Home » date » 2010 » Dec » 08 »

*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, 08 Dec 2010 12:37:55 +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/08/t1291811752vrrijl2f30tgovj.htm/, Retrieved Wed, 08 Dec 2010 13:35:59 +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/08/t1291811752vrrijl2f30tgovj.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:
» Textbox « » Textfile « » CSV «
1145.11 1176.86 1206.41 1192.72 1214.82 1199.07 1157.47 1100.1 1095.63 1105.63 1137.79 1124.72 1152.6 1211.85 1239.62 1244.13 1198.42 1227.99 1304.92 1340.26 1307.32 1356.51 1383.29 1437.87 1494.56 1521.42 1498.76 1488.75 1524.62 1439.27 1423.11 1466.85 1425.83 1363.45 1389.18 1395.89 1368.43 1349.03 1299.88 1365.41 1451.04 1433.75 1464.65 1475.57 1471.16 1429.12 1452.46 1538.09 1631.59 1665.5 1690.6 1711.74 1734.1 1748.09 1703.45 1745.74 1751.01 1795.65 1852.13 1877.1 1989.31 2097.76 2154.87 2152.18 2250.27 2346.9 2525.56 2409.36 2394.36 2401.33 2354.32 2450.41 2504.67 2661.39 2880.4 3064.42 3141.12 3327.7 3564.95 3403.13 3149.9 3006.84 3230.66 3361.13 3484.74 3411.13 3288.18 3280.37 3173.95 3165.26 3092.71 3053.05 3181.96 2999.93 3249.57 3210.52 3030.29 2803.47 2767.63 2882.6 2863.36 2897.06 3012.61 3142.95 3032.93 3045.78 3110.52 3013.24 2987.1 2995.55 2833.18 2848.96 2794.83 2845.26 2915.02 2 etc...
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time15 seconds
R Server'George Udny Yule' @ 72.249.76.132


