Aantal bouwvergunningen in Vlaanderen-Wendy van Weelde-MAR202B

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 05 Jun 2009 03:09:23 -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/05/t1244193002yw36ruwho9tl01b.htm/, Retrieved Fri, 05 Jun 2009 11:10:02 +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/05/t1244193002yw36ruwho9tl01b.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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1528 1816 1420 1757 1544 1678 1655 1391 1403 1744 1266 1358 1596 1819 1416 1521 1638 1543 1623 1530 1336 1700 1615 1494 1578 1607 1767 1505 1938 1862 2571 2082 1781 1869 1785 1682 1556 2080 2027 1887 1935 1798 1590 1592 1387 1849 1470 1437 1500 2081 1552 1586 1914 1639 1633 1693 1224 1417 1577 1225 1510 1515 1393 1455 1532 1268 1365 1282 1063 1296 1639 1247 1515 1547 1299

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 0.341994826009028 beta 0 gamma 0.441083878543025 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 1596 1625.57291666667 -29.5729166666674 14 1819 1834.00079884334 -15.0007988433376 15 1416 1422.87060325291 -6.87060325291395 16 1521 1530.14589248886 -9.14589248885636 17 1638 1631.3097112451 6.69028875490062 18 1543 1518.38942205045 24.6105779495513 19 1623 1652.88944570762 -29.8894457076201 20 1530 1375.70907659000 154.290923409997 21 1336 1440.51744076304 -104.517440763044 22 1700 1755.77301679438 -55.7730167943778 23 1615 1264.61560028645 350.384399713548 24 1494 1478.15358543610 15.8464145639020 25 1578 1719.94820106751 -141.948201067513 26 1607 1894.17366293501 -287.173662935014 27 1767 1392.32142721807 374.678572781928 28 1505 1629.4241908755 -124.424190875499 29 1938 1695.75964960590 242.240350394098 30 1862 1668.59736639099 193.402633609013 31 2571 1845.00555954260 725.994440457398 32 2082 1879.78924533455 202.210754665452 33 1781 1885.87057554576 -104.870575545763 34 1869 2215.15274231588 -346.152742315884 35 1785 1742.56825250011 42.4317474998882 36 1682 1753.69323316395 -71.6932331639482 37 1556 1919.75214710064 -363.752147100644 38 2080 1975.97222623882 104.027773761181 39 2027 1800.00185531290 226.998144687097 40 1887 1841.74134935184 45.2586506481609 41 1935 2072.52651897017 -137.526518970166 42 1798 1901.31149345085 -103.311493450849 43 1590 2130.82202598402 -540.822025984016 44 1592 1580.34042830217 11.6595716978263 45 1387 1432.12834434283 -45.1283443428267 46 1849 1711.81340097912 137.186599020876 47 1470 1517.30946879319 -47.3094687931896 48 1437 1464.62029991883 -27.6202999188304 49 1500 1560.98607159841 -60.9860715984094 50 2081 1856.51690922318 224.483090776825 51 1552 1757.43199740569 -205.431997405693 52 1586 1598.53537199705 -12.5353719970512 53 1914 1756.50454450728 157.495455492719 54 1639 1696.11592197115 -57.115921971153 55 1633 1814.44402403782 -181.444024037822 56 1693 1547.21760211804 145.782397881960 57 1224 1428.39296301991 -204.392963019913 58 1417 1706.52460815152 -289.524608151518 59 1577 1312.54034717415 264.459652825853 60 1225 1372.18910006863 -147.189100068626 61 1510 1417.97903017788 92.0209698221165 62 1515 1848.69076203581 -333.690762035807 63 1393 1433.93667103901 -40.9366710390102 64 1455 1387.28203970624 67.7179602937615 65 1532 1622.04641448273 -90.046414482727 66 1268 1414.71191827773 -146.711918277729 67 1365 1466.31422751109 -101.314227511086 68 1282 1321.46449716409 -39.4644971640889 69 1063 1037.65306648560 25.3469335144041 70 1296 1369.64634416173 -73.6463441617313 71 1639 1210.27721722589 428.722782774113 72 1247 1206.62803964790 40.3719603521026 73 1515 1385.99013006081 129.009869939194 74 1547 1705.79522799096 -158.795227990956 75 1299 1435.82212716730 -136.822127167295 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 76 1387.91059440295 988.15704730923 1787.66414149667 77 1553.72695899882 1131.24202543981 1976.21189255783 78 1360.74153128029 916.687323153951 1804.79573940662 79 1475.69457778778 1011.07133210904 1940.31782346653 80 1383.44477486989 899.125271757116 1867.76427798266 81 1131.94057435205 628.695105653376 1635.18604305072 82 1426.53397101763 905.04895451563 1948.01898751963 83 1438.15685454201 899.049033131078 1977.26467595294 84 1175.17351834387 619.001005739384 1731.34603094836 85 1366.45447292564 793.72549299959 1939.18345285169 86 1558.60761374451 969.787518029801 2147.42770945922 87 1349.31903262688 744.836009053984 1953.80205619977

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244193002yw36ruwho9tl01b/145u81244192958.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244193002yw36ruwho9tl01b/145u81244192958.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244193002yw36ruwho9tl01b/2vk351244192958.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244193002yw36ruwho9tl01b/2vk351244192958.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244193002yw36ruwho9tl01b/3g9t61244192958.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244193002yw36ruwho9tl01b/3g9t61244192958.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')

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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