Triple exponential smoothing - USA huisprijzen - Yannick Geerts

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 02 Jun 2010 09:07:40 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jun/02/t1275469744h7yb2d6cxt1s6se.htm/, Retrieved Wed, 02 Jun 2010 11:09:08 +0200

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Jun/02/t1275469744h7yb2d6cxt1s6se.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

178600 181600 178500 176700 183500 175900 179800 186500 182700 182800 178600 183300 182900 191400 189300 192200 187900 193900 189100 193100 194800 200200 211500 202100 200300 199200 204900 207300 200000 197700 202200 200200 208300 215100 210700 208100 209000 211000 210200 205500 211400 211700 209300 207500 203300 207100 206900 228700 226900 265000 227100 228100 226500 225200 217800 221300 215300 231300 227100 237800 230200 233400 231100 237200 243700 239700 248400 241000 254500 242800 268300 253900 262100 264100 261000 269300 260400 263200 279200 272200 269200 289600 283200 284300 283000 289100 289600 289100 287400 279600 289300 295000 299600 293600 294400 290200 301000 307900 298800 310300 293900 305000 311300 317300 296200 306800 291800 301900 314600 321500 329400 311700 309700 306500 307100 301300 292200 310100 316800 284400 284600 301200 287600 314300 298200 299400 301900 265500 etc...

