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Exponential Smoothing gemiddelde consumptieprijs Cola-limonade

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 18 Jan 2010 06:41:19 -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/18/t1263822185rofp3qw8j1b92uk.htm/, Retrieved Mon, 18 Jan 2010 14:43:09 +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/18/t1263822185rofp3qw8j1b92uk.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:

KDGP2W61

Dataseries X:

» Textbox « » Textfile « » CSV «

1,14 1,15 1,15 1,14 1,14 1,14 1,15 1,14 1,14 1,15 1,15 1,14 1,15 1,17 1,17 1,17 1,17 1,17 1,17 1,17 1,17 1,17 1,17 1,17 1,17 1,18 1,19 1,19 1,19 1,19 1,18 1,19 1,19 1,2 1,21 1,21 1,2 1,21 1,21 1,21 1,21 1,21 1,21 1,2 1,21 1,22 1,22 1,23 1,22 1,23 1,23 1,23 1,23 1,23 1,22 1,22 1,23 1,24 1,24 1,25 1,25 1,25 1,26 1,26 1,26 1,26 1,27 1,27 1,29 1,31 1,32 1,32 1,33 1,33 1,32 1,32 1,31 1,3 1,31 1,29 1,3 1,3 1,32 1,31 1,35 1,35 1,36 1,37 1,37 1,37 1,32 1,32 1,31 1,31 1,34 1,31 1,26 1,27 1,24 1,25 1,27 1,25 1,26 1,27 1,26 1,26 1,28 1,27 1,28 1,27 1,26 1,27 1,27 1,28 1,27 1,26 1,3 1,31 1,28 1,29 1,31 1,29 1,29 1,32 1,3 1,29 1,31 1,29 1,33 1,35 1,32 1,33

