 58 1472 1243.30312460142 228.696875398582 59 1240 1102.68691746106 137.313082538945 60 1276 1264.09093857611 11.9090614238919 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 1157.25632836129 764.223469620714 1550.28918710186 62 1257.78117658554 857.598200073775 1657.9641530973 63 1431.67381321704 1021.52327289308 1841.824353541 64 1292.04092888945 879.900562583412 1704.18129519548 65 1211.11628185114 795.723883921102 1626.50867978118 66 1677.70612523804 1231.32306931772 2124.08918115836 67 1376.85871814492 942.52767929552 1811.18975699431 68 1444.72916648403 999.351495591984 1890.10683737607 69 1303.14915896263 861.528353882617 1744.76996404265 70 1288.30397275952 841.242726294637 1735.3652192244 71 1064.31959077632 628.922683579437 1499.71649797319 72 1097.47385209602 887.763111925516 1307.18459226653

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Jan/17/t12952244751yji5ybo7rbcwfb/16u8p1295224604.png (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/17/t12952244751yji5ybo7rbcwfb/16u8p1295224604.ps (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/17/t12952244751yji5ybo7rbcwfb/2sy3o1295224604.png (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/17/t12952244751yji5ybo7rbcwfb/2sy3o1295224604.ps (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/17/t12952244751yji5ybo7rbcwfb/3xeku1295224604.png (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/17/t12952244751yji5ybo7rbcwfb/3xeku1295224604.ps (open in new window)

Parameters (Session):

par1 = 12 ;

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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