Home » date » 2010 » May » 28 »

Exponential Smoothing eigen gegevens

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 28 May 2010 10:47:09 +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/28/t1275043767hhjzhin6yil5neh.htm/, Retrieved Fri, 28 May 2010 12:49:31 +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/28/t1275043767hhjzhin6yil5neh.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 «

81.28 69.39 67.63 51.25 103.97 133.83 162.37 172.91 163.01 151.50 111.73 88.58 74.29 63.98 61.18 76.48 107.98 124.97 145.57 140.20 143.84 138.80 104.06 74.70 60.18 55.16 35.62 56.18 85.44 114.08 133.64 67.14 95.58 89.37 75.24 69.18 54.49 57.50 62.16 76.67 110.04 127.38 156.47 167.56 153.54 124.08 100.97 79.17 68.13 61.77 54.31 60.30 84.18 104.05 114.66 105.55 96.61 70.94 63.91 58.61 44.53 49.58 57.39 76.76 104.57 125.41 143.11 136.35 135.15 131.70 96.87 70.63 66.29 63.49 62.97 66.43 101.49 127.69 133.21 158.72 148.61 134.31 100.99 75.16 59.74 52.87 52.07 57.38 79.43 101.40 120.19 134.38 135.97 113.83 84.38 70.28 65.96 56.36 49.57 68.33 90.32 117.06 134.69 131.67 129.25 118.77 88.44 76.79 75.28 73.89 76.24 88.58 105.83 115.84 127.76 131.75 119.63 93.38 75.55 51.79

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	0.74849268925821
beta	0
gamma	0.105416678642104