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 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.458431564192018 beta 0 gamma 0.181610953212879 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 182900 176965.155579880 5934.84442012027 14 191400 188445.349798312 2954.65020168756 15 189300 187997.306510601 1302.69348939907 16 192200 191306.444594224 893.555405775842 17 187900 186404.032890278 1495.96710972194 18 193900 191965.68801862 1934.31198137999 19 189100 192094.375243636 -2994.37524363567 20 193100 198267.566327154 -5167.56632715376 21 194800 192056.088728708 2743.91127129228 22 200200 193310.959446464 6889.04055353641 23 211500 192109.284489929 19390.7155100714 24 202100 206287.940775720 -4187.9407757204 25 200300 204369.896168068 -4069.89616806776 26 199200 211879.599998405 -12679.5999984053 27 204900 203847.199872669 1052.80012733137 28 207300 207133.913531152 166.086468847760 29 2e+05 201451.743538031 -1451.74353803066 30 197700 205983.873525062 -8283.87352506205 31 202200 200833.002757067 1366.99724293308 32 200200 209147.760854121 -8947.76085412118 33 208300 201776.102796220 6523.89720377969 34 215100 205122.714065893 9977.28593410732 35 210700 206211.987778346 4488.01222165412 36 208100 211286.821834192 -3186.82183419238 37 209000 209806.216977001 -806.216977001139 38 211000 218199.445553946 -7199.44555394645 39 210200 213934.779083474 -3734.77908347431 40 205500 215002.296545961 -9502.29654596126 41 211400 204613.535989314 6786.46401068577 42 211700 212357.148924390 -657.148924390378 43 209300 211574.596376989 -2274.59637698889 44 207500 217435.390967366 -9935.39096736582 45 203300 211003.170770206 -7703.17077020579 46 207100 208142.069715966 -1042.06971596589 47 206900 203707.827582774 3192.1724172261 48 228700 207410.803144618 21289.1968553815 49 226900 217354.899634915 9545.10036508532 50 265000 230270.869124007 34729.1308759932 51 227100 245313.692234208 -18213.6922342077 52 228100 239290.855097122 -11190.8550971222 53 226500 229081.595426891 -2581.59542689088 54 225200 232065.152869932 -6865.152869932 55 217800 228142.047851911 -10342.0478519109 56 221300 229845.229287021 -8545.22928702127 57 215300 224076.663401462 -8776.6634014617 58 231300 221395.809843861 9904.19015613873 59 227100 221989.007231999 5110.99276800075 60 237800 228521.564834521 9278.43516547879 61 230200 231661.132096924 -1461.13209692389 62 233400 242150.644114789 -8750.64411478877 63 231100 232321.415878742 -1221.41587874194 64 237200 234726.928633717 2473.07136628326 65 243700 231563.774266804 12136.2257331958 66 239700 240975.883431095 -1275.88343109511 67 248400 239135.666356938 9264.33364306192 68 241000 250512.630073953 -9512.63007395333 69 254500 243987.000816995 10512.9991830052 70 242800 252250.820802007 -9450.82080200658 71 268300 242989.103899339 25310.8961006614 72 253900 259642.715979594 -5742.71597959386 73 262100 254519.419234319 7580.5807656812 74 264100 269522.054232833 -5422.05423283263 75 261000 261190.57480932 -190.574809320009 76 269300 264719.276164265 4580.72383573541 77 260400 262870.43460679 -2470.43460678984 78 263200 264412.595223461 -1212.59522346064 79 279200 263496.920991561 15703.0790084389 80 272200 276416.950694722 -4216.95069472247 81 269200 274117.190944808 -4917.19094480819 82 289600 273363.620580620 16236.3794193803 83 283200 278818.008015629 4381.99198437115 84 284300 282904.150626815 1395.84937318455 85 283000 282118.236810350 881.763189650315 86 289100 293608.791797489 -4508.79179748870 87 289600 285611.008200384 3988.99179961625 88 289100 291826.345180788 -2726.34518078784 89 287400 285437.609176044 1962.39082395629 90 279600 289301.819961965 -9701.81996196514 91 289300 286134.363994055 3165.63600594504 92 295000 291496.96899198 3503.03100801975 93 299600 292559.853277554 7040.14672244573 94 293600 299548.963460424 -5948.96346042375 95 294400 293449.270544507 950.729455492808 96 290200 295701.405161618 -5501.40516161849 97 301000 291618.665833493 9381.33416650724 98 307900 306918.809861528 981.190138471895 99 298800 301927.448016464 -3127.4480164643 100 310300 304335.944196178 5964.055803822 101 293900 302061.557556553 -8161.5575565531 102 305000 300153.764376167 4846.23562383285 103 311300 305016.956893982 6283.04310601793 104 317300 312040.330381487 5259.66961851279 105 296200 314158.891597974 -17958.8915979736 106 306800 308449.967021670 -1649.96702166955 107 291800 304854.911626939 -13054.9116269391 108 301900 300049.341412819 1850.65858718136 109 314600 300754.870559267 13845.1294407328 110 321500 317589.516217238 3910.48378276231 111 329400 313268.151595155 16131.8484048450 112 311700 325644.926006498 -13944.9260064982 113 309700 312563.644983304 -2863.64498330437 114 306500 314455.793152962 -7955.79315296229 115 307100 313631.033810826 -6531.03381082579 116 301300 314695.890035702 -13395.8900357022 117 292200 306005.737167801 -13805.7371678005 118 310100 303759.177799010 6340.82220099046 119 316800 302694.055091098 14105.9449089023 120 284400 311867.546794029 -27467.5467940287 121 284600 300284.482903393 -15684.4829033932 122 301200 302182.366317398 -982.366317397682 123 287600 297122.015972044 -9522.01597204432 124 314300 294666.787746325 19633.2122536746 125 298200 298364.205412652 -164.205412652169 126 299400 300916.429426254 -1516.42942625372 127 301900 303117.26724659 -1217.26724659029 128 265500 305861.502323839 -40361.5023238392 129 287100 284977.367973402 2122.63202659832 130 274000 291801.285710803 -17801.2857108031 131 290100 280733.013106238 9366.98689376237 132 263100 283739.576001709 -20639.5760017087 133 245200 276325.894226481 -31125.8942264812 134 258600 271633.909418633 -13033.9094186330 135 259800 260972.012121791 -1172.0121217907 136 269800 264761.880251737 5038.11974826292 137 274600 260865.933516035 13734.0664839647 138 274800 269504.669443312 5295.33055668755 139 271100 274681.365786238 -3581.36578623787 140 257800 272415.507552164 -14615.5075521643 141 290300 267465.020165797 22834.9798342034 142 262200 281694.041620673 -19494.0416206730 143 270000 272550.080019718 -2550.08001971780 144 290600 267344.138091802 23255.861908198 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 145 278851.652072713 266969.162478297 290734.141667129 146 290965.791206565 275324.750422770 306606.83199036 147 286985.703436384 268722.894252073 305248.512620694 148 292315.461143935 271390.176525797 313240.745762074 149 286339.199557518 263646.250254348 309032.148860689 150 287878.024990257 263133.060148915 312622.989831598 151 289798.848287068 263125.288177991 316472.408396145 152 287878.767987302 259706.456534833 316051.07943977 153 293610.987214270 263379.898151688 323842.076276851 154 293073.160486438 261445.854646713 324700.466326164 155 294564.959400048 261415.384454246 327714.534345851 156 292751.610929177 260609.419203813 324893.80265454

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/02/t1275469744h7yb2d6cxt1s6se/1bmb51275469657.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275469744h7yb2d6cxt1s6se/1bmb51275469657.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275469744h7yb2d6cxt1s6se/24vaq1275469657.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275469744h7yb2d6cxt1s6se/24vaq1275469657.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275469744h7yb2d6cxt1s6se/34vaq1275469657.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275469744h7yb2d6cxt1s6se/34vaq1275469657.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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