*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 17 May 2011 15:18:40 +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/17/t1305645283xg9gky6oxm6mxow.htm/, Retrieved Tue, 17 May 2011 17:14:47 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W101

Dataseries X:

» Textbox « » Textfile « » CSV «

41086 39690 43129 37863 35953 29133 24693 22205 21725 27192 21790 13253 37702 30364 32609 30212 29965 28352 25814 22414 20506 28806 22228 13971 36845 35338 35022 34777 26887 23970 22780 17351 21382 24561 17409 11514 31514 27071 29462 26105 22397 23843 21705 18089 20764 25316 17704 15548 28029 29383 36438 32034 22679 24319 18004 17537 20366 22782 19169 13807 29743 25591 29096 26482 22405 27044 17970 18730 19684 19785 18479 10698

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 3 seconds R Server 'George Udny Yule' @ 216.218.223.82 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.225679028753381 beta 0.00094149628695353 gamma 0.443442884267109 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 37702 41487.9961256582 -3785.99612565825 14 30364 32384.2423306442 -2020.24233064425 15 32609 34048.8239474299 -1439.82394742995 16 30212 30953.0817784332 -741.081778433225 17 29965 30167.1615625255 -202.161562525485 18 28352 28194.2876712476 157.712328752361 19 25814 22076.5443444744 3737.45565552559 20 22414 20801.9207532685 1612.07924673147 21 20506 21128.7820231163 -622.782023116299 22 28806 26754.5259191581 2051.47408084186 23 22228 22076.0673309998 151.932669000234 24 13971 13470.8643970093 500.135602990666 25 36845 37059.4733194597 -214.473319459685 26 35338 29795.4839704095 5542.51602959053 27 35022 33348.7244194935 1673.27558050646 28 34777 31163.7441308335 3613.25586916654 29 26887 31542.0186569764 -4655.01865697637 30 23970 28668.3449958547 -4698.34499585466 31 22780 22752.2259942229 27.7740057771371 32 17351 20061.3545527706 -2710.35455277056 33 21382 18709.042530073 2672.95746992701 34 24561 25498.9960342697 -937.996034269712 35 17409 20022.1189854636 -2613.11898546363 36 11514 11945.6711210862 -431.671121086232 37 31514 31811.1427395255 -297.14273952548 38 27071 27135.2239715721 -64.2239715721189 39 29462 27863.024180442 1598.975819558 40 26105 26585.9480635962 -480.948063596174 41 22397 23768.4474504742 -1371.44745047418 42 23843 21869.5638551779 1973.43614482211 43 21705 19509.1082062669 2195.89179373314 44 18089 16761.2809759647 1327.71902403528 45 20764 18040.7422278911 2723.25777210893 46 25316 23196.8285072111 2119.17149278885 47 17704 18102.3007276653 -398.300727665312 48 15548 11461.2235378706 4086.77646212937 49 28029 33585.8002125519 -5556.80021255188 50 29383 27714.0486189832 1668.95138101676 51 36438 29460.2103780262 6977.78962197377 52 32034 28524.1330124552 3509.8669875448 53 22679 25984.1070779224 -3305.1070779224 54 24319 24768.3603312258 -449.360331225813 55 18004 21738.5190502803 -3734.51905028026 56 17537 17326.1475284396 210.852471560382 57 20366 18790.723856743 1575.27614325702 58 22782 23364.3485694359 -582.348569435911 59 19169 17096.1467294074 2072.85327059258 60 13807 12536.4463062609 1270.55369373915 61 29743 29375.0615334885 367.938466511536 62 25591 27375.1673514976 -1784.16735149756 63 29096 29845.1799392545 -749.179939254514 64 26482 26329.5061513019 152.493848698105 65 22405 21403.1889229496 1001.81107705045 66 27044 22062.6515825358 4981.3484174642 67 17970 19291.1739870878 -1321.17398708778 68 18730 16843.7925925221 1886.20740747787 69 19684 19125.9670975998 558.032902400162 70 19785 22648.0790967229 -2863.07909672288 71 18479 16985.5773885734 1493.42261142662 72 10698 12280.7803828333 -1582.7803828333 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 26498.9818651467 23698.8806723079 29299.0830579855 74 23934.8633943198 20956.2883634246 26913.4384252151 75 26836.6936186301 23556.4925784439 30116.8946588164 76 24042.2333148082 20686.841609158 27397.6250204585 77 19769.0075844741 16442.3106804056 23095.7044885427 78 21288.4567562006 17662.4973863156 24914.4161260857 79 16072.1766150477 12656.4439047002 19487.9093253952 80 15124.8889897848 11597.6008055938 18652.1771739758 81 16273.7807682905 12429.5244948396 20118.0370417413 82 18070.9265236946 13805.6598493799 22336.1931980093 83 15008.4341904263 11001.7108928535 19015.157487999 84 9842.62588615847 7798.83392099744 11886.4178513195

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/17/t1305645283xg9gky6oxm6mxow/1ityd1305645516.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/17/t1305645283xg9gky6oxm6mxow/1ityd1305645516.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/17/t1305645283xg9gky6oxm6mxow/2y5al1305645516.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/17/t1305645283xg9gky6oxm6mxow/2y5al1305645516.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/17/t1305645283xg9gky6oxm6mxow/3jkke1305645516.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/17/t1305645283xg9gky6oxm6mxow/3jkke1305645516.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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