Home » date » 2011 » Jan » 05 »

Exponential Smoothing consumptieprijs koffie verbetering

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 05 Jan 2011 19:06:39 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Jan/05/t1294254289gylhmifidujvwor.htm/, Retrieved Wed, 05 Jan 2011 20:04:52 +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/2011/Jan/05/t1294254289gylhmifidujvwor.htm/},
    year = {2011},
}
@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 = {2011},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

Verbetering opgave 10

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W92 - Natasha Van Linden

Dataseries X:

» Textbox « » Textfile « » CSV «

97 100,7 101,4 101,5 101,8 101,5 102,2 101,8 98,5 98,4 97,5 97,7 98,3 99,6 99,4 96,7 96,9 96,1 97,9 99,2 97,8 94,9 93,3 91,5 89,1 92,3 91,8 92,1 94,4 92,8 92,6 92,3 92,1 89,8 87,4 87,7 86,3 89,1 90,4 87,1 86,7 84,4 88,4 88,9 88,5 87,2 86,2 83,4 87,5 85,7 87,4 86,8 87,9 85,9 87,7 87 86,8 86,2 86,1 87,5 85,7 88,9 89,8 91,4 95,2 94,1 96,8 96,1 96,6 94,2 93,9 96,5 93,4 95 95,2 94 97 96,9 96,3 96,3 97,3 95,7 96,4 95,1 94,6 95,9 96,2 94,3 98,3 95,9 92,1 94,6 94,7 96,7 97,5 96,2 97,1 95,9 94,5 99,4 101,3 101,4 100,9 101,4 103,1 102,4 101,1 102 103,9 101,7 101,2 101,9 101,1 103,1 103,3 101,4 102,8 103 102,6 102,2

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	1 seconds
R Server	'Gwilym Jenkins' @ www.wessa.org

