Home » date » 2010 » Aug » 17 »

exponential smoothing - verkocht aantal producten - mattias debbaut

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 17 Aug 2010 11:00:50 +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/Aug/17/t1282042824xkhpngemztvwc4l.htm/, Retrieved Tue, 17 Aug 2010 13:00:29 +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/2010/Aug/17/t1282042824xkhpngemztvwc4l.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:

mattias debbaut

Dataseries X:

» Textbox « » Textfile « » CSV «

376 375 374 372 370 369 370 372 373 373 374 376 371 374 369 363 357 366 362 366 361 362 358 363 360 360 348 345 332 333 323 327 332 337 336 337 343 337 326 321 309 302 293 287 292 292 289 302 310 295 276 264 257 243 227 226 226 229 224 240 244 226 208 199 193 180 167 164 166 173 169 191 193 166 143 147 139 129 115 108 106 116 108 135

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	0.208492559269248
beta	0.141775183847602
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	371	374.507612695369	-3.50761269536900
14	374	376.585977222432	-2.58597722243223
15	369	370.900310874623	-1.90031087462319
16	363	364.512486632936	-1.51248663293580
17	357	358.327983093222	-1.32798309322249
18	366	367.275602408463	-1.27560240846304
19	362	362.259368067115	-0.259368067115133
20	366	363.348897311218	2.65110268878215
21	361	364.141315833245	-3.14131583324479
22	362	362.978837078825	-0.978837078824654
23	358	363.534128010580	-5.53412801057959
24	363	363.689075557080	-0.689075557079548
25	360	355.207661774565	4.79233822543478
26	360	359.221874425834	0.778125574165642
27	348	354.678026407921	-6.67802640792121
28	345	347.420129010354	-2.42012901035366
29	332	340.998648946626	-8.99864894662642
30	333	347.223273111413	-14.2232731114133
31	323	339.459966416589	-16.4599664165887
32	327	337.626876307825	-10.6268763078251
33	332	329.446395054116	2.55360494588433
34	337	329.246157113717	7.75384288628317
35	336	326.678973067071	9.32102693292939
36	337	332.181743178418	4.81825682158205
37	343	328.512353910423	14.4876460895769
38	337	330.688218038543	6.31178196145709
39	326	321.687974243531	4.31202575646864
40	321	320.070617990564	0.92938200943621
41	309	309.799136350361	-0.799136350361437
42	302	313.364980153577	-11.3649801535774
43	293	304.905156915081	-11.9051569150807
44	287	308.456452468431	-21.4564524684312
45	292	308.030175139126	-16.0301751391261
46	292	307.072034845111	-15.0720348451113
47	289	299.842156329827	-10.8421563298269
48	302	295.547134678271	6.45286532172884
49	310	297.427836790954	12.5721632090459
50	295	291.637250416687	3.36274958331285
51	276	279.99921544962	-3.99921544962001
52	264	272.489107781961	-8.48910778196102
53	257	258.300935615494	-1.30093561549421
54	243	251.664688011571	-8.66468801157131
55	227	242.004060005047	-15.0040600050474
56	226	234.842887633332	-8.84288763333197
57	226	237.202346754043	-11.2023467540430
58	229	234.800738038305	-5.80073803830547
59	224	230.587396995002	-6.58739699500185
60	240	235.978409347671	4.02159065232914
61	244	238.356046961552	5.64395303844844
62	226	224.717177026988	1.28282297301206
63	208	208.508337883012	-0.508337883012217
64	199	198.142749386038	0.857250613961867
65	193	190.988079945307	2.01192005469309
66	180	180.152171035643	-0.152171035642596
67	167	168.571679084693	-1.57167908469299
68	164	167.166604134288	-3.16660413428838
69	166	166.528754607842	-0.528754607841677
70	173	168.027157848556	4.97284215144413
71	169	165.162675168869	3.83732483113073
72	191	176.167341592844	14.8326584071559
73	193	180.692380895518	12.3076191044825
74	166	169.159491556411	-3.15949155641064
75	143	154.659252026973	-11.6592520269731
76	147	144.624333053009	2.37566694699055
77	139	139.594335045257	-0.594335045256713
78	129	129.203786698198	-0.203786698197518
79	115	119.18633660126	-4.1863366012599
80	108	115.623060155510	-7.6230601555096
81	106	114.199953626781	-8.19995362678145
82	116	114.786471522282	1.21352847771753
83	108	109.975515644333	-1.97551564433303
84	135	119.308809947941	15.6911900520593

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	119.819716647760	104.639012598616	135.000420696903
86	101.102252568075	85.5872789328358	116.617226203313
87	86.3669660312759	70.5075809733362	102.226351089216
88	86.4262315199528	69.8606126703296	102.991850369576
89	79.6761004659766	62.5084533026233	96.8437476293298
90	71.8820577906944	54.1426827541905	89.6214328271982
91	62.5548068606408	44.4005017719048	80.7091119493768
92	57.6042086956578	38.6577929526939	76.5506244386217
93	55.4349501341775	35.213352063523	75.656548204832
94	58.3741924509213	35.5225518102470	81.2258330915955
95	52.3196010735664	28.4317561477341	76.2074459993987
96	60.7097872656778	34.5949566095994	86.8246179217563

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/17/t1282042824xkhpngemztvwc4l/1j9ga1282042847.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/17/t1282042824xkhpngemztvwc4l/1j9ga1282042847.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/17/t1282042824xkhpngemztvwc4l/2j9ga1282042847.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/17/t1282042824xkhpngemztvwc4l/2j9ga1282042847.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/17/t1282042824xkhpngemztvwc4l/3j9ga1282042847.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/17/t1282042824xkhpngemztvwc4l/3j9ga1282042847.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')

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