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*Unverified author*
R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)
Title produced by software: Exponential Smoothing
Date of computation: Sat, 23 Jan 2010 08:32:33 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/23/t1264260844ckgkec0ulsc2yek.htm/, Retrieved Sat, 23 Jan 2010 16:34:09 +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/Jan/23/t1264260844ckgkec0ulsc2yek.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 «
8357,00 7454,00 8076,00 7248,00 7339,00 7292,00 7359,00 7537,00 7441,00 8057,00 8037,00 8257,00 8692,00 8119,00 8236,00 7432,00 7669,00 7453,00 7566,00 7731,00 7657,00 8130,00 8401,00 8737,00 9009,00 7919,00 8228,00 7903,00 7912,00 7857,00 7965,00 8091,00 8024,00 8772,00 8656,00 8953,00 9014,00 8103,00 8876,00 8231,00 8173,00 8087,00 8296,00 8007,00 8382,00 9168,00 9137,00 9321,00 9234,00 8451,00 9101,00 8279,00 8284,00 8225,00 8597,00 8305,00 8620,00 9102,00 9258,00 9652,00 9522,00 8874,00 9415,00 8525,00 8862,00 8421,00 8626,00 8750,00 8852,00 9412,00 9570,00 9513,00 9986,00 8907,00 9663,00 8799,00 8931,00 8732,00 8936,00 9127,00 9070,00 9773,00 9670,00 9929,00 10095,00 9025,00 9659,00 8954,00 9022,00 8855,00 9034,00 9196,00 9038,00 9650,00 9715,00 10052,00 10436,00 9314,00 9717,00 8997,00 9062,00 8885,00 9058,00 9095,00 9149,00 9857,00 9848,00 10269,00 10341,00 9690,00 10125,00 9349,00 9224,00 9 etc...
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.249369978113487
beta0.0512362761576963
gamma0.657312630987632


