double

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 05 May 2008 07:14:57 -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/May/05/t1209993322z8wmwn1k9cixfth.htm/, Retrieved Mon, 05 May 2008 15:15:22 +0200

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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 3 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.580952155663673 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 53536 53152 384 4 52408 53375.0856277749 -967.085627774853 5 41454 52813.2551476077 -11359.2551476077 6 38271 46214.0713828713 -7943.07138287133 7 35306 41599.5269404018 -6293.5269404018 8 26414 37943.288897648 -11529.2888976480 9 31917 31245.3236592901 671.676340709866 10 38030 31635.5354773338 6394.46452266618 11 27534 35350.4134260916 -7816.41342609162 12 18387 30809.4511966452 -12422.4511966452 13 50556 23592.6013953274 26963.3986046726 14 43901 39257.0459387308 4643.95406126919 15 48572 41954.9610614282 6617.03893857179 16 43899 45799.1440969020 -1900.14409690195 17 37532 44695.2512877352 -7163.25128773516 18 40357 40533.7450105648 -176.745010564839 19 35489 40431.0646156744 -4942.0646156744 20 29027 37559.9615237692 -8532.9615237692 21 34485 32602.7191323403 1882.28086765969 22 42598 33696.2342599717 8901.7657400283 23 30306 38867.7342558542 -8561.73425585416 24 26451 33893.7762836962 -7442.77628369618 25 47460 29569.8793575604 17890.1206424396 26 50104 39963.1835098689 10140.8164901311 27 61465 45854.5127100003 15610.4872899997 28 53726 54923.458952086 -1197.45895208598 29 39477 54227.7925925529 -14750.7925925529 30 43895 45658.2878381615 -1763.28783816154 31 31481 44633.9019675261 -13152.9019675261 32 29896 36992.6952162588 -7096.69521625883 33 33842 32869.8548322852 972.145167714807 34 39120 33434.6246630871 5685.37533691287 35 33702 36737.5557208237 -3035.55572082374 36 25094 34974.043081174 -9880.043081174 37 51442 29234.210755116 22207.789244884 38 45594 42135.8737894559 3458.12621054411 39 52518 44144.8796660285 8373.12033397146 40 48564 49009.2619736806 -445.261973680586 41 41745 48750.5860702358 -7005.58607023579 42 49585 44680.6757410449 4904.32425895509 43 32747 47529.8534913585 -14782.8534913585 44 33379 38941.7228886935 -5562.72288869353 45 35645 35710.0470351474 -65.0470351473705 46 37034 35672.257819859 1361.74218014102 47 35681 36463.3648748701 -782.36487487005 48 20972 36008.8483142988 -15036.8483142988 49 58552 27273.1588717192 31278.8411282808 50 54955 45444.6690518555 9510.33094814451 51 65540 50969.716317255 14570.2836827450 52 51570 59434.354031377 -7864.35403137694 53 51145 54865.5406039462 -3720.54060394621 54 46641 52704.0845198494 -6063.08451984944 55 35704 49181.7224980719 -13477.7224980719 56 33253 41351.8105593802 -8098.81055938023 57 35193 36646.7891065966 -1453.78910659657 58 41668 35802.2071912389 5865.79280876107 59 34865 39209.9521681651 -4344.95216816515 60 21210 36685.7428398141 -15475.7428398141 61 56126 27695.0766765274 28430.9233234726 62 49231 44212.0828688074 5018.91713119259 63 59723 47127.8335952711 12595.1664047289 64 48103 54445.022669041 -6342.02266904102 65 47472 50760.6109281938 -3288.61092819376 66 50497 48850.0853203205 1646.91467967952 67 40059 49806.8639536744 -9747.86395367444 68 34149 44143.8213766711 -9994.82137667106 69 36860 38337.3083524207 -1477.30835242065 70 46356 37479.0628805019 8876.93711949808 71 36577 42636.1386357652 -6059.1386357652 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 72 39116.0689838524 18610.5722258014 59621.5657419033 73 39116.0689838524 15401.3453408626 62830.7926268422 74 39116.0689838524 12577.4021440822 65654.7358236226 75 39116.0689838524 10026.3189367781 68205.8190309267 76 39116.0689838524 7681.59303832086 70550.5449293839 77 39116.0689838524 5500.01629857804 72732.1216691267 78 39116.0689838524 3451.63686573112 74780.5011019736 79 39116.0689838524 1514.68019996542 76717.4577677393 80 39116.0689838524 -327.272135352519 78559.4101030572 81 39116.0689838524 -2086.96341444204 80319.1013821468 82 39116.0689838524 -3774.51971557958 82006.6576832843 83 39116.0689838524 -5398.14581493723 83630.283782642

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/05/t1209993322z8wmwn1k9cixfth/1leoi1209993291.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/05/t1209993322z8wmwn1k9cixfth/1leoi1209993291.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/05/t1209993322z8wmwn1k9cixfth/26xro1209993291.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/05/t1209993322z8wmwn1k9cixfth/26xro1209993291.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/05/t1209993322z8wmwn1k9cixfth/3y6cy1209993291.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/05/t1209993322z8wmwn1k9cixfth/3y6cy1209993291.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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