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Eigen reeks (Opgave 10)

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 18 Dec 2010 10:29:09 +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/18/t12926681307jdn3ie1xg1oukc.htm/, Retrieved Sat, 18 Dec 2010 11:28:50 +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/18/t12926681307jdn3ie1xg1oukc.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 «

98.4 96.5 97.4 99.2 100.8 101.8 102.7 100 100.8 101.7 99 101.7 100.2 101.2 99.5 100.8 100.7 99.5 99.4 101.1 97.2 98.1 97.8 95.5 96.3 93.6 96.7 95.1 97.7 96.5 98.1 97.3 97 93.7 95.6 94.6 95.1 94.5 93.6 92.1 95.9 98.1 98.2 96.2 94.1 95 93.4 95.4 93.5 94.5 94.3 95.7 98.4 99.4 99.2 99 99.4 99.3 98.6 98.7 96 98.7 100.1 100 101.5 101.5 103.8 104.1 101 104.9 104.4 105.6 103.4 101.7 103.5 101.2 105.4 105.4 108.6 110.6 110.2 106.2 108.6 107.5 106.9 108.4 109.9 108.6 106.5 105.7 105.6 104.2 105.1 102.7 108.3 104.2 105.4 104.6 106.4 111 111.7 113.8 115.9 117.3 113.6 113.6 114.6 113.2 112.8 109.6 111.1 109.7 113 111 113.3 111.8 107.2 106.4 110 108.2 108.2