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1386928548.66232091143143.337679088572
1481198023.7000900971295.2999099028793
1582368169.481341624666.5186583754003
1674327397.8207346580934.1792653419134
1776697648.200480192620.7995198074041
1874537427.7149964385925.2850035614083
1975667598.44488785889-32.4448878588855
2077317755.71198879056-24.7119887905565
2176577639.8915740204117.1084259795907
2281308286.65203467525-156.652034675255
2384018227.36023747515173.63976252485
2487378500.49708831971236.502911680291
2590099097.23287630184-88.232876301845
2679198466.0280075195-547.028007519495
2782288436.35517880576-208.355178805758
2879037557.2685429604345.731457039593
2979127882.673097129629.3269028704008
3078577657.07585408722199.924145912775
3179657846.85190019147118.148099808531
3280918053.3112479479837.6887520520186
3380247971.7587042390252.2412957609777
3487728567.71744196488204.28255803512
3586568775.66001583302-119.660015833022
3689539021.29804052152-68.2980405215221
3790149395.4329276704-381.432927670394
3881038431.71485293299-328.714852932986
3988768631.76307605621244.236923943788
4082318113.69363333018117.306366669819
4181738230.70430729582-57.704307295824
4280878061.1694881666225.8305118333783
4382968168.18391119161127.816088808388
4480078339.84475650069-332.84475650069
4583828164.77055208496217.229447915038
4691688888.58196810876279.418031891239
4791378951.16601916727185.833980832735
4893219308.7225000796312.2774999203684
4992349556.16180007207-322.161800072066
5084518599.30506630544-148.305066305436
5191019155.87752096593-54.8775209659252
5282798476.48027346981-197.480273469810
5382848424.83301748166-140.833017481658
5482258268.26822296387-43.2682229638667
5585978405.81277949528191.187220504722
5683058357.46770846207-52.4677084620726
5786208527.1610826135392.8389173864725
5891029265.12395011131-163.123950111309
5992589161.3127090470596.687290952952
6096529403.46064217936248.539357820642
6195229537.57826164334-15.5782616433353
6288748721.12160883256152.878391167438
6394159419.8185948305-4.81859483049811
6485258658.58048560047-133.580485600472
6588628653.38448638428208.615513615725
6684218634.89050222635-213.890502226353
6786268860.340629945-234.340629945000
6887508578.15524642156171.844753578436
6988528886.37440435157-34.3744043515671
7094129485.42011074136-73.4201107413592
7195709535.6686796318234.3313203681846
7295139846.76492259804-333.764922598042
7399869697.67727031745288.322729682553
7489079018.45659956016-111.456599560161
7596639577.4192085312885.5807914687248
7687998754.2488934128944.7511065871131
7789318963.896244905-32.8962449050014
7887328665.9965981681366.0034018318693
7989368954.8953605796-18.8953605796105
8091278926.35282553768200.647174462321
8190709146.00299447824-76.0029944782418
8297739733.4652668806439.5347331193607
8396709870.94145799384-200.941457993844
8499299942.57289149-13.5728914899919
851009510190.7613141764-95.761314176405
8690259192.2698425214-167.269842521408
8796599848.39537533675-189.395375336746
8889548916.7797339732737.2202660267321
8990229083.2375842558-61.2375842557922
9088558817.872444757837.1275552421994
9190349054.47436459077-20.4743645907674
9291969128.1129712380667.8870287619357
9390389170.45919614657-132.459196146574
9496509795.18450790367-145.184507903668
9597159756.09127649013-41.0912764901295
96100529950.98278995913101.017210040869
971043610179.6998236911256.300176308887
9893149217.3900538639196.60994613609
9997179940.7449940658-223.744994065793
10089979097.570878582-100.570878582004
10190629180.17584585839-118.175845858388
10288858943.57199518728-58.5719951872779
10390589125.45346179411-67.4534617941099
10490959226.91280897517-131.912808975174
10591499112.8891681182436.1108318817569
10698579771.072030630685.9279693693952
10798489838.734598909869.26540109014059
1081026910117.2782594510151.721740549019
1091034110436.4725050627-95.4725050626876
11096909297.62395618912392.376043810884
111101259940.41776090334184.582239096660
11293499246.94836594103102.051634058973
11392249379.52310059401-155.523100594015
11492249163.1465887526360.8534112473735
11594549383.0404345587270.959565441277
11693479498.55958523773-151.559585237732
11794309470.8612575514-40.8612575514107
118993310165.8085450773-232.808545077309
1191014810120.169753590327.8302464097178
1201067710487.3872203150189.612779685043
1211073510703.301317953231.6986820468064
12297609811.31170663398-51.3117066339801
1231056710250.0906302738316.909369726232
12493339530.63742867883-197.637428678832
12594099458.3778133175-49.377813317491
12695029372.77647567843129.223524321573
12793489618.92803529406-270.928035294060
12893199534.5549359088-215.554935908796
12995949540.9522548854553.0477451145543
1301016010167.0173484601-7.01734846014915
1311018210307.2232652350-125.223265234954
1321081010718.008903327891.9910966721909
1331110510827.8014351240277.198564876016
13498749939.50382730206-65.5038273020637
1351095810563.0296290246394.970370975407
13693119590.0358574624-279.035857462410
13796109569.386997699340.6130023006936
13893989593.55671546348-195.556715463485
13997849555.61160341727228.388396582734
14094259624.00204125265-199.002041252646
14195579772.71324168863-215.713241688629
1421016610308.6708856380-142.670885637965
1431033710353.8566286324-16.8566286324203
1441077010903.6756264918-133.675626491780
1451126511043.8318408342221.168159165794
146101839960.36324991165222.636750088348
1471094110890.117923479450.8820765206365
14896289486.2460519468141.753948053205
14997099730.9513695131-21.9513695131027
15096379620.0530231193816.9469768806230
15195799849.27991346124-270.279913461243
15297419576.20786233132164.792137668685
15397549809.57950400727-55.579504007268
1541050810435.279700423372.720299576742
1551074910604.6353901295144.364609870532
1561107911158.4005351526-79.4005351526084
1571160811505.5818424813102.418157518663
1581066810365.7092055812302.290794418832
1591093311262.4383274395-329.438327439499
16097039778.82993137044-75.8299313704356
16197999890.20791095798-91.207910957979
16296569778.4844879191-122.484487919101
16396489828.15242422552-180.152424225518
16497129789.97724271547-77.9772427154749
16597669849.54577236036-83.545772360365
1661054010530.02353638029.9764636198106
1671056410712.8844517297-148.884451729693
1681091111070.9316303691-159.931630369090
1691121811472.6181496528-254.618149652755
1701023010342.1171907060-112.117190706040
1711041010788.3328955721-378.332895572081
17292279435.88250930809-208.882509308087
17393789481.01981363205-103.019813632045
17491059333.63238072211-228.632380722114
17591289303.32683566798-175.326835667978


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1769291.523923881039044.406646590659538.6412011714
1779342.447669865849080.188937881799604.70640184988
17810033.55356992229751.2784322242410315.8287076202
17910107.76157488769808.4331707251210407.0899790500
18010457.409673915710136.842993795810777.9763540356
18110813.358069475310469.751358651911156.9647802986
1829842.247412966369497.2763747170610187.2184512157
18310154.65711052649785.2511221685410524.0630988842
1849009.853561467588646.951179987859372.7559429473
1859148.114338467068763.313638243349532.91503869078
1868963.459597612788564.657803660929362.26139156465
1879012.447126844568672.885999507289352.00825418184
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Jan/23/t1264260844ckgkec0ulsc2yek/130t41264260749.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Jan/23/t1264260844ckgkec0ulsc2yek/130t41264260749.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Jan/23/t1264260844ckgkec0ulsc2yek/2742n1264260749.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Jan/23/t1264260844ckgkec0ulsc2yek/2742n1264260749.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Jan/23/t1264260844ckgkec0ulsc2yek/3gx8r1264260749.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Jan/23/t1264260844ckgkec0ulsc2yek/3gx8r1264260749.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')
 




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Software written by Ed van Stee & Patrick Wessa


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