Home » date » 2010 » Jan » 19 »

bruin brood double

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 19 Jan 2010 12:58:54 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/19/t1263931176dvj2poovbjeln5x.htm/, Retrieved Tue, 19 Jan 2010 20:59:40 +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/2010/Jan/19/t1263931176dvj2poovbjeln5x.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 «

1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.44 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.57 1.58 1.58 1.58 1.58 1.59 1.6 1.6 1.61 1.61 1.61 1.62 1.63 1.63 1.64 1.64 1.64 1.64 1.64 1.65 1.65 1.65 1.65 1.65 1.66 1.66 1.67 1.68 1.68 1.68 1.68 1.69 1.7 1.7 1.71 1.72 1.73 1.74 1.74 1.75 1.75 1.75 1.76 1.79 1.83 1.84 1.85 1.87 1.87 1.87 1.88 1.88 1.88 1.88 1.89 1.89 1.89 1.9 1.89

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	1
beta	0.0335069746630998
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	1.38	1.38	0
4	1.38	1.38	0
5	1.38	1.38	0
6	1.38	1.38	0
7	1.38	1.38	0
8	1.38	1.38	0
9	1.38	1.38	0
10	1.38	1.38	0
11	1.38	1.38	0
12	1.38	1.38	0
13	1.38	1.38	0
14	1.38	1.38	0
15	1.38	1.38	0
16	1.38	1.38	0
17	1.38	1.38	0
18	1.38	1.38	0
19	1.38	1.38	0
20	1.38	1.38	0
21	1.38	1.38	0
22	1.38	1.38	0
23	1.38	1.38	0
24	1.43	1.38	0.05
25	1.43	1.43167534873315	-0.00167534873315489
26	1.43	1.4316192128656	-0.00161921286560140
27	1.43	1.43156495794114	-0.00156495794113942
28	1.43	1.43151252093506	-0.00151252093505683
29	1.43	1.43146184093441	-0.00146184093440849
30	1.43	1.43141285906726	-0.00141285906725774
31	1.43	1.43136551843429	-0.00136551843428867
32	1.43	1.43131976404271	-0.00131976404270895
33	1.43	1.43127554274237	-0.00127554274236874
34	1.43	1.43123280316402	-0.00123280316401830
35	1.43	1.43119149565964	-0.00119149565963705
36	1.43	1.43115157224476	-0.00115157224475837
37	1.43	1.43111298654273	-0.00111298654273062
38	1.43	1.43107569373084	-0.00107569373084293
39	1.43	1.43103965048826	-0.00103965048825838
40	1.43	1.43100481494569	-0.00100481494568982
41	1.43	1.43097114663676	-0.000971146636763454
42	1.43	1.43093860645101	-0.000938606451011292
43	1.44	1.43090715658844	0.00909284341156136
44	1.48	1.44121183026225	0.0387881697377548
45	1.48	1.48251150448288	-0.00251150448287629
46	1.48	1.48242735156580	-0.00242735156580220
47	1.48	1.48234601835839	-0.00234601835838855
48	1.48	1.48226741038069	-0.00226741038069478
49	1.48	1.48219143631852	-0.00219143631851804
50	1.48	1.48211800791732	-0.00211800791731753
51	1.48	1.48204703987970	-0.0020470398796959
52	1.48	1.48197844976631	-0.00197844976631245
53	1.48	1.48191215790012	-0.00191215790012045
54	1.48	1.48184808727381	-0.00184808727380936
55	1.48	1.48178616346035	-0.00178616346035043
56	1.48	1.48172631452654	-0.00172631452654048
57	1.48	1.48166847094944	-0.00166847094943900
58	1.48	1.48161256553561	-0.00161256553561007
59	1.48	1.48155853334307	-0.00155853334306588
60	1.48	1.48150631160583	-0.00150631160582804
61	1.48	1.48145583966102	-0.00145583966101692
62	1.48	1.48140705887838	-0.00140705887838166
63	1.48	1.48135991259219	-0.00135991259219437
64	1.48	1.48131434603542	-0.00131434603542369
65	1.48	1.48127030627612	-0.00127030627611613
66	1.48	1.48122774215591	-0.00122774215590793
67	1.48	1.48118660423060	-0.00118660423059702
68	1.48	1.48114684471271	-0.00114684471270743
69	1.48	1.48110841741598	-0.00110841741597612
70	1.48	1.48107127770170	-0.00107127770170279
71	1.48	1.48103538242689	-0.00103538242689472
72	1.48	1.48100068989415	-0.00100068989415014
73	1.48	1.48096715980322	-0.000967159803221262
74	1.57	1.4809347532042	0.0890652467958004
75	1.58	1.57391906017195	0.0060809398280508
76	1.58	1.58412281406870	-0.00412281406869552
77	1.58	1.58398467104216	-0.00398467104215516
78	1.58	1.58385115677050	-0.00385115677050485
79	1.59	1.58372211615817	0.00627788384182804
80	1.6	1.59393246905300	0.00606753094700219
