Exponential Smoothing Wisselkoers

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 18 May 2011 12:52:56 +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/18/t13057230432jbjxcg74d6l8go.htm/, Retrieved Wed, 18 May 2011 14:50:46 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

1,2638 1,2640 1,2261 1,1989 1,2000 1,2146 1,2266 1,2191 1,2224 1,2507 1,2997 1,3406 1,3123 1,3013 1,3185 1,2943 1,2697 1,2155 1,2041 1,2295 1,2234 1,2022 1,1789 1,1861 1,2126 1,1940 1,2028 1,2273 1,2767 1,2661 1,2681 1,2810 1,2722 1,2617 1,2888 1,3205 1,2993 1,3080 1,3246 1,3513 1,3518 1,3421 1,3726 1,3626 1,3910 1,4233 1,4683 1,4559 1,4728 1,4759 1,5520 1,5754 1,5554 1,5562 1,5759 1,4955 1,4342 1,3266 1,2744 1,3511 1,3244 1,2797 1,3050 1,3199 1,3646 1,4014 1,4092 1,4266 1,4575 1,4821 1,4908 1,4579 1,4266 1,3680 1,3570 1,3417 1,2563 1,2223 1,2811 1,2903 1,3103 1,3901 1,3654 1,3221

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' @ www.wessa.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 1.2261 1.2642 -0.0381 4 1.1989 1.2263 -0.0273999999999999 5 1.2 1.1991 0.000899999999999901 6 1.2146 1.2002 0.0144 7 1.2266 1.2148 0.0118 8 1.2191 1.2268 -0.00769999999999982 9 1.2224 1.2193 0.00309999999999988 10 1.2507 1.2226 0.0281 11 1.2997 1.2509 0.0488000000000002 12 1.3406 1.2999 0.0407 13 1.3123 1.3408 -0.0285 14 1.3013 1.3125 -0.0112000000000001 15 1.3185 1.3015 0.0170000000000001 16 1.2943 1.3187 -0.0244 17 1.2697 1.2945 -0.0247999999999999 18 1.2155 1.2699 -0.0544 19 1.2041 1.2157 -0.0116000000000001 20 1.2295 1.2043 0.0252000000000001 21 1.2234 1.2297 -0.00629999999999997 22 1.2022 1.2236 -0.0214000000000001 23 1.1789 1.2024 -0.0234999999999999 24 1.1861 1.1791 0.0069999999999999 25 1.2126 1.1863 0.0263 26 1.194 1.2128 -0.0187999999999999 27 1.2028 1.1942 0.00860000000000016 28 1.2273 1.203 0.0243 29 1.2767 1.2275 0.0491999999999999 30 1.2661 1.2769 -0.0107999999999999 31 1.2681 1.2663 0.00180000000000002 32 1.281 1.2683 0.0126999999999999 33 1.2722 1.2812 -0.0089999999999999 34 1.2617 1.2724 -0.0106999999999999 35 1.2888 1.2619 0.0268999999999999 36 1.3205 1.289 0.0315000000000001 37 1.2993 1.3207 -0.0214000000000001 38 1.308 1.2995 0.00850000000000017 39 1.3246 1.3082 0.0164 40 1.3513 1.3248 0.0265 41 1.3518 1.3515 0.000299999999999967 42 1.3421 1.352 -0.0098999999999998 43 1.3726 1.3423 0.0303 44 1.3626 1.3728 -0.0102 45 1.391 1.3628 0.0282 46 1.4233 1.3912 0.0321 47 1.4683 1.4235 0.0448 48 1.4559 1.4685 -0.0125999999999999 49 1.4728 1.4561 0.0167000000000002 50 1.4759 1.473 0.0028999999999999 51 1.552 1.4761 0.0759000000000001 52 1.5754 1.5522 0.0231999999999999 53 1.5554 1.5756 -0.0202 54 1.5562 1.5556 0.000600000000000156 55 1.5759 1.5564 0.0195000000000001 56 1.4955 1.5761 -0.0806 57 1.4342 1.4957 -0.0615000000000001 58 1.3266 1.4344 -0.1078 59 1.2744 1.3268 -0.0524 60 1.3511 1.2746 0.0765 61 1.3244 1.3513 -0.0268999999999999 62 1.2797 1.3246 -0.0448999999999999 63 1.305 1.2799 0.0250999999999999 64 1.3199 1.3052 0.0147000000000002 65 1.3646 1.3201 0.0445 66 1.4014 1.3648 0.0366 67 1.4092 1.4016 0.00760000000000005 68 1.4266 1.4094 0.0172000000000001 69 1.4575 1.4268 0.0306999999999999 70 1.4821 1.4577 0.0244 71 1.4908 1.4823 0.00849999999999995 72 1.4579 1.491 -0.0330999999999999 73 1.4266 1.4581 -0.0314999999999999 74 1.368 1.4268 -0.0588 75 1.357 1.3682 -0.0112000000000001 76 1.3417 1.3572 -0.0155000000000001 77 1.2563 1.3419 -0.0855999999999999 78 1.2223 1.2565 -0.0342 79 1.2811 1.2225 0.0586 80 1.2903 1.2813 0.00900000000000012 81 1.3103 1.2905 0.0198 82 1.3901 1.3105 0.0795999999999999 83 1.3654 1.3903 -0.0248999999999999 84 1.3221 1.3656 -0.0434999999999999 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 1.3223 1.25290875043269 1.39169124956731 86 1.3225 1.22436595375189 1.42063404624811 87 1.3227 1.20251083014873 1.44288916985127 88 1.3229 1.18411750086538 1.46168249913462 89 1.3231 1.16793644892384 1.47826355107616 90 1.3233 1.15332684594596 1.49327315405404 91 1.3235 1.13990801048088 1.50709198951912 92 1.3237 1.12743190750378 1.51996809249622 93 1.3239 1.11572625129807 1.53207374870193 94 1.3241 1.10466560168212 1.54353439831788 95 1.3243 1.09415526145132 1.55444473854868 96 1.3245 1.08412166029745 1.56487833970255

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/18/t13057230432jbjxcg74d6l8go/1l8mu1305723174.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t13057230432jbjxcg74d6l8go/1l8mu1305723174.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t13057230432jbjxcg74d6l8go/2fdz11305723174.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t13057230432jbjxcg74d6l8go/2fdz11305723174.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t13057230432jbjxcg74d6l8go/3d0gs1305723174.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t13057230432jbjxcg74d6l8go/3d0gs1305723174.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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