Home » date » 2010 » Dec » 29 »

Paper Exponential Smoothing Single

*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: Tue, 28 Dec 2010 23:08:22 +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/29/t1293577613hhe2fr0ymfs2usl.htm/, Retrieved Wed, 29 Dec 2010 00:06:57 +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/29/t1293577613hhe2fr0ymfs2usl.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 «

1203 1319 1328 1260 1286 1274 1389 1255 1244 1336 1214 1239 1174 1061 1116 1123 1086 1074 965 1035 1016 941 1003 998 891 828 833 887 842 793 778 699 686 727 641 619 627 593 535 536 504 487 477 435 433 393 389 377 339 370 350 341 367 396 408 405 391 396 368 356

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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.79903298900027
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	1319	1203	116
3	1328	1295.68782672403	32.3121732759687
4	1260	1321.50631911782	-61.5063191178233
5	1286	1272.36074111070	13.6392588892954
6	1274	1283.25895890877	-9.25895890876677
7	1389	1275.86074529686	113.139254703136
8	1255	1366.26274215557	-111.262742155574
9	1244	1277.36014072664	-33.3601407266392
10	1336	1250.70428776836	85.295712231637
11	1214	1318.85837566171	-104.858375661715
12	1239	1235.07307433502	3.9269256649784
13	1174	1238.21081748669	-64.2108174866912
14	1061	1186.90425606415	-125.904256064150
15	1116	1086.30260201336	29.6973979866432
16	1123	1110.03180269215	12.968197307845
17	1086	1120.39382014899	-34.3938201489877
18	1074	1092.91202323220	-18.9120232322043
19	965	1077.80069278093	-112.800692780934
20	1035	987.669218066883	47.3307819331169
21	1016	1025.48807422662	-9.4880742266214
22	941	1017.90678991747	-76.9067899174677
23	1003	956.455727695298	46.5442723047024
24	998	993.646136715766	4.35386328423351
25	891	997.125017109466	-106.125017109466
26	828	912.327627480785	-84.3276274807846
27	833	844.947071239512	-11.9470712395118
28	887	835.400967197206	51.5990328027945
29	842	876.630296607145	-34.6302966071454
30	793	848.959547199172	-55.959547199172
31	778	804.246022937516	-26.2460229375159
32	699	783.274584780383	-84.274584780383
33	686	715.936411406557	-29.936411406557
34	727	692.016231120434	34.983768879566
35	641	719.969416534768	-78.9694165347682
36	619	656.870247601385	-37.870247601385
37	627	626.61067046627	0.389329533730006
38	593	626.921757607312	-33.9217576073123
39	535	599.817154234199	-64.817154234199
40	536	548.026109747956	-12.0261097479555
41	504	538.416851330001	-34.4168513300014
42	487	510.916651739812	-23.9166517398124
43	477	491.806458013272	-14.8064580132716
44	435	479.97560961042	-44.9756096104202
45	433	444.038613831297	-11.0386138312969
46	393	435.218397227256	-42.218397227256
47	389	401.484505099961	-12.4845050999609
48	377	391.50897367375	-14.5089736737501
49	339	379.915825071887	-40.9158250718873
50	370	347.222731067285	22.777268932715
51	350	365.422520343855	-15.4225203438552
52	341	353.099417815587	-12.0994178155871
53	367	343.431583833235	23.5684161667646
54	396	362.263525848968	33.7364741510324
55	408	389.220081628197	18.7799183718026
56	405	404.225855938	0.774144062000119
57	391	404.844422581777	-13.8444225817766
58	396	393.782272225277	2.21772777472319
59	368	395.554309877903	-27.5543098779028
60	356	373.537507296322	-17.5375072963225

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	359.524460421728	259.615045741503	459.433875101953
62	359.524460421728	231.638313208750	487.410607634706
63	359.524460421728	208.766899562533	510.282021280923
64	359.524460421728	188.934842732232	530.114078111224
65	359.524460421728	171.179582151352	547.869338692104
66	359.524460421728	154.959632853748	564.089287989707
67	359.524460421728	139.934514875144	579.114405968312
68	359.524460421728	125.873610450267	593.175310393189
69	359.524460421728	112.612137522241	606.436783321215
70	359.524460421728	100.027503393606	619.02141744985
71	359.524460421728	88.0255723685921	631.023348474864
72	359.524460421728	76.5321960021442	642.516724841312

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293577613hhe2fr0ymfs2usl/100y11293577699.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293577613hhe2fr0ymfs2usl/100y11293577699.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293577613hhe2fr0ymfs2usl/200y11293577699.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293577613hhe2fr0ymfs2usl/200y11293577699.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293577613hhe2fr0ymfs2usl/3tsfm1293577699.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/29/t1293577613hhe2fr0ymfs2usl/3tsfm1293577699.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; 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