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Opgave 10 triple exponential smoothing visproducten

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 30 Dec 2010 14:16:27 +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/Dec/30/t1293718466d05ka1ax4q75sfo.htm/, Retrieved Thu, 30 Dec 2010 15:14:27 +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/Dec/30/t1293718466d05ka1ax4q75sfo.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:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

96,1 96,5 96,9 97,8 98,9 100,2 101,2 101 101,6 102,4 103,7 103,7 104,6 104,5 104,5 105,6 106,1 107,6 107,7 108,3 108,1 108,1 108 108,2 108,9 109,8 109,9 109,8 110,9 111,1 112,2 112,7 114,6 114,2 114,7 114,7 116 116,3 116,4 116,6 118,1 117,2 108,3 109,5 110,5 110,6 111,2 111,1 111 112,4 112,5 112,4 111,8 111,6 112,9 112,8 113,7 113,8 114 113,8 113,9 114,4 114,4 114,5 113,8 114,3 115 115,4 115,3 114,9 114,3 114,5 115,5 115,8 115,8 116 114,9 114,1 114,1 113,5 115 114,7 115,4 116,1 116,6 117,2 118,2 118 117,7 118,5 117,5 118 117,7 116,3 115 115,7 113,6 114,8 114,9 117,3 117,3 117,7 120 119,6 119,2 117,3 117,5 119 112,5 118,9 118,4 119,4 120,6 118,6 122 122,6 120,6 117,4 116,4 122,2 121 122,4 124,9 126,1 124,5 123,2 126,4 123,9 116 126,6 125,9 126,6 116,7 126,4 129 128,7 128,4 129,2 133,3 128,9 132,7 127,7 131,8 133,9

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	3 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.474740092278407
beta	0.0325150620496534
gamma	0.446603668717535

