Home » date » 2010 » Jan » 20 »

KDGP2W61

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 20 Jan 2010 15:20:58 -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/20/t1264026122dibv7jhavo2fn9m.htm/, Retrieved Wed, 20 Jan 2010 23:22:07 +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/20/t1264026122dibv7jhavo2fn9m.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:

KDGP2W61

Dataseries X:

» Textbox « » Textfile « » CSV «

39690 43129 37863 35953 29133 24693 22205 21725 27192 21790 13253 37702 30364 32609 30212 29965 28352 25814 22414 20506 28806 22228 13971 36845 35338 35022 34777 26887 23970 22780 17351 21382 24561 17409 11514 31514 27071 29462 26105 22397 23843 21705 18089 20764 25316 17704 15548 28029 29383 36438 32034 22679 24319 18004 17537 20366 22782 19169 13807 29743 25591 29096 26482 22405 27044 17970 18730 19684 19785 18479 10698

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	5 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.562791973128805
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	43129	39690	3439
3	37863	41625.44159559	-3762.44159558996
4	35953	39507.969666226	-3554.96966622600
5	29133	37507.2612733576	-8374.26127335762
6	24693	32794.2942478285	-8101.29424782854
7	22205	28234.9508731961	-6029.95087319608
8	21725	24841.3429234003	-3116.3429234003
9	27192	23087.4901405939	4104.50985940614
10	21790	25397.4753430957	-3607.47534309568
11	13253	23367.2171767413	-10114.2171767413
12	37702	17675.0169351898	20026.9830648102
13	30364	28946.0422500515	1417.95774994849
14	32609	29744.0574899583	2864.9425100417
15	30212	31356.4241380853	-1144.42413808526
16	29965	30712.351419316	-747.351419316026
17	28352	30291.7480394185	-1939.74803941855
18	25814	29200.0734129415	-3386.07341294145
19	22414	27294.4184757131	-4880.41847571314
20	20506	24547.7581320723	-4041.75813207227
21	28806	22273.0890980139	6532.91090198608
22	22228	25949.7589148174	-3721.75891481735
23	13971	23855.1828716376	-9884.18287163757
24	36845	18292.4440905427	18552.5559094573
25	35338	28733.6736374087	6604.32636259134
26	35022	32450.535502198	2571.46449780198
27	34777	33897.7350807467	879.264919253328
28	26887	34392.5783195562	-7505.57831955619
29	23970	30168.4990876204	-6198.49908762038
30	22780	26680.0335556614	-3900.03355566141
31	17351	24485.1259756022	-7134.12597560218
32	21382	20470.0971412436	911.902858756432
33	24561	20983.3087504249	3577.6912495751
34	17409	22996.8046680189	-5587.80466801893
35	11514	19852.0330534462	-8338.03305344621
36	31514	15159.4549792840	16354.5450207160
37	27071	24363.6616411166	2707.33835888336
38	29462	25887.3299380399	3574.67006196009
39	26105	27899.1255554949	-1794.12555549489
40	22397	26889.4060940771	-4492.40609407711
41	23843	24361.1160042956	-518.116004295585
42	21705	24069.5244759285	-2364.52447592846
43	18089	22738.7890806093	-4649.78908060933
44	20764	20121.9251093004	642.074890699565
45	25316	20483.2797039337	4832.7202960663
46	17704	23203.0958949365	-5499.09589493648
47	15548	20108.2488658007	-4560.24886580067
48	28029	17541.7774086583	10487.2225913417
49	29383	23443.9021034805	5939.09789651952
50	36438	26786.3787272678	9651.62127273216
51	32034	32218.2337072407	-184.233707240717
52	22679	32114.5484556259	-9435.54845562588
53	24319	26804.2975227317	-2485.29752273174
54	18004	25405.5920261014	-7401.59202610142
55	17537	21240.0354454374	-3703.03544543737
56	20366	19155.9968205338	1210.00317946623
57	22782	19836.9768973977	2945.0231026023
58	19169	21494.4122602212	-2325.41226022116
59	13807	20185.6889059534	-6378.68890595338
60	29743	16595.8139905971	13147.1860094029
61	25591	23994.9447459204	1596.05525407964
62	29096	24893.1918315864	4202.80816841356
63	26482	27258.4985333698	-776.498533369762
64	22405	26821.4913916430	-4416.49139164297
65	27044	24335.9254870338	2708.07451296616
66	17970	25860.0080855659	-7890.00808556589
67	18730	21419.5748670880	-2689.57486708804
68	19684	19905.9037207619	-221.903720761919
69	19785	19781.0180879097	3.98191209030483
70	18479	19783.2590760718	-1304.25907607182
71	10698	19049.2325371782	-8351.2325371782

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
72	14349.2258995222	1752.87577711768	26945.5760219267
73	14349.2258995222	-104.968162408100	28803.4199614525
74	14349.2258995222	-1749.82424493296	30448.2760439774
75	14349.2258995222	-3241.54171100073	31939.9935100452
76	14349.2258995222	-4616.29003601626	33314.7418350607
77	14349.2258995222	-5897.90931203067	34596.3611110751
78	14349.2258995222	-7103.09737439489	35801.5491734393
79	14349.2258995222	-8244.08867409417	36942.5404731386
80	14349.2258995222	-9330.16499205536	38028.6167910998
81	14349.2258995222	-10368.5661250472	39067.0179240916
82	14349.2258995222	-11365.0684159671	40063.5202150116
83	14349.2258995222	-12324.3681912138	41022.8199902583

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/20/t1264026122dibv7jhavo2fn9m/17pvm1264026052.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/20/t1264026122dibv7jhavo2fn9m/17pvm1264026052.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/20/t1264026122dibv7jhavo2fn9m/2c9gc1264026052.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/20/t1264026122dibv7jhavo2fn9m/2c9gc1264026052.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/20/t1264026122dibv7jhavo2fn9m/3vkfe1264026052.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/20/t1264026122dibv7jhavo2fn9m/3vkfe1264026052.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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')

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.

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