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Tijdreeks B - 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: Thu, 19 Aug 2010 23:16:18 +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/20/t1282259766khl3831gt14h1lh.htm/, Retrieved Fri, 20 Aug 2010 01:16:10 +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/20/t1282259766khl3831gt14h1lh.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:

Dieter Van Boxel

Dataseries X:

» Textbox « » Textfile « » CSV «

93 92 91 89 87 86 87 89 90 90 91 93 93 87 89 92 98 92 92 87 92 98 101 102 102 90 87 92 105 90 88 83 98 109 118 118 115 107 101 111 128 115 111 105 120 132 135 142 139 127 113 130 143 139 137 134 139 157 152 153 147 132 117 123 139 134 134 128 118 144 140 151 144 135 122 124 146 146 147 148 132 161 159 173

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	0.373511042776394
beta	0.00909734578251893
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	93	90.7626399476373	2.23736005236272
14	87	85.885787896059	1.11421210394097
15	89	88.6114326732123	0.388567326787694
16	92	91.6676461733725	0.332353826627482
17	98	97.3412364056725	0.658763594327468
18	92	91.168401138645	0.831598861355047
19	92	90.0878122556585	1.91218774434149
20	87	93.4508464783774	-6.45084647837741
21	92	92.6931746271342	-0.693174627134184
22	98	92.716936536819	5.28306346318102
23	101	95.4667733386968	5.5332266613032
24	102	99.2675375076998	2.73246249230019
25	102	101.692979736729	0.307020263271014
26	90	94.7887630758412	-4.7887630758412
27	87	94.9788281228176	-7.97882812281763
28	92	94.9499166765758	-2.94991667657584
29	105	99.687138556331	5.31286144366892
30	90	95.1041093141956	-5.10410931419564
31	88	92.4343723119153	-4.43437231191533
32	83	88.0748444720858	-5.07484447208577
33	98	91.3458622739151	6.65413772608485
34	109	97.8405971954542	11.1594028045458
35	118	102.887990859300	15.1120091406997
36	118	108.494246261581	9.50575373841885
37	115	111.934036314501	3.0659636854986
38	107	101.713438392532	5.28656160746831
39	101	103.518259211184	-2.51825921118447
40	111	109.802419307191	1.19758069280938
41	128	123.445761586353	4.55423841364714
42	115	109.522841086785	5.47715891321491
43	111	111.163069326092	-0.163069326092099
44	105	107.185085362127	-2.18508536212738
45	120	122.379409751109	-2.37940975110898
46	132	129.700417036171	2.29958296382898
47	135	134.058208951342	0.941791048657706
48	142	130.181452402792	11.8185475972083
49	139	129.875616334130	9.1243836658702
50	127	121.687176658782	5.31282334121799
51	113	117.840334277878	-4.84033427787783
52	130	127.035302786418	2.96469721358189
53	143	145.798997223635	-2.79899722363479
54	139	127.688213888111	11.3117861118893
55	137	127.423662240653	9.57633775934681
56	134	124.914865419943	9.08513458005665
57	139	147.786908234961	-8.78690823496126
58	157	157.979956774861	-0.97995677486125
59	152	160.838013178872	-8.83801317887244
60	153	160.315987937495	-7.31598793749484
61	147	150.314188458132	-3.31418845813235
62	132	134.002251470766	-2.00225147076577
63	117	120.382999554911	-3.38299955491098
64	123	135.825886484309	-12.8258864843092
65	139	145.114987861629	-6.11498786162855
66	134	134.322702108223	-0.322702108222501
67	134	128.575952189562	5.42404781043794
68	128	124.277599055681	3.72240094431938
69	118	133.217807005481	-15.2178070054806
70	144	144.256997137560	-0.256997137560319
71	140	142.371677286859	-2.37167728685895
72	151	144.771578776355	6.22842122364494
73	144	142.415576828681	1.5844231713194
74	135	129.065124727371	5.93487527262945
75	122	117.548478509584	4.45152149041594
76	124	129.869070846281	-5.8690708462806
77	146	146.564514681817	-0.564514681816547
78	146	141.19988053239	4.80011946761013
79	147	140.769207503633	6.23079249636666
80	148	135.172348446859	12.8276515531415
81	132	134.791961754875	-2.79196175487539
82	161	163.374736171705	-2.37473617170534
83	159	159.004491639959	-0.00449163995881463
84	173	168.832959185330	4.16704081466963

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	161.858561825761	150.123013955486	173.594109696037
86	149.213768800595	136.795030289055	161.632507312136
87	132.981614256612	120.082387859530	145.880840653694
88	137.489660098904	123.725832588980	151.253487608828
89	162.139783985959	146.731885454870	177.547682517048
90	160.131188383047	144.165785027919	176.096591738174
91	158.618845241228	142.098391841271	175.139298641184
92	154.229969759351	137.341785262358	171.118154256344
93	138.602498657158	122.057751410036	155.147245904281
94	169.950555024538	150.625180674227	189.275929374849
95	167.821139854713	148.101900772924	187.540378936501
96	180.908500239743	150.662431825259	211.154568654228

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/20/t1282259766khl3831gt14h1lh/1topt1282259776.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/20/t1282259766khl3831gt14h1lh/1topt1282259776.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/20/t1282259766khl3831gt14h1lh/2topt1282259776.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/20/t1282259766khl3831gt14h1lh/2topt1282259776.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/20/t1282259766khl3831gt14h1lh/3mxow1282259776.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/20/t1282259766khl3831gt14h1lh/3mxow1282259776.ps (open in new window)

Parameters (Session):

par1 = multiplicative ; par2 = 12 ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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

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