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	104.6	100.866372863248	3.73362713675211
14	104.5	102.59719311511	1.90280688489034
15	104.5	103.588221706064	0.911778293936095
16	105.6	105.28951035431	0.310489645690467
17	106.1	106.201802622241	-0.101802622241209
18	107.6	107.96679177485	-0.36679177484973
19	107.7	108.300318080196	-0.600318080196118
20	108.3	107.792880120374	0.507119879625762
21	108.1	108.656515365481	-0.556515365480948
22	108.1	109.214943165044	-1.11494316504383
23	108	110.007719076527	-2.00771907652695
24	108.2	109.062333575723	-0.862333575722971
25	108.9	110.452409464733	-1.55240946473307
26	109.8	109.189757248796	0.610242751203941
27	109.9	109.260223425464	0.639776574535659
28	109.8	110.612679245938	-0.812679245938483
29	110.9	110.799053378796	0.100946621203605
30	111.1	112.505275379692	-1.40527537969247
31	112.2	112.182121941232	0.0178780587679768
32	112.7	112.128606556148	0.571393443851562
33	114.6	112.674890391988	1.92510960801241
34	114.2	114.22040036075	-0.0204003607499317
35	114.7	115.280218126212	-0.580218126212301
36	114.7	115.260096277888	-0.56009627788778
37	116	116.615325403069	-0.615325403068979
38	116.3	116.302880177104	-0.00288017710359156
39	116.4	116.077750328174	0.322249671825645
40	116.6	116.922390418307	-0.322390418306753
41	118.1	117.547062078164	0.552937921835962
42	117.2	119.112722087452	-1.91272208745173
43	108.3	118.872871602086	-10.5728716020862
44	109.5	113.748227723022	-4.24822772302151
45	110.5	112.076485986073	-1.57648598607256
46	110.6	111.20169625179	-0.601696251790017
47	111.2	111.543684499657	-0.343684499657016
48	111.1	111.333684751072	-0.233684751071877
49	111	112.529067115873	-1.52906711587259
50	112.4	111.610545016562	0.789454983438475
51	112.5	111.534112729783	0.965887270216783
52	112.4	112.239301465297	0.160698534702945
53	111.8	113.012318708271	-1.21231870827108
54	111.6	112.847956574348	-1.247956574348
55	112.9	110.588852395158	2.31114760484206
56	112.8	112.959982607497	-0.159982607497184
57	113.7	113.814506592089	-0.114506592089342
58	113.8	113.843680265151	-0.0436802651510817
59	114	114.500953966612	-0.50095396661159
60	113.8	114.229516245773	-0.429516245772732
61	113.9	115.012452048033	-1.11245204803343
62	114.4	114.826427836268	-0.426427836267976
63	114.4	114.186214766161	0.213785233839161
64	114.5	114.305916844033	0.194083155967107
65	113.8	114.733661853709	-0.933661853708713
66	114.3	114.65849592189	-0.358495921889542
67	115	113.635556271611	1.36444372838872
68	115.4	114.941946095987	0.4580539040129
69	115.3	116.074467869488	-0.774467869487779
70	114.9	115.770681998778	-0.870681998777584
71	114.3	115.879046297837	-1.57904629783695
72	114.5	115.046881460982	-0.546881460982434
73	115.5	115.546410948045	-0.0464109480452777
74	115.8	115.976381221242	-0.176381221242366
75	115.8	115.55789059433	0.242109405670462
76	116	115.639686923577	0.360313076422969
77	114.9	115.837633494259	-0.937633494259103
78	114.1	115.851280272102	-1.75128027210195
79	114.1	114.505577159086	-0.405577159085951
80	113.5	114.665995808558	-1.16599580855785
81	115	114.620270602632	0.379729397367583
82	114.7	114.741557862007	-0.0415578620067407
83	115.4	114.989868547939	0.410131452061378
84	116.1	115.287377959417	0.812622040583463
85	116.6	116.513909206286	0.086090793713538
86	117.2	116.942528942391	0.257471057608697
87	118.2	116.801107596592	1.3988924034081
88	118	117.45059152539	0.549408474609749
89	117.7	117.427539735712	0.272460264288
90	118.5	117.837184761774	0.662815238226457
91	117.5	118.0028790488	-0.502879048800438
92	118	117.986871727855	0.0131282721451811
93	117.7	118.929874482049	-1.22987448204903
94	116.3	118.229694870561	-1.92969487056135
95	115	117.699947640108	-2.69994764010795
96	115.7	116.579745238994	-0.879745238994346
97	113.6	116.770636252919	-3.17063625291927
98	114.8	115.581314731849	-0.781314731849307
99	114.9	115.086418005956	-0.186418005955801
100	117.3	114.63146569634	2.6685343036597
101	117.3	115.429640475063	1.87035952493707
102	117.7	116.594268402684	1.10573159731594
103	120	116.608443142467	3.39155685753283
104	119.6	118.534104899392	1.06589510060813
105	119.2	119.673339350611	-0.473339350611042
106	117.3	119.167857753131	-1.86785775313113
107	117.5	118.487439828374	-0.987439828373653
108	119	118.634317659878	0.365682340122206
109	112.5	118.925379233257	-6.42537923325713
110	118.9	116.747474315413	2.15252568458691
111	118.4	117.826308648487	0.573691351513247
112	119.4	118.455033940191	0.944966059809346
113	120.6	118.274218117927	2.32578188207302
114	118.6	119.50920915679	-0.90920915679034
115	122	119.105448026496	2.89455197350368
116	122.6	120.244350592489	2.35564940751112
117	120.6	121.649463464064	-1.04946346406393
118	117.4	120.549107749505	-3.14910774950516
119	116.4	119.45294793779	-3.05294793778954
120	122.2	118.890769890221	3.30923010977887
121	121	118.985725367809	2.0142746321908
122	122.4	122.956510778649	-0.556510778649113
123	124.9	122.466889544522	2.43311045547841
124	126.1	124.182153091154	1.91784690884626
125	124.5	124.918839042663	-0.418839042662526
126	123.2	124.181328363591	-0.98132836359052
127	126.4	124.72386759369	1.67613240630983
128	123.9	125.227352922982	-1.32735292298221
129	116	124.097796518375	-8.09779651837529
130	126.6	119.062555345207	7.53744465479305
131	125.9	123.131029348811	2.76897065118931
132	126.6	126.98381809783	-0.383818097830272
133	116.7	125.123364145429	-8.4233641454286
134	126.4	123.476407044305	2.92359295569538
135	129	125.334450134405	3.66554986559495
136	128.7	127.527159429278	1.17284057072166
137	128.4	127.36374354723	1.03625645277029
138	129.2	127.209265103767	1.99073489623281
139	133.3	129.856224917405	3.44377508259512
140	128.9	130.59166805435	-1.69166805435049
141	132.7	127.792655590743	4.90734440925677
142	127.7	132.891717955207	-5.19171795520701
143	131.8	129.894535160677	1.90546483932343
144	133.9	132.680453160381	1.21954683961874

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
145	129.802650577125	125.352785565395	134.252515588855
146	135.053840765468	130.098135759507	140.009545771429
147	135.890293728639	130.447767175451	141.332820281826
148	135.893796322636	129.977971400085	141.809621245186
149	135.259165491255	128.87981472758	141.638516254929
150	134.938262920505	128.102480112309	141.774045728701
151	137.051894143682	129.764792375331	144.338995912032
152	134.965487249412	127.230674435004	142.70030006382
153	134.561442255238	126.381357033234	142.741527477243
154	134.929821018225	126.305977128069	143.55366490838
155	136.110471645627	127.043640156897	145.177303134356
156	137.84970956157	128.340057621961	147.359361501179

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/30/t1293718466d05ka1ax4q75sfo/1f8y41293718582.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/30/t1293718466d05ka1ax4q75sfo/1f8y41293718582.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/30/t1293718466d05ka1ax4q75sfo/2qhy71293718582.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/30/t1293718466d05ka1ax4q75sfo/2qhy71293718582.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/30/t1293718466d05ka1ax4q75sfo/3qhy71293718582.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/30/t1293718466d05ka1ax4q75sfo/3qhy71293718582.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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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