Martin Horemans - Opgave 10 - Oef 2

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 02 Jun 2009 12:29:46 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/02/t12439675011xpk655z9xsc1ni.htm/, Retrieved Tue, 02 Jun 2009 20:31:44 +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/2009/Jun/02/t12439675011xpk655z9xsc1ni.htm/}, year = {2009}, } @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 = {2009}, 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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1746 1271 1363 1664 2179 2305 2098 2231 1407 1966 2293 2045 1532 1333 1583 1712 2641 2267 2126 2231 1517 2010 2628 2115 1829 1636 1787 2122 2620 2555 2337 2524 1801 2417 2389 2267 2135 1760 1905 2176 2344 2674 2766 2783 2000 2588 2736 2704 2466 1976 2171 2397 2942 2707 2861 2765 1814 2611 2606 2518 2267 1730 1901 2124 2448 2489 2521 2466 1827 2278 2373 2356 2075 1606 1699 2311 2093 2064 2180 2136

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 1 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.279673175984277 beta 0.105814685840969 gamma 0.78536497988161 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 1532 1461.32451923077 70.6754807692303 14 1333 1292.14960396448 40.8503960355224 15 1583 1561.42565325019 21.5743467498050 16 1712 1703.11583634011 8.88416365989133 17 2641 2632.14482937862 8.8551706213807 18 2267 2257.34443625948 9.65556374052358 19 2126 2204.84530050069 -78.8453005006945 20 2231 2333.67820292190 -102.678202921904 21 1517 1477.72373809470 39.2762619052953 22 2010 2046.21578582993 -36.2157858299286 23 2628 2350.43964656270 277.560353437296 24 2115 2179.21560048522 -64.2156004852159 25 1829 1703.57144991363 125.428550086370 26 1636 1540.23909556032 95.7609044396831 27 1787 1822.99452763994 -35.9945276399433 28 2122 1948.72871381541 173.271286184586 29 2620 2935.90432526461 -315.904325264612 30 2555 2473.30778251156 81.6922174884371 31 2337 2395.59809608675 -58.59809608675 32 2524 2521.91943884728 2.08056115272302 33 1801 1783.97835235479 17.0216476452104 34 2417 2311.28922691044 105.710773089564 35 2389 2844.66568156603 -455.665681566025 36 2267 2265.28020063706 1.71979936293701 37 2135 1907.56458843248 227.435411567518 38 1760 1751.19878443253 8.80121556746508 39 1905 1927.74539989475 -22.7453998947549 40 2176 2168.61093155192 7.38906844808389 41 2344 2820.78870880933 -476.788708809333 42 2674 2521.49522099752 152.504779002478 43 2766 2369.69054082385 396.309459176148 44 2783 2656.49233463977 126.507665360232 45 2000 1964.41278510354 35.5872148964602 46 2588 2550.24868591158 37.7513140884166 47 2736 2748.18552767517 -12.1855276751658 48 2704 2565.85397137374 138.14602862626 49 2466 2392.29471768894 73.7052823110639 50 1976 2083.00957052961 -107.009570529613 51 2171 2219.65370142218 -48.653701422184 52 2397 2479.88753334324 -82.8875333432361 53 2942 2839.80347393924 102.196526060758 54 2707 3082.46931401563 -375.469314015630 55 2861 2929.33399331702 -68.3339933170246 56 2765 2928.20941041026 -163.209410410261 57 1814 2089.74860599598 -275.748605995978 58 2611 2566.60328441252 44.3967155874766 59 2606 2715.21186676898 -109.211866768981 60 2518 2564.98222464364 -46.9822246436352 61 2267 2271.90567319405 -4.90567319405318 62 1730 1804.78835867401 -74.7883586740134 63 1901 1950.79760594561 -49.7976059456057 64 2124 2158.65157818861 -34.6515781886083 65 2448 2605.49775285329 -157.497752853291 66 2489 2466.35821387092 22.6417861290806 67 2521 2571.14683632024 -50.1468363202389 68 2466 2494.80458474976 -28.8045847497588 69 1827 1607.61384605312 219.386153946877 70 2278 2396.05591370195 -118.055913701951 71 2373 2399.52298152739 -26.5229815273888 72 2356 2297.26227090758 58.7377290924205 73 2075 2050.32345397171 24.6765460282932 74 1606 1545.58811496899 60.4118850310088 75 1699 1741.19066886177 -42.1906688617651 76 2311 1957.60928603307 353.390713966933 77 2093 2452.83633609464 -359.836336094642 78 2064 2362.38098007643 -298.380980076427 79 2180 2330.07442315643 -150.074423156432 80 2136 2228.76584063650 -92.7658406365035 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 81 1453.10735371171 1135.99658362481 1770.2181237986 82 1971.81721176882 1639.88752183333 2303.74690170431 83 2046.0987618704 1697.20886461394 2394.98865912686 84 1986.28981850676 1618.3551782775 2354.22445873603 85 1688.71666093899 1299.73250802994 2077.70081384805 86 1181.62796535169 769.683053326427 1593.57287737696 87 1284.8347077243 848.117576845865 1721.55183860273 88 1720.63361476536 1257.43329986197 2183.83392966875 89 1686.87486483945 1195.57782286799 2178.17190681090 90 1715.80592397974 1194.89063095480 2236.72121700469 91 1843.66192850033 1291.69223383100 2395.63162316966 92 1814.00044837101 1229.61844799555 2398.38244874647

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439675011xpk655z9xsc1ni/163y81243967384.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439675011xpk655z9xsc1ni/163y81243967384.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439675011xpk655z9xsc1ni/2kan31243967384.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439675011xpk655z9xsc1ni/2kan31243967384.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439675011xpk655z9xsc1ni/3tdv51243967384.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439675011xpk655z9xsc1ni/3tdv51243967384.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=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')

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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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