Home » date » 2010 » Aug » 18 »

tijdreeks 2 stap 27

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 18 Aug 2010 12:07:22 +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/Aug/18/t1282133203yisx0d6e8e9dwel.htm/, Retrieved Wed, 18 Aug 2010 14:06:44 +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/18/t1282133203yisx0d6e8e9dwel.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:

Magali De Reu

Dataseries X:

» Textbox « » Textfile « » CSV «

120 119 118 116 114 113 114 116 117 117 118 120 123 125 120 116 111 108 113 112 126 124 124 118 119 122 114 108 104 101 107 104 123 125 134 131 127 124 123 117 112 118 123 124 144 148 152 154 146 132 136 128 120 124 126 121 140 142 142 139 131 117 122 112 98 103 108 102 126 129 126 126 112 99 106 104 90 98 99 91 118 115 119 123

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.989880786698701
beta	0.00360535147989007
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	118	118	0
4	116	117	-1
5	114	115.006550345142	-1.00655034514206
6	113	113.003024384004	-0.0030243840043056
7	114	111.992858697122	2.00714130287761
8	116	112.979680624453	3.02031937554719
9	117	114.980207181073	2.01979281892662
10	117	115.997540096993	1.00245990300682
11	118	116.011412352997	1.98858764700346
12	120	117.008530523148	2.99146947685203
13	123	119.009058308161	3.990941691839
14	125	122.013187580358	2.98681241964178
15	120	124.034008118388	-4.03400811838775
16	116	119.090656455834	-3.09065645583438
17	111	115.070080333726	-4.07008033372648
18	108	110.065465752751	-2.06546575275068
19	113	107.03780925526	5.9621907447401
20	112	111.97785395956	0.0221460404395657
21	126	111.038041575241	14.9619584247589
22	124	124.940259684065	-0.940259684064742
23	124	123.097821958224	0.902178041776153
24	118	123.082397692369	-5.08239769236896
25	119	117.124818483444	1.87518151655634
26	122	118.061105530975	3.93889446902489
27	114	121.05427977447	-7.05427977446952
28	108	113.140346255024	-5.14034625502431
29	104	107.10263353542	-3.10263353541953
30	101	103.070940595729	-2.07094059572874
31	107	100.053109760859	6.94689023914121
32	104	105.986648942506	-1.98664894250591
33	123	103.069959242866	19.930040757134
34	125	121.919307272807	3.08069272719256
35	134	124.100804005693	9.89919599430729
36	131	133.067135042123	-2.06713504212334
37	127	130.180847565882	-3.18084756588223
38	124	126.180765434869	-2.18076543486922
39	123	123.162862526143	-0.1628625261434
40	117	122.141861701305	-5.1418617013048
41	112	116.17389462948	-4.17389462948026
42	118	111.149203484569	6.85079651543133
43	123	117.062091872842	5.93790812715828
44	124	122.09252119641	1.90747880358957
45	144	123.140113510798	20.859886489202
46	148	143.022776239551	4.97722376044925
47	152	147.201259346896	4.79874065310435
48	154	151.220191528251	2.77980847174913
49	146	153.250542303578	-7.25054230357847
50	132	145.326165332996	-13.3261653329964
51	136	131.340086531228	4.65991346877232
52	128	135.174712180182	-7.17471218018213
53	120	127.268863679613	-7.26886367961336
54	124	119.243874802579	4.75612519742128
55	126	123.139165358965	2.86083464103531
56	121	125.168554150032	-4.16855415003194
57	140	120.22480901441	19.7751909855896
58	142	139.053092199602	2.94690780039755
59	142	141.233898312065	0.766101687934878
60	139	141.258700470207	-2.25870047020669
61	131	138.28124808425	-7.2812480842498
62	117	130.306086500425	-13.3060865004248
63	122	116.319565457029	5.68043454297148
64	112	121.147709522712	-9.14770952271184
65	98	111.265111706129	-13.2651117061293
66	103	97.2594351422738	5.74056485772621
67	108	102.087599966325	5.91240003367457
68	102	107.106961705752	-5.1069617057522
69	126	101.200242904616	24.7997570953845
70	129	124.986117501379	4.01388249862056
71	126	128.210779217522	-2.21077921752237
72	126	125.2658779176	0.734122082400063
73	112	125.23869781812	-13.2386978181196
74	99	111.332844596001	-12.3328445960008
75	106	98.279663777635	7.72033622236505
76	104	105.104294225687	-1.10429422568701
77	90	103.189651462995	-13.1896514629955
78	98	89.2648736435645	8.73512635643553
79	99	97.0741866545465	1.92581334545352
80	91	98.1499645192691	-7.14996451926913
81	118	90.216286970645	27.783713029355
82	115	116.961942044908	-1.96194204490753
83	119	114.255942760897	4.74405723910347
84	123	118.20501423857	4.7949857614305

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	122.221611553997	106.5114034321	137.931819675894
86	121.49174459169	99.3468020848194	143.636687098562
87	120.761877629384	93.6373575168301	147.886397741938
88	120.032010667078	88.6817273428426	151.382293991312
89	119.302143704771	84.2064632680227	154.397824141519
90	118.572276742465	80.0710372698533	157.073516215076
91	117.842409780158	76.1919293687375	159.492890191579
92	117.112542817852	72.5147367596157	161.710348876088
93	116.382675855545	69.0016977291876	163.763653981903
94	115.652808893239	65.6253448892086	165.680272897269
95	114.922941930932	62.3649664013723	167.480917460492
96	114.193074968626	59.2044917294697	169.181658207782

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/18/t1282133203yisx0d6e8e9dwel/1frtj1282133237.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/18/t1282133203yisx0d6e8e9dwel/1frtj1282133237.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/18/t1282133203yisx0d6e8e9dwel/2qis41282133237.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/18/t1282133203yisx0d6e8e9dwel/2qis41282133237.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/18/t1282133203yisx0d6e8e9dwel/3qis41282133237.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/18/t1282133203yisx0d6e8e9dwel/3qis41282133237.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