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gamma0.145692113538071


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131152.61138.4260603632514.1739396367516
141211.851205.695438519816.15456148018666
151239.621230.788771853158.83122814685294
161244.131234.852105186489.27789481351965
171198.421187.7333551864810.6866448135202
181227.991214.7087718531513.2812281468528
191304.921283.1433551864821.7766448135201
201340.261255.7758551864884.4841448135198
211307.321342.94418851981-35.6241885198135
221356.511323.7900218531532.719978146853
231383.291397.20710518648-13.9171051864801
241437.871379.6941885198158.1758114801864
251494.561468.3971051864826.1628948135199
261521.421547.65543851981-26.2354385198132
271498.761540.35877185315-41.5987718531471
281488.751493.99210518648-5.24210518648056
291524.621432.3533551864892.26664481352
301439.271540.90877185315-101.638771853147
311423.111494.42335518648-71.3133551864801
321466.851373.9658551864892.88414481352
331425.831469.53418851981-43.7041885198134
341363.451442.30002185315-78.850021853147
351389.181404.14710518648-14.96710518648
361395.891385.5841885198110.3058114801865
371368.431426.41710518648-57.9871051864802
381349.031421.52543851981-72.4954385198134
391299.881367.96877185315-68.0887718531469
401365.411295.1121051864870.2978948135194
411451.041309.01335518648142.02664481352
421433.751467.32877185315-33.5787718531471
431464.651488.90335518648-24.2533551864799
441475.571415.5058551864860.0641448135198
451471.161478.25418851981-7.09418851981331
461429.121487.63002185315-58.5100218531472
471452.461469.81710518648-17.3571051864799
481538.091448.8641885198189.2258114801864
491631.591568.6171051864862.9728948135198
501665.51684.68543851981-19.1854385198133
511690.61684.438771853156.16122814685286
521711.741685.8321051864825.9078948135195
531734.11655.3433551864878.75664481352
541748.091750.38877185315-2.29877185314717
551703.451803.24335518648-99.7933551864799
561745.741654.3058551864891.4341448135199
571751.011748.424188519812.58581148018652
581795.651767.4800218531528.1699781468531
591852.131836.3471051864815.78289481352
601877.11848.5341885198128.5658114801863
611989.311907.6271051864881.6828948135199
622097.762042.4054385198155.3545614801869
632154.872116.6987718531538.1712281468526
642152.182150.102105186482.07789481351938
652250.272095.78335518648154.486644813520
662346.92266.5587718531580.3412281468532
672525.562402.05335518648123.50664481352
682409.362476.41585518648-67.0558551864801
692394.362412.04418851981-17.6841885198132
702401.332410.83002185315-9.50002185314725
712354.322442.02710518648-87.70710518648
722450.412350.7241885198199.6858114801862
732504.672480.9371051864823.7328948135200
742661.392557.76543851981103.624561480186
752880.42680.32877185315200.071228146853
763064.422875.63210518648188.787894813519
773141.123008.02335518648133.09664481352
783327.73157.40877185315170.291228146853
793564.953382.85335518648182.09664481352
803403.133515.80585518648-112.67585518648
813149.93405.81418851981-255.914188519813
823006.843166.37002185315-159.530021853147
833230.663047.53710518648183.122894813519
843361.133227.06418851981134.065811480187
853484.743391.6571051864893.0828948135195
863411.133537.83543851981-126.705438519813
873288.183430.06877185315-141.888771853147
883280.373283.41210518648-3.04210518648051
893173.953223.97335518648-50.0233551864799
903165.263190.23877185315-24.9787718531466
913092.713220.41335518648-127.703355186480
923053.053043.565855186489.48414481351983
933181.963055.73418851981126.225811480187
942999.933198.43002185315-198.500021853147
953249.573040.62710518648208.94289481352
963210.523245.97418851981-35.4541885198137
973030.293241.04710518648-210.757105186480
982803.473083.38543851981-279.915438519814
992767.632822.40877185315-54.7787718531467
1002882.62762.86210518648119.737894813519
1012863.362826.2033551864837.1566448135204
1022897.062879.6487718531517.4112281468529
1033012.612952.2133551864860.3966448135202
1043142.952963.46585518648179.484144813519
1053032.933145.63418851981-112.704188519813
1063045.783049.40002185315-3.62002185314668
1073110.523086.4771051864824.0428948135195
1083013.243106.92418851981-93.6841885198137
1092987.13043.76710518648-56.6671051864801
1102995.553040.19543851981-44.6454385198131
1112833.183014.48877185315-181.308771853147
1122848.962828.4121051864820.5478948135196
1132794.832792.563355186482.26664481352009
1142845.262811.1187718531534.1412281468533
1152915.022900.4133551864814.6066448135198
1162892.632865.8758551864826.7541448135198
1172604.422895.31418851981-290.894188519813
1182641.652620.8900218531520.7599781468530
1192659.812682.34710518648-22.5371051864804
1202638.532656.21418851981-17.6841885198132
1212720.252669.0571051864851.1928948135196
1222745.882773.34543851981-27.4654385198132
1232735.72764.81877185315-29.1187718531473
1242811.72730.9321051864880.7678948135194
1252799.432755.3033551864844.1266448135202
1262555.282815.71877185315-260.438771853147
1272304.982610.43335518648-305.45335518648
1282214.952255.83585518648-40.8858551864805
1292065.812217.63418851981-151.824188519813
1301940.492082.28002185315-141.790021853147
13120421981.1871051864860.8128948135197
1321995.372038.40418851981-43.0341885198136
1331946.812025.89710518648-79.0871051864801
1341765.91999.90543851981-234.005438519813
1351635.251784.83877185315-149.588771853147
1361833.421630.48210518648202.937894813520
1371910.431777.02335518648133.406644813520
1381959.671926.7187718531532.9512281468531
1391969.62014.82335518648-45.2233551864801
1402061.411920.45585518648140.954144813520
1412093.482064.0941885198129.3858114801869
1422120.882109.9500218531510.9299781468530
1432174.562161.5771051864812.9828948135196
1442196.722170.9641885198125.7558114801864
1452350.442227.24710518648123.19289481352
1462440.252403.5354385198136.7145614801866
1472408.642459.18877185315-50.5487718531472
1482472.812403.8721051864868.9378948135195
1492407.62416.41335518648-8.81335518647984
1502454.622423.8887718531530.731228146853
1512448.052509.77335518648-61.7233551864797
1522497.842398.9058551864898.9341448135197
1532645.642500.52418851981145.115811480186
1542756.762662.1100218531594.6499781468533
1552849.272797.4571051864851.8128948135195
1562921.442845.6741885198175.7658114801866
1572981.852951.9671051864829.8828948135197
1583080.583034.9454385198145.6345614801867
1593106.223099.518771853156.70122814685283
1603119.313101.4521051864817.8578948135196
1613061.263062.91335518648-1.65335518647953
1623097.313077.5487718531519.7612281468528
1633161.693152.463355186489.22664481352012
1643257.163112.54585518648144.614144813519
1653277.013259.8441885198117.1658114801871
1663295.323293.480021853151.8399781468529
1673363.993336.0171051864827.9728948135194
1683494.173360.39418851981133.775811480187
1693667.033524.69710518648142.33289481352
1703813.063720.1254385198192.9345614801864
1713917.963831.9987718531585.961228146853
1723895.513913.19210518648-17.6821051864804
1733801.063839.11335518648-38.0533551864801
1743570.123817.34877185315-247.228771853147
1753701.613625.2733551864876.3366448135203
1763862.273652.46585518648209.804144813520
1773970.13864.95418851981105.145811480187
1784138.523986.57002185315151.949978146853
1794199.754179.2171051864820.5328948135202
1804290.894196.1541885198194.7358114801864
1814443.914321.41710518648122.492894813519
1824502.644497.005438519815.63456148018759
1834356.984521.57877185315-164.598771853148
1844591.274352.21210518648239.05789481352
1854696.964534.87335518648162.086644813520
1864621.44713.24877185315-91.8487718531478
1874562.844676.55335518648-113.713355186479
1884202.524513.69585518648-311.175855186480
1894296.494205.2041885198191.2858114801857
1904435.234312.96002185315122.269978146853
1914105.184475.92710518648-370.747105186479
1924116.684101.5841885198115.0958114801861
1933844.494147.20710518648-302.717105186481
1943720.983897.58543851981-176.605438519813
1953674.43739.91877185315-65.518771853147
1963857.623669.63210518648187.987894813519
1973801.063801.22335518648-0.163355186479748
1983504.373817.34877185315-312.978771853147
1993032.63559.52335518648-526.92335518648
2003047.032983.4558551864863.57414481352
2012962.343049.71418851981-87.3741885198133
2022197.822978.81002185315-780.990021853147
2032014.452238.51710518648-224.067105186480
2041862.832010.85418851981-148.024188519814
2051905.411893.3571051864812.0528948135200
2061810.991958.50543851981-147.515438519813
2071670.071829.92877185315-159.858771853147
2081864.441665.30210518648199.137894813520
2092052.021808.04335518648243.97664481352
2102029.62068.30877185315-38.708771853147
2112070.832084.75335518648-13.9233551864800
2122293.412021.68585518648271.724144813520
2132443.272296.09418851981147.175811480187
2142513.172459.7400218531553.429978146853
2152466.922553.86710518648-86.9471051864803
2162502.662463.3241885198139.3358114801863