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	74.29	73.9403611099298	0.349638890070239
14	63.98	64.6912005135862	-0.711200513586213
15	61.18	62.1791200456466	-0.999120045646642
16	76.48	77.2457571681103	-0.765757168110298
17	107.98	108.403843873499	-0.423843873499322
18	124.97	125.327597717670	-0.357597717670401
19	145.57	150.560664175104	-4.99066417510409
20	140.2	155.995349759207	-15.7953497592069
21	143.84	135.495970582961	8.34402941703857
22	138.8	129.873828284223	8.92617171577743
23	104.06	98.9415392666272	5.11846073337283
24	74.7	81.0765682372002	-6.37656823720023
25	60.18	64.1470623862881	-3.96706238628814
26	55.16	53.2426132870618	1.91738671293820
27	35.62	52.924864229907	-17.3048642299070
28	56.18	50.0958968719459	6.08410312805406
29	85.44	77.0744390135175	8.36556098648252
30	114.08	96.4410631378694	17.6389368621306
31	133.64	131.767674531578	1.87232546842216
32	67.14	141.103337539617	-73.963337539617
33	95.58	80.529662110612	15.0503378893880
34	89.37	83.7893621415126	5.58063785848745
35	75.24	63.4640873668122	11.7759126331878
36	69.18	56.6559767110528	12.5240232889472
37	54.49	55.4764753113273	-0.98647531132729
38	57.5	47.7224815623175	9.77751843768252
39	62.16	52.6181478350113	9.54185216498865
40	76.67	76.246233489518	0.423766510482011
41	110.04	108.232643320302	1.80735667969819
42	127.38	127.281784120441	0.098215879559362
43	156.47	152.617946490412	3.85205350958793
44	167.56	161.113657385402	6.44634261459765
45	153.54	161.200553578699	-7.66055357869945
46	124.08	142.181983996835	-18.1019839968354
47	100.97	93.3659841320764	7.60401586792356
48	79.17	77.9019480809574	1.26805191904263
49	68.13	65.9722406964607	2.15775930353934
50	61.77	59.3267780723277	2.44322192767229
51	54.31	58.4775322174813	-4.16753221748134
52	60.3	70.3034402120837	-10.0034402120837
53	84.18	88.6959212452881	-4.51592124528811
54	104.05	98.8661350545624	5.18386494543761
55	114.66	123.010550881149	-8.35055088114902
56	105.55	120.756598292350	-15.2065982923496
57	96.61	105.652630103138	-9.0426301031379
58	70.94	89.8723850666105	-18.9323850666105
59	63.91	54.980782438769	8.92921756123096
60	58.61	48.2089974292791	10.4010025707209
61	44.53	46.7339612442915	-2.2039612442915
62	49.58	39.4461578855268	10.1338421144732
63	57.39	44.7435870772542	12.6464129227458
64	76.76	68.6814747894087	8.0785252105913
65	104.57	105.953836131095	-1.38383613109522
66	125.41	122.109366109465	3.30063389053487
67	143.11	148.881218725698	-5.77121872569847
68	136.35	149.493664080602	-13.1436640806019
69	135.15	135.362769212441	-0.212769212440804
70	131.7	122.710894572195	8.9891054278049
71	96.87	95.5027202216624	1.36727977833762
72	70.63	75.8540139476447	-5.22401394764471
73	66.29	59.8029919220972	6.48700807790281
74	63.49	57.1487245984807	6.34127540151931
75	62.97	59.0339261919402	3.93607380805975
76	66.43	78.3361487778237	-11.9061487778237
77	101.49	98.0656799999367	3.4243200000633
78	127.69	117.206540064767	10.4834599352330
79	133.21	149.187182864173	-15.9771828641726
80	158.72	141.654181455443	17.0658185445569
81	148.61	150.160184673231	-1.55018467323075
82	134.31	135.583012920392	-1.27301292039161
83	100.99	99.214030933917	1.77596906608306
84	75.16	78.8518713111839	-3.69187131118389
85	59.74	63.5664037170366	-3.82640371703663
86	52.87	53.6288643023088	-0.758864302308758
87	52.07	50.4985612444984	1.57143875550164
88	57.38	64.8213137810088	-7.44131378100882
89	79.43	84.0520226134744	-4.62202261347444
90	101.4	93.8253991405378	7.57460085946222
91	120.19	117.860597971883	2.32940202811672
92	134.38	124.074671892463	10.3053281075366
93	135.97	127.583773974502	8.3862260254984
94	113.83	121.715057179198	-7.88505717919814
95	84.38	85.3111441316457	-0.931144131645723
96	70.28	66.1556347357461	4.12436526425391
97	65.96	57.7838575722381	8.17614242776192
98	56.36	56.5526307231324	-0.192630723132424
99	49.57	53.7732891473396	-4.20328914733956
100	68.33	63.2342288915095	5.09577110849053
101	90.32	95.3816340095591	-5.06163400955913
102	117.06	107.126508098302	9.93349190169766
103	134.69	135.654762487717	-0.96476248771711
104	131.67	140.328159021533	-8.65815902153287
105	129.25	129.538107198813	-0.288107198813236
106	118.77	117.148323053472	1.62167694652797
107	88.44	87.337613256133	1.10238674386690
108	76.79	69.082331157393	7.70766884260705
109	75.28	62.6143024380525	12.6656975619475
110	73.89	63.631057718951	10.258942281049
111	76.24	67.9393905836877	8.30060941631234
112	88.58	93.2425600715202	-4.66256007152019
113	105.83	127.476367216397	-21.6463672163974
114	115.84	130.818857639880	-14.9788576398797
115	127.76	141.319582691019	-13.5595826910191
116	131.75	136.178176242322	-4.42817624232239
117	119.63	128.793420868578	-9.1634208685779
118	93.38	110.449148843292	-17.0691488432919
119	75.55	71.9470579183833	3.6029420816167
120	51.79	58.5446657421842	-6.75466574218419

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	44.6962662586782	27.8923503336645	61.5001821836918
122	39.2576865681958	17.1248583829175	61.3905147534741
123	37.1917991982208	10.4702798047833	63.9133185916583
124	46.3148294515892	9.11858477355128	83.5110741296271
125	65.189461790653	10.0085767818953	120.370346799411
126	76.4354264307423	9.09730288897072	143.773549972514
127	90.0040091335248	8.252607843439	171.755410423611
128	93.2868471630865	6.08784036517878	180.485853960994
129	90.024187813059	3.37882098114349	176.669554644974
130	81.0858415420205	0.474262489647515	161.697420594394
131	59.967722270763	-2.55556753736494	122.491012078891
132	46.7077712362005	-5.62863102895467	99.0441735013557

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/28/t1275043767hhjzhin6yil5neh/10qwa1275043627.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/28/t1275043767hhjzhin6yil5neh/10qwa1275043627.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/May/28/t1275043767hhjzhin6yil5neh/2y2k11275043627.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/28/t1275043767hhjzhin6yil5neh/2y2k11275043627.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/May/28/t1275043767hhjzhin6yil5neh/3y2k11275043627.png (open in new window)

http://www.freestatistics.org/blog/date/2010/May/28/t1275043767hhjzhin6yil5neh/3y2k11275043627.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