exponential smoothing double

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 29 Apr 2008 06:09:24 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Apr/29/t12094710117s6ilyidti6b0ya.htm/, Retrieved Tue, 29 Apr 2008 14:10:20 +0200

User-defined keywords:

exponential,smoothing,double

Dataseries X:

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56421 53152 53536 52408 41454 38271 35306 26414 31917 38030 27534 18387 50556 43901 48572 43899 37532 40357 35489 29027 34485 42598 30306 26451 47460 50104 61465 53726 39477 43895 31481 29896 33842 39120 33702 25094 51442 45594 52518 48564 41745 49585 32747 33379 35645 37034 35681 20972 58552 54955 65540 51570 51145 46641 35704 33253 35193 41668 34865 21210 56126 49231 59723 48103 47472 50497 40059 34149 36860 46356 36577

Text written by user:

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.580952155659036 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 53536 53152 384 4 52408 53375.0856277731 -967.085627773064 5 41454 52813.2551476114 -11359.2551476114 6 38271 46214.0713829256 -7943.07138292557 7 35306 41599.5269404614 -6293.52694046136 8 26414 37943.2888977021 -11529.2888977021 9 31917 31245.3236593663 671.676340633712 10 38030 31635.5354773626 6394.46452263738 11 27534 35350.413426074 -7816.41342607403 12 18387 30809.4511966741 -12422.4511966741 13 50556 23592.6013953971 26963.3986046029 14 43901 39257.045938635 4643.954061365 15 48572 41954.9610613665 6617.03893863347 16 43899 45799.1440968454 -1900.14409684543 17 37532 44695.2512877203 -7163.25128772028 18 40357 40533.7450105918 -176.745010591818 19 35489 40431.0646156865 -4942.06461568653 20 29027 37559.9615237972 -8532.9615237972 21 34485 32602.7191323916 1882.28086760840 22 42598 33696.2342599845 8901.76574001554 23 30306 38867.7342558182 -8561.73425581824 24 26451 33893.7762837208 -7442.77628372082 25 47460 29569.8793576053 17890.1206423947 26 50104 39963.1835098047 10140.8164901953 27 61465 45854.5127099264 15610.4872900736 28 53726 54923.4589519826 -1197.45895198263 29 39477 54227.7925925151 -14750.7925925151 30 43895 45658.2878382141 -1763.28783821412 31 31481 44633.9019675563 -13152.9019675563 32 29896 36992.6952163325 -7096.69521633247 33 33842 32869.854832349 972.14516765104 34 39120 33434.6246631093 5685.37533689065 35 33702 36737.5557208067 -3035.55572080669 36 25094 34974.0430811809 -9880.04308118093 37 51442 29234.2107551647 22207.7892448353 38 45594 42135.8737893733 3458.12621062667 39 52518 44144.8796659779 8373.1203340221 40 48564 49009.2619736206 -445.261973620552 41 41745 48750.5860702127 -7005.5860702127 42 49585 44680.6757410677 4904.32425893228 43 32747 47529.8534913453 -14782.8534913453 44 33379 38941.7228887566 -5562.72288875656 45 35645 35710.0470351996 -65.0470351995755 46 37034 35672.2578198812 1361.74218011885 47 35681 36463.3648748730 -782.364874873034 48 20972 36008.8483143036 -15036.8483143036 49 58552 27273.158871791 31278.841128209 50 54955 45444.6690517405 9510.33094825948 51 65540 50969.7163171627 14570.2836828373 52 51570 59434.3540312707 -7864.3540312707 53 51145 54865.5406039382 -3720.54060393816 54 46641 52704.0845198633 -6063.08451986332 55 35704 49181.7224981058 -13477.7224981058 56 33253 41351.8105594569 -8098.81055945695 57 35193 36646.7891066663 -1453.78910666627 58 41668 35802.2071912749 5865.79280872512 59 34865 39209.952168153 -4344.95216815301 60 21210 36685.7428398291 -15475.7428398291 61 56126 27695.0766766055 28430.9233233945 62 49231 44212.0828687083 5018.9171312917 63 59723 47127.8335952063 12595.1664047937 64 48103 54445.0226689555 -6342.02266895545 65 47472 50760.6109281873 -3288.61092818731 66 50497 48850.085320333 1646.91467966697 67 40059 49806.8639536721 -9747.86395367207 68 34149 44143.8213767153 -9994.82137671526 69 36860 38337.3083524855 -1477.30835248552 70 46356 37479.0628805360 8876.93711946404 71 36577 42636.1386357383 -6059.1386357383 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 72 39116.0689838692 18610.5722258184 59621.56574192 73 39116.0689838692 15401.3453409273 62830.792626811 74 39116.0689838692 12577.4021441846 65654.7358235538 75 39116.0689838692 10026.3189369119 68205.8190308264 76 39116.0689838692 7681.59303848207 70550.5449292563 77 39116.0689838692 5500.01629876361 72732.1216689748 78 39116.0689838692 3451.63686593878 74780.5011017996 79 39116.0689838692 1514.68020019341 76717.457767545 80 39116.0689838692 -327.272135105646 78559.410102844 81 39116.0689838692 -2086.96341417748 80319.1013819159 82 39116.0689838692 -3774.51971529832 82006.6576830367 83 39116.0689838692 -5398.14581464016 83630.2837823785

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/29/t12094710117s6ilyidti6b0ya/1zemy1209470962.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/29/t12094710117s6ilyidti6b0ya/1zemy1209470962.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/29/t12094710117s6ilyidti6b0ya/23qb51209470962.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/29/t12094710117s6ilyidti6b0ya/23qb51209470962.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/29/t12094710117s6ilyidti6b0ya/30q2i1209470962.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/29/t12094710117s6ilyidti6b0ya/30q2i1209470962.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=0, beta=0) if (par2 == 'Double') fit <- HoltWinters(x, gamma=0) 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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