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Tijdreeks 2 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: Wed, 11 Aug 2010 21:53:03 +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/11/t1281563639kxh8szcxmek1y1o.htm/, Retrieved Wed, 11 Aug 2010 23:53:59 +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/11/t1281563639kxh8szcxmek1y1o.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:

Marianne Nykjaer

Dataseries X:

» Textbox « » Textfile « » CSV «

190 189 188 186 184 183 184 186 187 187 188 190 190 190 197 187 185 182 182 191 183 192 178 181 179 175 183 179 178 175 170 179 169 178 161 168 167 165 181 181 184 181 177 183 162 166 151 162 159 152 164 158 160 161 151 149 131 138 130 147 151 140 149 143 145 139 136 133 118 130 121 142 148 131 137 128 130 119 107 113 93 106 98 118

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.568079894207184
beta	0.000575352159398017
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	188	188	0
4	186	187	-1
5	184	185.431593259799	-1.43159325979897
6	183	183.617539155709	-0.617539155709011
7	184	182.265730980750	1.73426901924967
8	186	182.250504583899	3.74949541610104
9	187	183.38131329293	3.61868670706988
10	187	184.438994957627	2.56100504237335
11	188	184.896665988376	3.10333401162416
12	190	185.663437514892	4.33656248510823
13	190	187.132198730233	2.86780126976689
14	190	187.767523559104	2.23247644089611
15	197	188.042662802384	8.95733719761637
16	187	192.140987902678	-5.14098790267758
17	185	188.228657660198	-3.22865766019768
18	182	185.401628505733	-3.40162850573324
19	182	182.475226282986	-0.47522628298637
20	191	181.211098999538	9.78890100046155
21	183	185.781015520477	-2.78101552047681
22	192	183.209306230226	8.7906937697743
23	178	187.214125532419	-9.2141255324185
24	181	180.987757390185	0.0122426098149049
25	179	180.002707487556	-1.00270748755614
26	175	178.440757110062	-3.44075711006178
27	183	175.492675163265	7.50732483673465
28	179	178.766432189624	0.23356781037603
29	178	177.908190434663	0.0918095653368596
30	175	176.969448678446	-1.9694486784461
31	170	174.859103850756	-4.8591038507565
32	179	171.105615839858	7.89438416014173
33	169	174.599708196800	-5.59970819680032
34	178	170.426247752998	7.57375224700206
35	161	173.738840775034	-12.7388407750336
36	168	165.508094462964	2.49190553703585
37	167	165.930443373893	1.06955662610659
38	165	165.545134046275	-0.545134046274711
39	181	164.242373237433	16.7576267625668
40	181	172.774440121544	8.22555987845578
41	184	176.462299844054	7.5377001559458
42	181	179.76186395527	1.23813604472991
43	177	179.483177032441	-2.48317703244112
44	183	177.089675353956	5.91032464604399
45	162	179.466284986945	-17.4662849869454
46	166	168.557403907428	-2.55740390742821
47	151	166.117122537089	-15.1171225370889
48	162	156.536976565400	5.46302343459979
49	159	158.649783307401	0.350216692599275
50	152	157.858221803227	-5.85822180322677
51	164	153.537856478825	10.4621435211753
52	158	158.492182071028	-0.492182071028481
53	160	157.223414671964	2.77658532803605
54	161	157.812475826939	3.18752417306109
55	151	158.636024907028	-7.63602490702755
56	149	153.308437566603	-4.30843756660343
57	131	149.869777494934	-18.8697774949343
58	138	138.152945466085	-0.152945466085100
59	130	137.068719406465	-7.06871940646536
60	147	132.053470835814	14.946529164186
61	151	139.549527557302	11.4504724426977
62	140	145.063287287351	-5.0632872873507
63	149	141.194257221825	7.80574277817519
64	143	144.638415670228	-1.63841567022797
65	145	142.717002076788	2.28299792321172
66	139	143.024010891378	-4.0240108913776
67	136	139.746819573972	-3.7468195739722
68	133	136.625870437866	-3.62587043786621
69	118	133.572444972977	-15.5724449729770
70	130	123.72732091879	6.27267908120999
71	121	126.294022826277	-5.29402282627674
72	142	122.288183607680	19.7118163923197
73	148	132.494101615165	15.5058983848348
74	131	140.315790206682	-9.31579020668195
75	137	134.033731740378	2.96626825962232
76	128	134.729833261155	-6.7298332611553
77	130	129.915574836747	0.0844251632531439
78	119	128.972387211203	-9.97238721120311
79	107	122.312867241108	-15.3128672411078
80	113	112.614522991297	0.385477008703418
81	93	111.834218473762	-18.8342184737621
82	106	100.129435490999	5.87056450900097
83	98	102.460861781987	-4.46086178198679
84	118	98.9217545037784	19.0782454962216

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	108.760976446016	93.0027355991867	124.519217292846
86	107.762230705102	89.6362377274199	125.888223682783
87	106.763484964187	86.5428672163812	126.984102711993
88	105.764739223273	83.6448954247714	127.884583021774
89	104.765993482358	80.8956353538283	128.636351610888
90	103.767247741444	78.2644448033138	129.270050679574
91	102.768502000529	75.7299291040873	129.807074896971
92	101.769756259615	73.2764509061585	130.263061613071
93	100.771010518700	70.8921703835138	130.649850653887
94	99.7722647777857	68.567867797423	130.976661758148
95	98.7735190368712	66.296197529809	131.250840543933
96	97.7747732959567	64.0711947771293	131.478351814784

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/11/t1281563639kxh8szcxmek1y1o/1mzje1281563579.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/11/t1281563639kxh8szcxmek1y1o/1mzje1281563579.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/11/t1281563639kxh8szcxmek1y1o/2xq0z1281563579.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/11/t1281563639kxh8szcxmek1y1o/2xq0z1281563579.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/11/t1281563639kxh8szcxmek1y1o/3xq0z1281563579.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/11/t1281563639kxh8szcxmek1y1o/3xq0z1281563579.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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