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
2172533.187105186482271.017388047292795.35682232567
2182586.282543706292215.518574084532957.04651332805
2192605.221315559442151.13004526843059.31258585048
2202600.453420745922076.113986467543124.7928550243
2212544.05677593241957.827466767283130.28608509752
2222560.345547785551918.163514784733202.52758078636
2232615.498902972031921.863030129583309.13477581447
2242566.354758158511824.826818914993307.88269740203
2252569.038946678321782.529795260753355.54809809589
2262585.508968531471756.455528849543414.56240821339
2272626.206073717951756.687490573653495.72465686225
2282622.610262237761714.427721655683530.79280281984
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/08/t1291811752vrrijl2f30tgovj/1c0ov1291811860.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/08/t1291811752vrrijl2f30tgovj/1c0ov1291811860.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/08/t1291811752vrrijl2f30tgovj/2c0ov1291811860.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/08/t1291811752vrrijl2f30tgovj/2c0ov1291811860.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/08/t1291811752vrrijl2f30tgovj/3c0ov1291811860.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/08/t1291811752vrrijl2f30tgovj/3c0ov1291811860.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

Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa


Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.


Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

  • personalize online software applications according to your needs
  • enforce strict security rules with respect to the data that you upload (e.g. statistical data)
  • manage user sessions of online applications
  • alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by