Home » date » 2010 » May » 26 »

Exponential smooting wisselkoersen

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 26 May 2010 16:43:38 +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/May/26/t12748923288ikkzvfiau5wq66.htm/, Retrieved Wed, 26 May 2010 18:45:32 +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/May/26/t12748923288ikkzvfiau5wq66.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:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

1.1591 1.1203 1.0886 1.0701 1.0630 1.0377 1.0370 1.0605 1.0497 1.0706 1.0328 1.0110 1.0131 0.9834 0.9643 0.9449 0.9059 0.9505 0.9386 0.9045 0.8695 0.8525 0.8552 0.8983 0.9376 0.9205 0.9083 0.8925 0.8753 0.8530 0.8615 0.9014 0.9114 0.9050 0.8883 0.8912 0.8832 0.8707 0.8766 0.8860 0.9170 0.9561 0.9935 0.9781 0.9806 0.9812 1.0013 1.0194 1.0622 1.0785 1.0797 1.0862 1.1556 1.1674 1.1365 1.1155 1.1267 1.1714 1.1710 1.2298 1.2638 1.2640 1.2261 1.1989 1.2000 1.2146 1.2266 1.2191 1.2224 1.2507 1.2997 1.3406 1.3123 1.3013 1.3185 1.2943 1.2697 1.2155 1.2041 1.2295 1.2234 1.2022 1.1789 1.1861 1.2126 1.1940 1.2028 1.2273 1.2767 1.2661 1.2681 1.2810 1.2722 1.2617 1.2888 1.3205 1.2993 1.3080 1.3246 1.3513 1.3518 1.3421 1.3726 1.3626 1.3910 1.4233 1.4683 1.4559 1.4728 1.4759 1.5520 1.5754 1.5554 1.5562 1.5759 1.4955 1.4342 1.3266 1.2744 1.3511 1.3244 1.2797 1.3050 1.3199 1.3646 1.4014 1.4092 1.4266 etc...