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	0.812685219892519
beta	0.060457480341854
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	1.15	1.16	-0.01
4	1.14	1.16138181879402	-0.0213818187940171
5	1.14	1.15246325089893	-0.0124632508989266
6	1.14	1.15018031564590	-0.0101803156458962
7	1.15	1.14925249969319	0.000747500306808258
8	1.14	1.15724228510931	-0.0172422851093077
9	1.14	1.14976487432649	-0.0097648743264922
10	1.15	1.14788446816925	0.00211553183075197
11	1.15	1.15576303471770	-0.00576303471769624
12	1.14	1.15695565206573	-0.0169556520657328
13	1.15	1.14821911435376	0.00178088564623979
14	1.17	1.15479698398989	0.0152030160101084
15	1.17	1.17302978886826	-0.00302978886826222
16	1.17	1.17629620038917	-0.00629620038917333
17	1.17	1.17659869695641	-0.00659869695640825
18	1.17	1.17633114591204	-0.00633114591203654
19	1.17	1.17596996208354	-0.00596996208354295
20	1.17	1.17560898545986	-0.00560898545986221
21	1.17	1.17526578347731	-0.00526578347731399
22	1.17	1.17494277345669	-0.00494277345669181
23	1.17	1.17463941610825	-0.0046394161082477
24	1.17	1.17435464482225	-0.00435464482225068
25	1.17	1.17408734661977	-0.00408734661977261
26	1.18	1.17383645452013	0.00616354547986719
27	1.19	1.18221914378864	0.00778085621135882
28	1.19	1.19229849362024	-0.00229849362024481
29	1.19	1.19407357315876	-0.00407357315876156
30	1.19	1.19420592532667	-0.00420592532666531
31	1.18	1.19402406753244	-0.0140240675324419
32	1.19	1.18517410756322	0.00482589243678144
33	1.19	1.19188034155046	-0.00188034155046157
34	1.2	1.19304413166044	0.0069558683395603
35	1.21	1.20173074093636	0.0082692590636435
36	1.21	1.21189101612616	-0.00189101612616405
37	1.2	1.21370127473161	-0.0137012747316145
38	1.21	1.20524032735438	0.00475967264562382
39	1.21	1.21201617557932	-0.00201617557932243
40	1.21	1.21318633154508	-0.00318633154507553
41	1.21	1.21324896534107	-0.00324896534107211
42	1.21	1.21310106648530	-0.00310106648529729
43	1.21	1.21292099845195	-0.0029209984519456
44	1.2	1.21274375192097	-0.0127437519209728
45	1.21	1.20395756132932	0.00604243867067855
46	1.22	1.21073551270882	0.00926448729118379
47	1.22	1.22058716651414	-0.000587166514138149
48	1.23	1.22240367768634	0.0075963223136597
49	1.22	1.23124401862602	-0.0112440186260154
50	1.23	1.22422064169559	0.00577935830440524
51	1.23	1.2313158682269	-0.00131586822689966
52	1.23	1.23258025660149	-0.00258025660148942
53	1.23	1.23269031974045	-0.00269031974044998
54	1.23	1.23257875298045	-0.00257875298044796
55	1.22	1.23243115326320	-0.0124311532631978
56	1.22	1.22366587483675	-0.00366587483675307
57	1.23	1.22184389357137	0.0081561064286313
58	1.24	1.23003019491751	0.00996980508248768
59	1.24	1.24018030779616	-0.000180307796157742
60	1.25	1.24207271491304	0.00792728508695784
61	1.25	1.25094353344598	-0.000943533445983968
62	1.25	1.25255881033374	-0.00255881033374128
63	1.26	1.25273565379473	0.00726434620526839
64	1.26	1.26125254978846	-0.00125254978846168
65	1.26	1.26278634888434	-0.00278634888433982
66	1.26	1.26293675072165	-0.00293675072164734
67	1.27	1.26282063212713	0.00717936787287399
68	1.27	1.27127847676588	-0.00127847676588044
69	1.29	1.27279994080258	0.0172000591974206
70	1.31	1.29018372670259	0.0198162732974145
71	1.32	1.31066730212201	0.00933269787798885
72	1.32	1.32308957326460	-0.00308957326459747
73	1.33	1.32526464855567	0.00473535144432624
74	1.33	1.33403158605679	-0.004031586056785
75	1.32	1.33547567950961	-0.0154756795096069
76	1.32	1.32685896233355	-0.00685896233355199
77	1.31	1.32490792313519	-0.0149079231351921
78	1.3	1.31568314295071	-0.0156831429507140
79	1.31	1.30505779477464	0.00494220522535782
80	1.29	1.31143718709501	-0.0214371870950059
81	1.3	1.29532516598191	0.00467483401808622
82	1.3	1.30066368664458	-0.000663686644579942
83	1.32	1.30163106161860	0.0183689383814016
84	1.31	1.31896848887255	-0.0089684888725523
85	1.35	1.31364854517407	0.0363514548259252
86	1.35	1.34694550230618	0.00305449769381649
87	1.36	1.35333259084153	0.00666740915847086
88	1.37	1.36298342827713	0.00701657172287273
89	1.37	1.37326276948991	-0.00326276948990945
90	1.37	1.37502793269946	-0.00502793269945823
91	1.32	1.37511153693983	-0.0551115369398307
92	1.32	1.3317851465829	-0.0117851465828993
93	1.31	1.32309043486348	-0.0130904348634793
94	1.31	1.31269176361439	-0.00269176361439039
95	1.34	1.31061168464157	0.0293883153584322
96	1.31	1.33604654488336	-0.0260465448833587
97	1.26	1.31515057123636	-0.0551505712363562
98	1.27	1.26789247799249	0.00210752200751174
99	1.24	1.26727073951667	-0.0272707395166698
100	1.25	1.24143383157717	0.00856616842283353
101	1.27	1.24514192974929	0.0248580702507060
102	1.25	1.26331156483824	-0.0133115648382387
103	1.26	1.24980726584827	0.0101927341517285
104	1.27	1.25590536184638	0.0140946381536176
105	1.26	1.26586698801315	-0.00586698801315366
106	1.26	1.25931783348968	0.000682166510322268
107	1.28	1.25812459686964	0.0218754031303605
108	1.27	1.27522959242229	-0.00522959242229382
109	1.28	1.27004981365884	0.00995018634116263
110	1.27	1.27769529825518	-0.00769529825518456
111	1.26	1.27062246599717	-0.0106224659971661
112	1.27	1.26064885521200	0.00935114478799615
113	1.27	1.26736695156818	0.00263304843181733
114	1.28	1.26875471961704	0.0112452803829648
115	1.27	1.27769403452734	-0.00769403452733597
116	1.26	1.27086361790069	-0.0108636179006871
117	1.3	1.26092356665368	0.0390764333463214
118	1.31	1.29348899545533	0.0165110045446704
119	1.28	1.30852706733619	-0.0285270673361875
120	1.29	1.28556174630016	0.00443825369984041
121	1.31	1.28960491871746	0.0203950812825353
122	1.29	1.30761803857114	-0.0176180385711400
123	1.29	1.29387283241798	-0.00387283241798464
124	1.32	1.29110786865923	0.0288921313407686
125	1.3	1.31639006089787	-0.0163900608978749
126	1.29	1.30406679354518	-0.0140667935451844
127	1.31	1.29294046886138	0.0170595311386199
128	1.29	1.3079482324472	-0.0179482324471998
129	1.33	1.29362385526266	0.0363761447373399
130	1.35	1.3252353620033	0.0247646379966995
131	1.32	1.34862712733485	-0.0286271273348464
132	1.33	1.32722166031264	0.0027783396873593

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
133	1.33147546005119	1.30325428527781	1.35969663482457
134	1.33347134418998	1.29621586095356	1.3707268274264
135	1.33546722832877	1.29020269643896	1.38073176021859
136	1.33746311246756	1.28470896185157	1.39021726308356
137	1.33945899660635	1.27950748315788	1.39941051005483
138	1.34145488074514	1.27447522880968	1.40843453268061
139	1.34345076488393	1.26953787638222	1.41736365338565
140	1.34544664902273	1.26464718641235	1.42624611163311
141	1.34744253316152	1.25977022715031	1.43511483917272
142	1.34943841730031	1.25488366813451	1.44399316646611
143	1.3514343014391	1.24997051254310	1.45289809033510
144	1.35343018557789	1.24501811015802	1.46184226099776

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/18/t1263822185rofp3qw8j1b92uk/1wcg21263822077.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/18/t1263822185rofp3qw8j1b92uk/1wcg21263822077.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/18/t1263822185rofp3qw8j1b92uk/2xjaa1263822077.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/18/t1263822185rofp3qw8j1b92uk/2xjaa1263822077.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/18/t1263822185rofp3qw8j1b92uk/3qla31263822077.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/18/t1263822185rofp3qw8j1b92uk/3qla31263822077.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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