Datareeks-exponential smoothing gokuitgaven per maand-sam dejonghe

*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 14:37:00 +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/t1305815674ex6mrylvmlw4lg0.htm/, Retrieved Thu, 19 May 2011 16:34:47 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

5.81 5.76 5.99 6.12 6.03 6.25 5.80 5.67 5.89 5.91 5.86 6.07 6.27 6.68 6.77 6.71 6.62 6.50 5.89 6.05 6.43 6.47 6.62 6.77 6.70 6.95 6.73 7.07 7.28 7.32 6.76 6.93 6.99 7.16 7.28 7.08 7.34 7.87 6.28 6.30 6.36 6.28 5.89 6.04 5.96 6.10 6.26 6.02 6.25 6.41 6.22 6.57 6.18 6.26 6.10 6.02 6.06 6.35 6.21 6.48 6.74 6.53 6.80 6.75 6.56 6.66 6.18 6.40 6.43 6.54 6.44 6.64 6.82 6.97 7.00 6.91 6.74 6.98 6.37 6.56 6.63 6.87 6.68 6.75 6.84 7.15 7.09 6.97 7.15

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 'Herman Ole Andreas Wold' @ www.yougetit.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.747355048775388 beta 0.0237084331610309 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 5.99 5.71 0.28 4 6.12 5.87422062647912 0.245779373520885 5 6.03 6.01722116562715 0.012778834372849 6 6.25 5.9863139987503 0.263686001249696 7 5.8 6.14759572113559 -0.347595721135595 8 5.67 5.84587404654151 -0.175874046541509 9 5.89 5.66937318752962 0.220626812470379 10 5.91 5.793108449383 0.116891550617004 11 5.86 5.84138779619602 0.0186122038039809 12 6.07 5.81654735949283 0.253452640507168 13 6.27 5.9717069391373 0.298293060862697 14 6.68 6.16566357388893 0.514336426111071 15 6.77 6.53019463867066 0.239805361329338 16 6.71 6.69380254554713 0.0161974544528691 17 6.62 6.69058295076879 -0.0705829507687863 18 6.5 6.62125694972623 -0.121256949726231 19 5.89 6.51191097424355 -0.62191097424355 20 6.05 6.01737928334969 0.0326207166503059 21 6.43 6.01259315022067 0.417406849779331 22 6.47 6.30277474858123 0.167225251418769 23 6.62 6.40894486651598 0.21105513348402 24 6.77 6.55161107322225 0.21838892677775 25 6.7 6.70362777717224 -0.00362777717224194 26 6.95 6.68965489731766 0.260345102682343 27 6.73 6.87757643718208 -0.147576437182083 28 7.07 6.75802090432327 0.311979095676734 29 7.28 6.98744435731654 0.29255564268346 30 7.32 7.20753527609932 0.112464723900678 31 6.76 7.2950270568849 -0.535027056884906 32 6.93 6.88913264663575 0.0408673533642459 33 6.99 6.91435994443894 0.0756400555610552 34 7.16 6.96691503397958 0.19308496602042 35 7.28 7.11066436890913 0.169335631090873 36 7.08 7.23966491170327 -0.159664911703271 37 7.34 7.1199561963362 0.220043803663798 38 7.87 7.2879235783918 0.582076421608201 39 6.28 7.73677145459763 -1.45677145459763 40 6.3 6.6360641010529 -0.336064101052899 41 6.36 6.3669684552111 -0.00696845521109868 42 6.28 6.34370063042866 -0.0637006304286558 43 5.89 6.27690504098203 -0.386905040982032 44 6.04 5.96170558119966 0.0782944188003416 45 5.96 5.99556255521052 -0.0355625552105243 46 6.1 5.94369782555289 0.15630217444711 47 6.26 6.03799362868672 0.222006371313278 48 6.02 6.18532744098824 -0.165327440988238 49 6.25 6.04025599946173 0.209744000538274 50 6.41 6.17921246707155 0.230787532928451 51 6.22 6.33798516081268 -0.117985160812681 52 6.57 6.23401028710914 0.335989712890864 53 6.18 6.47526910039816 -0.295269100398162 54 6.26 6.2395216923244 0.020478307675603 55 6.1 6.24011255110735 -0.14011255110735 56 6.02 6.1182024201307 -0.098202420130697 57 6.06 6.02587402604177 0.0341259739582327 58 6.35 6.03304659044141 0.316953409558588 59 6.21 6.25720764291018 -0.0472076429101804 60 6.48 6.2083746400944 0.271625359905596 61 6.74 6.40263591742902 0.337364082570978 62 6.53 6.652004986091 -0.122004986090999 63 6.8 6.55590050238954 0.244099497610455 64 6.75 6.73773115852379 0.0122688414762138 65 6.56 6.74651939024106 -0.18651939024106 66 6.66 6.60343736766724 0.0565626323327626 67 6.18 6.64302613356184 -0.463026133561836 68 6.4 6.28609342915402 0.113906570845978 69 6.43 6.36235256111685 0.067647438883145 70 6.54 6.40523831633088 0.134761683669121 71 6.44 6.5006700319195 -0.0606700319195008 72 6.64 6.44896987909974 0.191030120900264 73 6.82 6.58876389585736 0.231236104142642 74 6.97 6.76270324119923 0.207296758800766 75 7 6.92242440785592 0.0775755921440808 76 6.91 6.98657233790162 -0.0765723379016245 77 6.74 6.93416027822437 -0.194160278224367 78 6.98 6.79042802602234 0.189571973977659 79 6.37 6.93683896312427 -0.566838963124274 80 6.56 6.50789876482035 0.0521012351796468 81 6.63 6.54244981045182 0.087550189548181 82 6.87 6.60504507940069 0.264954920599312 83 6.68 6.8049193045963 -0.124919304596299 84 6.75 6.71120566186286 0.0387943381371354 85 6.84 6.74053161860748 0.0994683813925157 86 7.15 6.81696507008416 0.333034929915841 87 7.09 7.07385657926934 0.0161434207306641 88 6.97 7.09420365824349 -0.12420365824349 89 7.15 7.00746092208751 0.142539077912489 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 90 7.1225953118825 6.57055317959621 7.67463744416878 91 7.13120240215179 6.43612507824346 7.82627972606012 92 7.13980949242109 6.32135206668633 7.95826691815585 93 7.14841658269038 6.21827568858537 8.0785574767954 94 7.15702367295968 6.12300606472916 8.1910412811902 95 7.16563076322897 6.03330797181561 8.29795355464234 96 7.17423785349827 5.94776286197276 8.40071284502378 97 7.18284494376756 5.86540736677891 8.50028252075622 98 7.19145203403686 5.78555415378108 8.59734991429264 99 7.20005912430616 5.70769405547871 8.6924241931336 100 7.20866621457545 5.63143856182887 8.78589386732204 101 7.21727330484475 5.55648406114611 8.87806254854339

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/19/t1305815674ex6mrylvmlw4lg0/126ej1305815818.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305815674ex6mrylvmlw4lg0/126ej1305815818.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305815674ex6mrylvmlw4lg0/2wght1305815818.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305815674ex6mrylvmlw4lg0/2wght1305815818.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305815674ex6mrylvmlw4lg0/33fs81305815818.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305815674ex6mrylvmlw4lg0/33fs81305815818.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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