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Tijdreeks A - Stap 32

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 10 Aug 2010 16:31:59 +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/10/t1281457904741aenpfigeuxwn.htm/, Retrieved Tue, 10 Aug 2010 18:31:48 +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/10/t1281457904741aenpfigeuxwn.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:

Platini Olivier

Dataseries X:

» Textbox « » Textfile « » CSV «

94 93 92 90 110 109 94 84 85 85 86 88 93 94 90 91 104 103 88 79 82 88 93 89 94 96 94 92 113 122 107 98 103 110 113 110 123 124 118 117 139 146 134 121 123 122 127 122 139 136 127 123 140 146 138 120 122 115 115 102 119 114 108 102 121 109 102 95 98 92 94 90 113 111 103 90 108 99 95 91 85 72 90 90 114 115 104 93 101 90 79 75 71 61 84 87 107 99 93 74 87 71 67 61 63 52 80 84 102 93 87 72 83 72 66 64 64 47 77 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	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.365777387991567
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	93	94.5619658119659	-1.56196581196586
14	94	95.2432564147553	-1.24325641475525
15	90	90.9161237083847	-0.916123708384688
16	91	91.3753154155436	-0.375315415543625
17	104	103.615655900796	0.384344099204498
18	103	102.217195992448	0.782804007551817
19	88	91.9644837085955	-3.96448370859551
20	79	80.3086542572194	-1.30865425721936
21	82	80.6659338321853	1.33406616781467
22	88	80.9898607814122	7.01013921858778
23	93	84.5566335718669	8.4433664281331
24	89	89.9393151340941	-0.939315134094144
25	94	93.8993899050004	0.100610094999595
26	96	95.3909458867479	0.609054113252128
27	94	91.9488214465689	2.05117855343114
28	92	93.8363780725177	-1.83637807251775
29	113	106.024088117090	6.97591188290978
30	122	107.289386939289	14.7106130607113
31	107	99.1203150560555	7.87968494394453
32	98	93.4812017690377	4.51879823096229
33	103	97.6461047445488	5.35389525545118
34	110	103.040288153836	6.9597118461641
35	113	107.497600856162	5.50239914383845
36	110	105.853834278932	4.1461657210683
37	123	112.333607048810	10.6663929511903
38	124	118.012354179097	5.98764582090315
39	118	117.452224894107	0.547775105892953
40	117	116.324294216278	0.675705783722094
41	139	135.019821285508	3.9801787144915
42	146	140.094871038333	5.9051289616668
43	134	124.372623108693	9.62737689130746
44	121	117.241225667423	3.75877433257693
45	123	121.657766502723	1.34223349727658
46	122	126.603019945168	-4.60301994516817
47	127	125.906686146231	1.09331385376878
48	122	121.790021964285	0.209978035714784
49	139	130.965301828747	8.03469817125347
50	136	132.714067290540	3.28593270946033
51	127	127.715623426682	-0.715623426681802
52	123	126.206706662264	-3.2067066622639
53	140	145.577906501360	-5.57790650135954
54	146	148.377671783479	-2.37767178347923
55	138	131.986496436504	6.01350356349587
56	120	119.811225405218	0.188774594782117
57	122	121.389316220708	0.610683779292174
58	115	122.296371150803	-7.29637115080284
59	115	124.227614083759	-9.22761408375862
60	102	115.775556289368	-13.7755562893678
61	119	124.797858381330	-5.79785838133036
62	114	118.47521300308	-4.47521300307987
63	108	108.100040147905	-0.100040147904664
64	102	105.236388510888	-3.23638851088785
65	121	123.092862845378	-2.09286284537787
66	109	129.197039514833	-20.1970395148332
67	102	111.609815529802	-9.60981552980158
68	95	90.0257128280314	4.9742871719686
69	98	93.6218202792357	4.37817972076428
70	92	90.8921070030122	1.10789299698779
71	94	94.672601786576	-0.672601786575981
72	90	86.4653662595795	3.53463374042047
73	113	106.878980851325	6.12101914867459
74	111	105.754842970346	5.24515702965358
75	103	101.709995232254	1.29000476774644
76	90	97.365647542735	-7.36564754273498
77	108	114.436982128694	-6.43698212869378
78	99	107.47009997801	-8.47009997800993
79	95	100.886982155598	-5.88698215559765
80	91	89.9141754306875	1.08582456931245
81	85	91.709906363049	-6.70990636304892
82	72	82.8503321332926	-10.8503321332926
83	90	81.127548511388	8.87245148861194
84	90	79.0800015448966	10.9199984551034
85	114	103.835359660628	10.1646403393723
86	115	103.634795415925	11.3652045840753
87	104	99.3200756882346	4.67992431176539
88	93	90.7260734980385	2.27392650196151
89	101	111.912326903993	-10.9123269039928
90	90	102.019015518124	-12.0190155181241
91	79	95.776056371702	-16.7760563717020
92	75	85.2425842164814	-10.2425842164814
93	71	77.9504105386372	-6.95041053863723
94	61	66.3769136729022	-5.37691367290218
95	84	79.1648181035855	4.8351818964145
96	87	76.9391297963404	10.0608702036596
97	107	100.901173027148	6.0988269728521
98	99	99.9748511803374	-0.97485118033741
99	93	86.9064621711573	6.09353782884267
100	74	77.3035896254469	-3.30358962544692
101	87	88.0866936731075	-1.08669367310749
102	71	81.0854898022608	-10.0854898022608
103	67	72.5327477662147	-5.53274776621473
104	61	70.2554994408607	-9.25549944086075
105	63	65.4123500431171	-2.41235004311707
106	52	56.4967203841547	-4.49672038415467
107	80	76.0833215429755	3.91667845702447
108	84	76.835915134572	7.16408486542801
109	102	97.2255623840558	4.77443761594418
110	93	91.3285222227689	1.67147777723112
111	87	83.7110326475485	3.28896735245145
112	72	67.1224409191098	4.87755908089021
113	83	82.3040297127886	0.695970287211424
114	72	70.247644023051	1.75235597694895
115	66	68.912370241473	-2.91237024147304
116	64	65.2325434717181	-1.23254347171812
117	64	67.6640900377397	-3.66409003773971
118	47	56.9686473910139	-9.96864739101389
119	77	79.8897091709066	-2.88970917090664
120	79	80.212258648891	-1.21225864889095

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	96.0224605264407	83.440745007033	108.604176045848
122	86.4110717509991	73.0140961739883	99.80804732801
123	79.2080418636299	65.042649394279	93.3734343329808
124	62.4239410432473	47.5297229365301	77.3181591499646
125	73.1693708494714	57.5803643958778	88.758377303065
126	61.5283986573916	45.2742757524206	77.7825215623626
127	56.593677837182	39.7006052744532	73.4867503999108
128	55.0445143688531	37.5357939755936	72.5532347621126
129	56.3847556522234	38.2813118083284	74.4881994961185
130	43.0310614567175	24.3518198177006	61.7103030957343
131	74.088051729307	54.850238511363	93.325864947251
132	76.5314685314685	56.7508505783251	96.3120864846119

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/10/t1281457904741aenpfigeuxwn/1m8kg1281457916.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/10/t1281457904741aenpfigeuxwn/1m8kg1281457916.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/10/t1281457904741aenpfigeuxwn/2m8kg1281457916.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/10/t1281457904741aenpfigeuxwn/2m8kg1281457916.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/10/t1281457904741aenpfigeuxwn/3eh111281457916.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/10/t1281457904741aenpfigeuxwn/3eh111281457916.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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