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.787135282216426
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	100.7	97	3.7
3	101.4	99.9124005442008	1.48759945579923
4	101.5	101.083342561666	0.416657438333687
5	101.8	101.411308331977	0.388691668023327
6	101.5	101.717261257781	-0.217261257781388
7	102.2	101.546247256323	0.653752743677074
8	101.8	102.060839106717	-0.260839106716944
9	98.5	101.855523442838	-3.35552344283822
10	98.4	99.214272550676	-0.81427255067591
11	97.5	98.5733298966986	-1.07332989669855
12	97.7	97.7284740655494	-0.0284740655494033
13	98.3	97.7060611239273	0.59393887607267
14	99.6	98.173571368764	1.42642863123589
15	99.4	99.2963636719736	0.103636328026454
16	96.7	99.3779394822825	-2.67793948228253
17	96.9	97.2700388321376	-0.370038832137567
18	96.1	96.978768211572	-0.878768211571938
19	97.9	96.2870587473534	1.61294125264656
20	99.2	97.556661715454	1.64333828454609
21	97.8	98.8501912598371	-1.05019125983715
22	94.9	98.023548666144	-3.12354866614399
23	93.3	95.564893305302	-2.26489330530201
24	91.5	93.782115874243	-2.28211587424302
25	89.1	91.9857819515202	-2.88578195152016
26	92.3	89.7142811606953	2.58571883930473
27	91.8	91.7495916890037	0.050408310996275
28	92.1	91.7892698491058	0.310730150894173
29	94.4	92.033856514123	2.36614348587696
30	92.8	93.8963315346434	-1.09633153464337
31	92.6	93.033370302719	-0.433370302719084
32	92.3	92.692249247184	-0.392249247184083
33	92.1	92.3834960253027	-0.283496025302668
34	89.8	92.1603463014188	-2.3603463014188
35	87.4	90.302434449323	-2.90243444932301
36	87.7	88.0178258899405	-0.317825889940465
37	86.3	87.7676539183665	-1.46765391836649
38	89.1	86.612411737137	2.48758826286294
39	90.4	88.570480226464	1.82951977353606
40	87.1	90.0105597897268	-2.91055978972679
41	86.7	87.7195554882324	-1.0195554882324
42	84.4	86.9170273912673	-2.51702739126728
43	88.4	84.9357863252956	3.46421367470437
44	88.9	87.662591133792	1.23740886620794
45	88.5	88.6365993109118	-0.136599310911762
46	87.2	88.5290771737667	-1.32907717376666
47	86.2	87.4829136375064	-1.28291363750644
48	83.4	86.4730870493885	-3.0730870493885
49	87.5	84.0541518074924	3.44584819250755
50	85.7	86.7665004969768	-1.06650049697684
51	87.4	85.927020327305	1.47297967269499
52	86.8	87.0864545976708	-0.28645459767084
53	87.9	86.860976077091	1.039023922909
54	85.9	87.6788284658796	-1.7788284658796
55	87.7	86.2786498193749	1.42135018062514
56	87	87.3974446949296	-0.39744469492959
57	86.8	87.0846019528208	-0.284601952820765
58	86.2	86.8605817143678	-0.660581714367837
59	86.1	86.3406145402019	-0.240614540201904
60	87.5	86.1512183461947	1.3487816538053
61	85.7	87.212891973911	-1.51289197391107
62	88.9	86.0220413230636	2.87795867693639
63	89.8	88.2873841384412	1.51261586155884
64	91.4	89.4780174515143	1.92198254848569
65	95.2	90.9908777272316	4.20912227276837
66	94.1	94.3040263752906	-0.20402637529061
67	96.8	94.1434300167966	2.65656998320337
68	96.1	96.234509980253	-0.1345099802531
69	96.6	96.1286324289857	0.471367571014341
70	94.2	96.4996624750237	-2.29966247502369
71	93.9	94.6895170037434	-0.789517003743384
72	96.5	94.0680603141872	2.43193968581282
73	93.4	95.9823258451128	-2.58232584511276
74	95	93.9496860622451	1.05031393775485
75	95.2	94.7764252200557	0.423574779944332
76	94	95.1098358740069	-1.1098358740069
77	97	94.2362449001066	2.76375509989343
78	96.9	96.4116940506383	0.488305949361731
79	96.3	96.796056891897	-0.496056891897084
80	96.3	96.4055930102983	-0.105593010298279
81	97.3	96.322477026337	0.977522973662943
82	95.7	97.0919198480843	-1.39191984808427
83	96.4	95.9962906256398	0.403709374360176
84	95.1	96.3140645179602	-1.21406451796024
85	94.6	95.3584315009866	-0.758431500986646
86	95.9	94.7614433074157	1.13855669258432
87	96.2	95.6576414509524	0.542358549047563
88	94.3	96.0845510005195	-1.78455100051949
89	98.3	94.679867945096	3.62013205490402
90	95.9	97.5294016117936	-1.62940161179358
91	92.1	96.2468421142505	-4.14684211425055
92	94.6	92.982716376343	1.61728362365702
93	94.7	94.2557373778743	0.444262622125748
94	96.7	94.6054321623194	2.09456783768059
95	97.5	96.2541404083536	1.24585959164642
96	96.2	97.2348004496262	-1.03480044962622
97	97.1	96.420272505672	0.679727494327992
98	95.9	96.9553099987501	-1.05530999875013
99	94.5	96.1246382650581	-1.62463826505814
100	99.4	94.845828165792	4.55417183420801
101	101.3	98.4305774977734	2.86942250222657
102	101.4	100.689201188862	0.710798811138304
103	100.9	101.248696011666	-0.348696011666149
104	101.4	100.974225078116	0.425774921884425
105	103.1	101.309367541414	1.79063245858623
106	102.4	102.718837527049	-0.318837527048927
107	101.1	102.467869260214	-1.36786926021409
108	102	101.39117110404	0.608828895959704
109	103.9	101.870401808883	2.02959819111695
110	101.7	103.467970153834	-1.76797015383384
111	101.2	102.076338467846	-0.876338467845628
112	101.9	101.386541540641	0.513458459359157
113	101.1	101.790702809955	-0.690702809954928
114	103.1	101.247026258713	1.85297374128662
115	103.3	102.705567267501	0.594432732499357
116	101.4	103.173466244155	-1.7734662441552
117	102.8	101.777508391561	1.0224916084392
118	103	102.582347612334	0.417652387666479
119	102.6	102.911096542368	-0.31109654236775
120	102.2	102.666221477695	-0.466221477694546

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	102.299242103274	98.8707257081588	105.727758498389
122	102.299242103274	97.9360162399013	106.662467966647
123	102.299242103274	97.1688663667382	107.42961783981
124	102.299242103274	96.502366180739	108.096118025809
125	102.299242103274	95.9049645268393	108.693519679709
126	102.299242103274	95.358795360612	109.239688845936
127	102.299242103274	94.8525773296349	109.745906876913
128	102.299242103274	94.3786467017787	110.219837504769
129	102.299242103274	93.9315156033567	110.666968603192
130	102.299242103274	93.507094354251	111.091389852297
131	102.299242103274	93.1022383898965	111.496245816652
132	102.299242103274	92.7144681066108	111.884016099937

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Jan/05/t1294254289gylhmifidujvwor/1r68q1294254398.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/05/t1294254289gylhmifidujvwor/1r68q1294254398.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/05/t1294254289gylhmifidujvwor/2a0bx1294254398.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/05/t1294254289gylhmifidujvwor/2a0bx1294254398.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/05/t1294254289gylhmifidujvwor/3j0jg1294254398.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/05/t1294254289gylhmifidujvwor/3j0jg1294254398.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