*The author of this computation has been verified*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 29 Dec 2010 14:09:04 +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/Dec/29/t1293631630zq2qc1w4xwbo4mi.htm/, Retrieved Wed, 29 Dec 2010 15:07:10 +0100

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/Dec/29/t1293631630zq2qc1w4xwbo4mi.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:

Dataseries X:

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3106.54 3125.67 3039.71 3051.67 3112.83 3228.01 3223.98 3328.8 3264.26 3394.14 3549.25 3744.63 3839.25 3912.28 3911.06 3675.8 3703.32 3795.91 3906.01 4070.78 4144.38 4140.3 4388.53 4433.57 4305.23 4471.65 4614.76 4697.86 4639.4 4384.47 4350.83 4325.29 4441.82 4162.5 4127.47 3722.23 3757.12 3719.52 3925.43 3751.41 3168.22 2994.38 3136 2672.2 2100.18 1881.46 1908.64 1900.09 1696.58 1748.74 1953.35 2071.37 2030.98 2169.14 2229.85 2480.93 2525.93 2475.14 2529.66 2453.37 2386.53 2517.3 2457.46 2589.73 2679.07 2506.13 2592.31

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 1 beta 0 gamma 0.486860364521044 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 3839.25 3450.75455176768 388.495448232321 14 3912.28 3852.94625 59.3337499999998 15 3911.06 3843.4725 67.5875000000001 16 3675.8 3608.03833333333 67.7616666666668 17 3703.32 3637.26 66.059999999999 18 3795.91 3732.23416666667 63.6758333333341 19 3906.01 3894.05291666667 11.9570833333337 20 4070.78 3947.525 123.255000000001 21 4144.38 3937.15833333333 207.221666666666 22 4140.3 4211.94833333333 -71.6483333333335 23 4388.53 4244.80083333333 143.729166666666 24 4433.57 4535.64375 -102.073750000000 25 4305.23 4476.10958333333 -170.879583333333 26 4471.65 4318.92625 152.72375 27 4614.76 4402.8425 211.917500000001 28 4697.86 4311.73833333333 386.121666666666 29 4639.4 4659.32 -19.920000000001 30 4384.47 4668.31416666667 -283.844166666665 31 4350.83 4482.61291666667 -131.782916666667 32 4325.29 4392.345 -67.0549999999994 33 4441.82 4191.66833333333 250.151666666666 34 4162.5 4509.38833333333 -346.888333333333 35 4127.47 4267.00083333333 -139.530833333333 36 3722.23 4274.58375 -552.35375 37 3757.12 3764.76958333333 -7.6495833333338 38 3719.52 3770.81625 -51.2962500000003 39 3925.43 3650.7125 274.717500000001 40 3751.41 3622.40833333333 129.001666666667 41 3168.22 3712.87 -544.650000000001 42 2994.38 3197.13416666667 -202.754166666665 43 3136 3092.52291666667 43.4770833333332 44 2672.2 3177.515 -505.315 45 2100.18 2538.57833333333 -438.398333333334 46 1881.46 2167.74833333333 -286.288333333333 47 1908.64 1985.96083333333 -77.3208333333334 48 1900.09 2055.75375 -155.66375 49 1696.58 1942.62958333333 -246.049583333333 50 1748.74 1710.27625 38.4637499999997 51 1953.35 1679.9325 273.417500000000 52 2071.37 1650.32833333333 421.041666666667 53 2030.98 2032.83 -1.85000000000082 54 2169.14 2059.89416666667 109.245833333334 55 2229.85 2267.28291666667 -37.4329166666666 56 2480.93 2271.365 209.565000000001 57 2525.93 2347.30833333333 178.621666666666 58 2475.14 2593.49833333333 -118.358333333334 59 2529.66 2579.64083333333 -49.9808333333335 60 2453.37 2676.77375 -223.403749999999 61 2386.53 2495.90958333333 -109.379583333333 62 2517.3 2400.22625 117.073750000000 63 2457.46 2448.4925 8.96750000000065 64 2589.73 2154.43833333333 435.291666666667 65 2679.07 2551.19 127.879999999999 66 2506.13 2707.98416666667 -201.854166666666 67 2592.31 2604.27291666667 -11.9629166666668 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 68 2633.825 2183.29492664018 3084.35507335982 69 2500.20333333333 1863.05759333093 3137.34907333573 70 2567.77166666667 1787.43068926973 3348.11264406361 71 2672.2725 1771.21235328036 3573.33264671964 72 2819.38625 1811.97038005948 3826.80211994052 73 2861.92583333333 1758.35703982311 3965.49462684356 74 2875.62208333333 1683.63155106757 4067.6126155991 75 2806.81458333333 1532.52310332853 4081.10606333813 76 2503.79291666667 1152.20269658721 3855.38313674612 77 2465.25291666667 1040.55173044689 3889.95410288644 78 2494.16708333333 999.927873227522 3988.40629343914 79 2592.31 1031.62804520612 4152.99195479388

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293631630zq2qc1w4xwbo4mi/1o3491293631740.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293631630zq2qc1w4xwbo4mi/1o3491293631740.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293631630zq2qc1w4xwbo4mi/2zulc1293631740.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293631630zq2qc1w4xwbo4mi/2zulc1293631740.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293631630zq2qc1w4xwbo4mi/3zulc1293631740.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/29/t1293631630zq2qc1w4xwbo4mi/3zulc1293631740.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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=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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