*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 15:14:42 +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/t1305817834qes68n6oyk2jauj.htm/, Retrieved Thu, 19 May 2011 17:10:34 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

7989 41102 9123 22109 47115 9105 5496 23102 6994 84101 5884 6383 6292 36109 49127 26116 63120 60115 77117 18110 3999 79105 2286 7487 7789 3788 83108 52100 93102 598 8983 3488 2780 7974 9171 3071 4166 7968 6580 7183 2779 5273 1568 1860 9853 6757 6745 5144 9444 2248 7349 8149 7949 3545 1043 4038 4335 5432 8027 8626 24 4829 931 232 9034 1337 5138 9736 7730 7133 8126 424

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 0.130272576604942 beta 0 gamma 0.756196503879971 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 6292 3969.89518223453 2322.10481776547 14 36109 24218.9941513265 11890.0058486735 15 49127 37503.2804385287 11623.7195614713 16 26116 22073.2566650677 4042.74333493228 17 63120 57952.2485069266 5167.75149307344 18 60115 58656.1857239198 1458.81427608016 19 77117 9000.85779641506 68116.142203585 20 18110 77741.508506714 -59631.508506714 21 3999 20338.4378290079 -16339.4378290079 22 79105 208355.093671417 -129250.093671417 23 2286 13327.3391535333 -11041.3391535333 24 7487 12001.2948668556 -4514.29486685558 25 7789 13376.7178792542 -5587.71787925417 26 3788 66467.1031031926 -62679.1031031926 27 83108 75982.2971036828 7125.70289631725 28 52100 39835.9983689874 12264.0016310126 29 93102 98687.992310571 -5585.992310571 30 598 92585.4502551047 -91987.4502551047 31 8983 42059.566646475 -33076.566646475 32 3488 20870.6444833256 -17382.6444833256 33 2780 5119.41688566289 -2339.41688566289 34 7974 75784.64362913 -67810.64362913 35 9171 3311.83712660538 5859.16287339462 36 3071 7850.61766997836 -4779.61766997836 37 4166 8163.82272799007 -3997.82272799007 38 7968 16670.7621802862 -8702.7621802862 39 6580 73579.1865338919 -66999.1865338919 40 7183 38136.3750859982 -30953.3750859982 41 2779 66325.4788897944 -63546.4788897944 42 5273 14475.6405510821 -9202.64055108208 43 1568 11966.8807954418 -10398.8807954418 44 1860 5432.85327309944 -3572.85327309944 45 9853 2452.37968369345 7400.62031630655 46 6757 26344.8634434983 -19587.8634434983 47 6745 6841.41442528839 -96.414425288388 48 5144 3841.18647505779 1302.81352494221 49 9444 5262.20340381263 4181.79659618737 50 2248 12136.3145672137 -9888.3145672137 51 7349 25980.0288444426 -18631.0288444426 52 8149 17335.7305034508 -9186.73050345076 53 7949 21665.7055815168 -13716.7055815168 54 3545 9551.71632794744 -6006.71632794744 55 1043 5120.4980987671 -4077.4980987671 56 4038 3450.25478430826 587.745215691737 57 4335 7901.08376871055 -3566.08376871055 58 5432 10890.7115911266 -5458.7115911266 59 8027 6341.70765262741 1685.29234737259 60 8626 4526.40615707874 4099.59384292126 61 24 8050.75015126546 -8026.75015126546 62 4829 4006.12339519448 822.876604805523 63 931 11822.1852087524 -10891.1852087524 64 232 10015.9619410109 -9783.96194101088 65 9034 10302.9809753101 -1268.98097531013 66 1337 4914.04300285116 -3577.04300285116 67 5138 1971.26444616337 3166.73555383663 68 9736 4743.13717922673 4992.86282077327 69 7730 7372.833264847 357.166735153004 70 7133 10141.4695586494 -3008.46955864941 71 8126 10818.5795433004 -2692.5795433004 72 424 9370.53568691316 -8946.53568691316 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 2094.44494119407 -41922.1561158906 46111.0459982788 74 5464.74013895725 -42242.7136658137 53172.1939437282 75 4300.82807973095 -42235.2046981596 50836.8608576215 76 3474.69829651008 -42464.3498660451 49413.7464590653 77 14041.2414442036 -59580.2743967862 87662.7572851935 78 3445.71919191919 -42801.5278714583 49692.9662552966 79 5970.33200457656 -45610.0213395986 57550.6853487517 80 10111.1696160544 -53516.7422450605 73739.0814771693 81 8826.03055893003 -50364.075373105 68016.1364909651 82 9285.47075522608 -51059.5295925545 69630.4711030067 83 10689.7387909515 -53767.0074406361 75146.4850225392 84 3240.56676757367 -10861.7437579791 17342.8772931264

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/19/t1305817834qes68n6oyk2jauj/11jnw1305818078.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305817834qes68n6oyk2jauj/11jnw1305818078.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305817834qes68n6oyk2jauj/2kmj51305818078.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305817834qes68n6oyk2jauj/2kmj51305818078.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305817834qes68n6oyk2jauj/3wsfi1305818078.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305817834qes68n6oyk2jauj/3wsfi1305818078.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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