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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, 17 Aug 2010 19:20:39 +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/17/t1282072938cwhd9h1fsydtiy0.htm/, Retrieved Tue, 17 Aug 2010 21:22:24 +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/17/t1282072938cwhd9h1fsydtiy0.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:

Schrauwen Nathalie

Dataseries X:

» Textbox « » Textfile « » CSV «

125 124 123 121 141 140 125 115 116 116 117 119 114 110 108 111 124 125 118 108 107 103 113 116 113 105 102 107 119 116 113 102 96 95 101 110 103 88 79 96 118 116 114 102 98 98 101 117 109 98 93 98 114 115 112 112 103 107 104 117 123 113 97 90 109 104 92 102 90 97 99 108 106 86 72 71 96 88 83 90 85 100 108 118 124 99 92 86 112 104 93 104 96 109 113 123 127 96 100 95 133 130 117 129 122 134 141 152 161 122 126 119 160 162 145 161 151 166 169 185

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	0.852574377903842
beta	0.0116103049718575
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	123	123	0
4	121	122	-1
5	141	120.137526973558	20.8624730264425
6	140	137.120948575210	2.87905142479033
7	125	138.800664410429	-13.8006644104294
8	115	126.123073967225	-11.1230739672251
9	116	115.618225130546	0.381774869454063
10	116	114.92589468893	1.07410531107014
11	117	114.834459633846	2.16554036615371
12	119	115.694990064854	3.30500993514612
13	114	117.559718186550	-3.5597181865503
14	110	113.536518601187	-3.53651860118705
15	108	109.498091633199	-1.49809163319894
16	111	107.18274618679	3.81725381321003
17	124	109.436913731577	14.5630862684230
18	125	120.996857569535	4.00314243046468
19	118	123.593289559116	-5.59328955911619
20	108	117.952683507563	-9.952683507563
21	107	108.496851756317	-1.49685175631714
22	103	106.235428690599	-3.23542869059904
23	113	102.459713105217	10.5402868947825
24	116	110.533154260691	5.46684573930912
25	113	114.335223863793	-1.33522386379326
26	105	112.324806294824	-7.32480629482389
27	102	105.135318527689	-3.13531852768861
28	107	101.486645271192	5.51335472880787
29	119	105.266183996776	13.7338160032239
30	116	116.190223597188	-0.190223597188449
31	113	115.241100840838	-2.24110084083844
32	102	112.521268824763	-10.5212688247633
33	96	102.637831398577	-6.63783139857702
34	95	95.9996076600766	-0.999607660076649
35	101	94.1584942530072	6.84150574699275
36	110	99.0702348919082	10.9297651080918
37	103	107.575710615723	-4.57571061572277
38	88	102.816321669003	-14.8163216690034
39	79	89.179388563341	-10.1793885633410
40	96	79.3950236258935	16.6049763741065
41	118	92.6106887876597	25.3893112123403
42	116	113.566972627762	2.43302737223837
43	114	114.975400736747	-0.97540073674736
44	102	113.468235222007	-11.4682352220072
45	98	102.901627843727	-4.90162784372738
46	98	97.885022174631	0.114977825369081
47	101	97.1465840881363	3.85341591186366
48	117	99.6335861373517	17.3664138626483
49	109	113.813328035276	-4.81332803527634
50	98	109.035544839988	-11.0355448399877
51	93	98.8436220434358	-5.84362204343577
52	98	93.0203556344782	4.97964436552184
53	114	96.474020600447	17.5259793995531
54	115	110.7978528634	4.20214713660005
55	112	113.803722701084	-1.80372270108359
56	112	111.671287381053	0.328712618946582
57	103	111.360165588103	-8.36016558810333
58	107	103.558374522214	3.44162547778619
59	104	105.852555573482	-1.85255557348248
60	117	103.614715711935	13.3852842880648
61	123	114.500763915703	8.49923608429749
62	113	121.305223562580	-8.30522356258025
63	97	113.70042099093	-16.7004209909300
64	90	98.7727765965878	-8.77277659658776
65	109	90.517200057757	18.482799942243
66	104	105.681984471569	-1.68198447156894