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' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.140884622689867
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	1.0886	1.0815	0.00709999999999988
4	1.0701	1.05080028082110	0.0192997191789019
5	1.063	1.03501931447564	0.0279806855243618
6	1.0377	1.03186136279834	0.00583863720165856
7	1.037	1.00738393699752	0.0296160630024795
8	1.0605	1.01085638485918	0.0496436151408162
9	1.0497	1.04135040684726	0.0083495931527413
10	1.0706	1.03172673612820	0.0388732638718032
11	1.0328	1.0581033812415	-0.0253033812414993
12	1.011	1.01673852392251	-0.00573852392251273
13	1.0131	0.994130054144893	0.0189699458551071
14	0.9834	0.998902627809137	-0.0155026278091366
15	0.9643	0.967018545939545	-0.00271854593954513
16	0.9449	0.947535544620587	-0.00263554462058735
17	0.9059	0.927764236911133	-0.0218642369111334
18	0.9505	0.885683902143507	0.0648160978564933
19	0.9386	0.939415493634248	-0.000815493634248154
20	0.9045	0.927400603121281	-0.0229006031212812
21	0.8695	0.890074260291169	-0.0205742602911689
22	0.8525	0.852175663392925	0.000324336607075426
23	0.8552	0.835221357433437	0.019978642566563
24	0.8983	0.840736040953283	0.0575639590467172
25	0.9376	0.891945917604115	0.0456540823958854
26	0.9205	0.937677875776711	-0.0171778757767109
27	0.9083	0.918157777229296	-0.0098577772292956
28	0.8925	0.904568968003786	-0.0120689680037857
29	0.8753	0.887068636000316	-0.0117686360003162
30	0.853	0.868210616157837	-0.0152106161578373
31	0.8615	0.84376767423956	0.0177323257604401
32	0.9014	0.854765886263733	0.0466341137362666
33	0.9114	0.901235915781944	0.0101640842180564
34	0.905	0.912667878951993	-0.0076678789519925
35	0.8883	0.90518759271901	-0.0168875927190095
36	0.8912	0.886108390590652	0.00509160940934827
37	0.8832	0.889725720061172	-0.00652572006117191
38	0.8707	0.880806346452574	-0.0101063464525739
39	0.8766	0.86688251764583	0.00971748235417003
40	0.886	0.874151561480793	0.0118484385192072
41	0.917	0.885220824271035	0.0317791757289647
42	0.9561	0.920698021453005	0.0354019785469945
43	0.9935	0.964785615843074	0.0287143841569265
44	0.9781	1.00623103102079	-0.0281310310207941
45	0.9806	0.986867801329553	-0.00626780132955251
46	0.9812	0.988484764504143	-0.0072847645041435
47	1.0013	0.988058453205593	0.0132415467944075
48	1.0194	1.01002398352955	0.00937601647044706
49	1.0622	1.02944492007233	0.0327550799276741
50	1.0785	1.07685960714911	0.00164039285088724
51	1.0797	1.09339071327697	-0.0136907132769730
52	1.0862	1.09266190230259	-0.00646190230259158
53	1.1556	1.09825151963483	0.0573484803651678
54	1.1674	1.17573103865292	-0.00833103865291607
55	1.1365	1.18635732341569	-0.0498573234156852
56	1.1155	1.14843319321794	-0.03293319321794
57	1.1267	1.12279341271746	0.00390658728254212
58	1.1714	1.13454379079276	0.0368562092072362
59	1.171	1.18443626392070	-0.0134362639207042
60	1.2298	1.18214330094787	0.0476566990521257
61	1.2638	1.24765739701248	0.0161426029875225
62	1.264	1.28393164154361	-0.0199316415436070
63	1.2261	1.28132357974515	-0.0552235797451464
64	1.1989	1.23564342654917	-0.0367434265491673
65	1.2	1.20326684276346	-0.00326684276345524
66	1.2146	1.20390659485334	0.0106934051466612
67	1.2266	1.22001313120270	0.00658686879730408
68	1.2191	1.23294111972791	-0.0138411197279116
69	1.2224	1.22349111879744	-0.00109111879743984
70	1.2507	1.22663739693735	0.0240626030626474
71	1.2997	1.25832744769077	0.0413725523092305
72	1.3406	1.31315620411257	0.0274437958874276
73	1.3123	1.35792261294135	-0.0456226129413504
74	1.3013	1.32319508833098	-0.0218950883309825
75	1.3185	1.30911040707271	0.00938959292728958
76	1.2943	1.32763325632948	-0.0333332563294833
77	1.2697	1.29873711308848	-0.0290371130884792
78	1.2155	1.27004623036701	-0.0545462303670059
79	1.2041	1.20816150528260	-0.00406150528259586
80	1.2295	1.19618930164330	0.0333106983566958
81	1.2234	1.22628226681282	-0.00288226681282344
82	1.2022	1.21977619974041	-0.0175761997404074
83	1.1789	1.19609998347166	-0.0171999834716581
84	1.1861	1.17037677028998	0.0157232297100180
85	1.2126	1.17979193157514	0.0328080684248562
86	1.194	1.21091408391636	-0.0169140839163628
87	1.2028	1.18993114958566	0.0128688504143388
88	1.2273	1.20054417272074	0.0267558272792621
89	1.2767	1.22881365735173	0.0478863426482679
90	1.2661	1.28496010666773	-0.0188601066677307
91	1.2681	1.27170300765596	-0.003603007655957
92	1.281	1.2731953992818	0.0078046007182011
93	1.2722	1.28719494750923	-0.0149949475092275
94	1.2617	1.27628238998714	-0.0145823899871356
95	1.2888	1.26372795547588	0.0250720445241184
96	1.3205	1.29436022100873	0.0261397789912745
97	1.2993	1.32974291390911	-0.0304429139091078
98	1.308	1.30425397546944	0.00374602453055717
99	1.3246	1.31348173272202	0.0111182672779824
100	1.3513	1.33164812561244	0.0196518743875587
101	1.3518	1.36111677252068	-0.00931677252068108
102	1.3421	1.36030418253942	-0.0182041825394175
103	1.3726	1.34803949315097	0.0245605068490258
104	1.3626	1.38199969089147	-0.0193996908914711
105	1.391	1.36926657275993	0.0217334272400738
106	1.4233	1.40072847845640	0.0225715215435984
107	1.4683	1.43620845875261	0.0320915412473921
108	1.4559	1.48572966343278	-0.0298296634327828
109	1.4728	1.46912712255509	0.00367287744491063
110	1.4759	1.48654457450810	-0.0106445745081021
111	1.552	1.48814491764483	0.0638550823551662
112	1.5754	1.57324111682927	0.00215888317072821
113	1.5554	1.59694527027021	-0.0415452702702113
114	1.5562	1.57109218054364	-0.0148921805436439
115	1.5759	1.56979410130672	0.00610589869327671
116	1.4955	1.59035432854031	-0.0948543285403083
117	1.4342	1.49659081225341	-0.0623908122534063
118	1.3266	1.42650090620977	-0.0999009062097707
119	1.2744	1.30482640473203	-0.0304264047320315
120	1.3511	1.24833979218155	0.10276020781845
121	1.3244	1.33951712528758	-0.0151171252875846
122	1.2797	1.31068735479529	-0.0309873547952877
123	1.305	1.26162171300680	0.0433782869932031
124	1.3199	1.29303304660277	0.0268669533972332
125	1.3646	1.31171818719496	0.0528818128050377
126	1.4014	1.36386842143916	0.0375315785608437
127	1.4092	1.40595604372366	0.00324395627634422
128	1.4266	1.41421306727967	0.0123869327203292
129	1.4575	1.43335819562226	0.0241418043777406
130	1.4821	1.46765940462307	0.01444059537693
131	1.4908	1.49429386245417	-0.00349386245416583
132	1.4579	1.50250163096058	-0.0446016309605801

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
133	1.46331794701135	1.40337610024520	1.52325979377749
134	1.46873589402269	1.37779761824064	1.55967416980475
135	1.47415384103404	1.35510398940588	1.5932036926622
136	1.47957178804538	1.33313084891834	1.62601272717243
137	1.48498973505673	1.31112586132605	1.65885360878741
138	1.49040768206808	1.28874808490339	1.69206727923276
139	1.49582562907942	1.26582254123141	1.72582871692743
140	1.50124357609077	1.24225369094295	1.76023346123859
141	1.50666152310212	1.21798827210082	1.79533477410342
142	1.51207947011346	1.19299717936198	1.83116176086494
143	1.51749741712481	1.16726580798767	1.86772902626195
144	1.52291536413615	1.14078856149906	1.90504216677325

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/26/t12748923288ikkzvfiau5wq66/1pxh71274892216.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/26/t12748923288ikkzvfiau5wq66/1pxh71274892216.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/May/26/t12748923288ikkzvfiau5wq66/2pxh71274892216.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/26/t12748923288ikkzvfiau5wq66/2pxh71274892216.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/May/26/t12748923288ikkzvfiau5wq66/3pxh71274892216.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/26/t12748923288ikkzvfiau5wq66/3pxh71274892216.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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