81	1.6	1.60413577365871	-0.00413577365870665
82	1.61	1.60399719639551	0.0060028036044879
83	1.61	1.61419833218380	-0.00419833218379528
84	1.61	1.61405765877369	-0.00405765877368558
85	1.62	1.61392169890396	0.00607830109603591
86	1.63	1.62412536438478	0.00587463561521617
87	1.63	1.63432220565150	-0.00432220565149777
88	1.64	1.63417738161624	0.00582261838375575
89	1.64	1.6443724799429	-0.00437247994290169
90	1.64	1.64422597136824	-0.00422597136823999
91	1.64	1.64408437185268	-0.00408437185267729
92	1.64	1.64394751690849	-0.00394751690849504
93	1.65	1.64381524755946	0.00618475244054006
94	1.65	1.65402247990278	-0.00402247990278259
95	1.65	1.65388769877060	-0.00388769877059714
96	1.65	1.65375743374639	-0.00375743374639304
97	1.65	1.65363153350905	-0.00363153350905443
98	1.66	1.65350985180778	0.00649014819222171
99	1.66	1.66372731703881	-0.00372731703881479
100	1.67	1.66360242592123	0.00639757407876607
101	1.68	1.67381678927380	0.00618321072620365
102	1.68	1.68402396995894	-0.00402396995893595
103	1.68	1.68388913889948	-0.00388913889947684
104	1.68	1.68375882562091	-0.0037588256209109
105	1.69	1.68363287874607	0.00636712125393202
106	1.7	1.6938462217166	0.0061537782833998
107	1.7	1.70405241620962	-0.00405241620962449
108	1.71	1.70391663200236	0.00608336799763576
109	1.72	1.71412046725973	0.00587953274027253
110	1.73	1.72431747261429	0.00568252738571351
111	1.74	1.73450787691542	0.00549212308457792
112	1.74	1.74469190134446	-0.00469190134446351
113	1.75	1.74453468992499	0.00546531007500706
114	1.75	1.75471781593120	-0.00471781593120224
115	1.75	1.75455973619233	-0.00455973619233019
116	1.76	1.75440695322726	0.00559304677273653
117	1.79	1.76459435930377	0.0254056406962331
118	1.83	1.79544562546288	0.0345543745371246
119	1.84	1.83660343801499	0.00339656198500982
120	1.85	1.84671724653136	0.00328275346863638
121	1.87	1.85682724166866	0.0131727583313377
122	1.87	1.87726862094831	-0.00726862094831371
123	1.87	1.87702507145036	-0.0070250714503628
124	1.88	1.87678968255927	0.00321031744073075
125	1.88	1.88689725058442	-0.00689725058441604
126	1.88	1.88666614458384	-0.00666614458383896
127	1.88	1.88644278224617	-0.00644278224616768
128	1.89	1.88622690410469	0.00377309589531438
129	1.89	1.89635332913325	-0.00635332913325137
130	1.89	1.89614044829496	-0.00614044829495719
131	1.9	1.89593470044952	0.00406529955048218
132	1.89	1.90607091633855	-0.0160709163385537

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
133	1.89553242855199	1.8739479324506	1.91711692465337
134	1.90106485710397	1.87002415531266	1.93210555889528
135	1.90659728565596	1.86794563350664	1.94524893780527
136	1.91212971420794	1.86676219568303	1.95749723273285
137	1.91766214275993	1.86611259509907	1.96921169042078
138	1.92319457131191	1.86581488221117	1.98057426041265
139	1.92872699986390	1.86576291140454	1.99169108832325
140	1.93425942841588	1.86588878315542	2.00263007367634
141	1.93979185696787	1.86614621255237	2.01343750138336
142	1.94532428551985	1.86650214404758	2.02414642699212
143	1.95085671407184	1.86693211461095	2.03478131353272
144	1.95638914262382	1.86741750504649	2.04536078020115

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/19/t1263931176dvj2poovbjeln5x/12ibz1263931131.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/19/t1263931176dvj2poovbjeln5x/12ibz1263931131.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/19/t1263931176dvj2poovbjeln5x/2zja61263931131.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/19/t1263931176dvj2poovbjeln5x/2zja61263931131.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/19/t1263931176dvj2poovbjeln5x/3awls1263931131.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/19/t1263931176dvj2poovbjeln5x/3awls1263931131.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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

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