67	92	103.638140985079	-11.6381409850785
68	102	92.9907316855148	9.0092683144852
69	90	100.035954105488	-10.0359541054881
70	97	90.7443654862721	6.25563451372788
71	99	95.4044902265872	3.59550977341283
72	108	97.8322514588458	10.1677485411542
73	106	105.963982039185	0.0360179608146325
74	86	105.458015252038	-19.4580152520378
75	72	88.139327171366	-16.139327171366
76	71	73.4903099892101	-2.49030998921013
77	96	70.4534444367942	25.5465555632058
78	88	91.5729684659963	-3.57296846599631
79	83	87.8305648520608	-4.83056485206085
80	90	82.9681507179086	7.03184928209143
81	85	88.2889327392391	-3.28893273923912
82	100	84.7779244599996	15.2220755400004
83	108	97.199605524605	10.8003944753951
84	118	105.958383915256	12.0416160847441
85	124	115.894591772799	8.10540822720124
86	99	122.555122252200	-23.5551222522002
87	92	101.989531777561	-9.98953177756073
88	86	92.8907332986035	-6.8907332986035
89	112	86.3656820579961	25.6343179420039
90	104	107.824401248976	-3.82440124897619
91	93	104.129514848028	-11.1295148480281
92	104	94.096308608965	9.903691391035
93	96	102.093508254810	-6.09350825480951
94	109	96.3915878678128	12.6084121321872
95	113	106.759251860694	6.24074813930596
96	123	111.759783658593	11.2402163414069
97	127	121.133996899810	5.86600310018953
98	96	125.984359133190	-29.9843591331898
99	100	99.972816455102	0.0271835448979232
100	95	99.5486151860766	-4.54861518607657
101	133	95.1781800175127	37.8218199824873
102	130	127.306077157401	2.69392284259881
103	117	129.511495441588	-12.5114954415883
104	129	118.629316795298	10.3706832047024
105	122	127.358553121602	-5.35855312160182
106	134	122.624403138078	11.3755968619217
107	141	132.269963701760	8.73003629823953
108	152	139.746402674700	12.2535973252996
109	161	150.348233551550	10.6517664484504
110	122	159.689822557451	-37.689822557451
111	126	127.443533082782	-1.44353308278231
112	119	126.085612281661	-7.08561228166147
113	160	119.847261331815	40.1527386681853
114	162	154.280575904178	7.71942409582229
115	145	161.138489347694	-16.1384893476941
116	161	147.496007845023	13.5039921549769
117	151	159.259617841229	-8.25961784122887
118	166	152.386372529904	13.6136274700962
119	169	164.296452246282	4.70354775371754
120	185	168.656585057495	16.3434149425053

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	183.102348116508	159.621775068916	206.582921164100
122	183.614134348091	152.606797653314	214.621471042868
123	184.125920579674	146.963567960784	221.288273198564
124	184.637706811257	142.091238989816	227.184174632697
125	185.149493042840	137.725370612698	232.573615472981
126	185.661279274422	133.722036996830	237.600521552014
127	186.173065506005	129.992797902333	242.353333109678
128	186.684851737588	126.478804110677	246.890899364499
129	187.196637969171	123.138617077901	251.254658860441
130	187.708424200754	119.941794355282	255.475054046225
131	188.220210432336	116.865221435005	259.575199429668
132	188.731996663919	113.890877706956	263.573115620882

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/17/t1282072938cwhd9h1fsydtiy0/152ya1282072837.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/17/t1282072938cwhd9h1fsydtiy0/152ya1282072837.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/17/t1282072938cwhd9h1fsydtiy0/252ya1282072837.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/17/t1282072938cwhd9h1fsydtiy0/252ya1282072837.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/17/t1282072938cwhd9h1fsydtiy0/352ya1282072837.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/17/t1282072938cwhd9h1fsydtiy0/352ya1282072837.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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