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	0.727358642373541
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	96.5	98.4	-1.90000000000001
3	97.4	97.0180185794903	0.381981420509732
4	99.2	97.2958560669241	1.90414393307586
5	100.8	98.68085161297	2.11914838702998
6	101.8	100.222232506748	1.57776749325177
7	102.7	101.369835328621	1.33016467137907
8	100	102.337342098128	-2.33734209812846
9	100.8	100.637256122871	0.162743877128776
10	101.7	100.755629288394	0.944370711605785
11	99	101.442525487085	-2.44252548708513
12	101.7	99.6659334648361	2.03406653516389
13	100.2	101.145429338350	-0.945429338350365
14	101.2	100.457763138348	0.742236861652273
15	99.5	100.997635534359	-1.49763553435872
16	100.8	99.9083173853172	0.891682614682807
17	100.7	100.556890441361	0.143109558639040
18	99.5	100.660982415643	-1.16098241564333
19	99.4	99.8165318219814	-0.416531821981437
20	101.1	99.5135638014396	1.58643619856035
21	97.2	100.667471881037	-3.46747188103674
22	98.1	98.1453762411774	-0.0453762411774363
23	97.8	98.1123714399986	-0.3123714399986
24	95.5	97.885165373485	-2.38516537348495
25	96.3	96.1502947255906	0.149705274409442
26	93.6	96.2591841507412	-2.65918415074117
27	96.7	94.3250035770368	2.37499642296318
28	95.1	96.0524777508853	-0.95247775088535
29	97.7	95.3596848271104	2.34031517288963
30	96.5	97.0619332939896	-0.561933293989568
31	98.1	96.6532062561688	1.44679374383117
32	97.3	97.7055441894764	-0.405544189476402
33	97	97.4105681183964	-0.41056811839637
34	93.7	97.1119378491977	-3.41193784919773
35	95.6	94.6302353673424	0.969764632657629
36	94.6	95.3356020539741	-0.735602053974105
37	95.1	94.8005555426683	0.299444457331688
38	94.5	95.0183590566194	-0.51835905661936
39	93.6	94.6413261169347	-1.04132611693468
40	92.1	93.883908566253	-1.78390856625296
41	95.9	92.5863672533847	3.31363274661534
42	98.1	94.9965666692873	3.10343333071269
43	98.2	97.2538757234113	0.94612427658872
44	96.2	97.9420473927475	-1.74204739274749
45	94.1	96.6749541662083	-2.57495416620831
46	95	94.802038999701	0.197961000299060
47	93.4	94.9460276441214	-1.54602764412137
48	95.4	93.8215110758213	1.57848892417871
49	93.5	94.9696386367136	-1.46963863671360
50	94.5	93.9006842731339	0.599315726866109
51	94.3	94.3366017465803	-0.0366017465803452
52	95.7	94.3099791498792	1.39002085012083
53	98.4	95.321022828294	3.07897717170603
54	99.4	97.5605434838052	1.8394565161948
55	99.2	98.8984880781298	0.301511921870187
56	99	99.1177953802808	-0.117795380280754
57	99.4	99.0321158924019	0.367884107598130
58	99.3	99.2996995774553	0.000300422544739831
59	98.6	99.2999180923895	-0.699918092389538
60	98.7	98.7908266189364	-0.09082661893639
61	96	98.7247630926954	-2.72476309269544
62	98.7	96.742883108803	1.95711689119705
63	100.1	98.1664089937504	1.93359100624963
64	100	99.5728231229618	0.427176877038221
65	101.5	99.8835339162977	1.61646608370233
66	101.5	101.059284492382	0.440715507617725
67	103.8	101.379842725676	2.42015727432393
68	104.1	103.140165035059	0.959834964941223
69	101	103.838309292061	-2.83830929206107
70	104.9	101.773840498751	3.12615950124868
71	104.4	104.047679629423	0.352320370577289
72	105.6	104.303942895846	1.29605710415363
73	103.4	105.246641231562	-1.84664123156213
74	101.7	103.903470772422	-2.20347077242209
75	103.5	102.300757262883	1.19924273711662
76	101.2	103.173036832029	-1.97303683202885
77	105.4	101.737931440531	3.66206855946865
78	105.4	104.401568656225	0.998431343774698
79	108.6	105.127786322936	3.47221367706354
80	110.6	107.653330949116	2.94666905088376
81	110.2	109.796616149491	0.403383850508817
82	106.2	110.090020879353	-3.89002087935269
83	108.6	107.260580573742	1.33941942625800
84	107.5	108.234818869194	-0.73481886919376
85	106.9	107.700342014107	-0.800342014106519
86	108.4	107.118206333291	1.28179366670851
87	109.9	108.050530034512	1.84946996548841
88	108.6	109.395757997720	-0.795757997719889
89	106.5	108.816956540840	-2.31695654084045
90	105.7	107.131698176856	-1.43169817685624
91	105.6	106.090340134649	-0.490340134649415
92	104.2	105.733687000010	-1.53368700000955
93	105.1	104.618146505857	0.481853494143337
94	102.7	104.968626809180	-2.26862680917969
95	108.3	103.318521493203	4.98147850679746
96	104.2	106.941842936920	-2.74184293691971
97	105.4	104.947539780720	0.452460219279700
98	104.6	105.276640631544	-0.676640631543634
99	106.4	104.784480220409	1.61551977959073
100	111	105.95954249402	5.04045750598
101	111.7	109.625762822511	2.07423717748887
102	113.8	111.134477159890	2.66552284010983
103	115.9	113.073268234088	2.82673176591189
104	117.3	115.129316013696	2.17068398630404
105	113.6	116.708181770996	-3.10818177099605
106	113.6	114.447418897794	-0.84741889779417
107	114.6	113.831041438773	0.76895856122708
108	113.2	114.390350093909	-1.19035009390855
109	112.8	113.524538665654	-0.724538665654009
110	109.6	112.997539205457	-3.39753920545678
111	111.1	110.526309701565	0.573690298435139
112	109.7	110.943588298178	-1.24358829817751
113	113	110.039053601943	2.96094639805651
114	111	112.192723554175	-1.19272355417471
115	113.3	111.325185769083	1.97481423091675
116	111.8	112.761583967023	-0.961583967022804
117	107.2	112.062167558241	-4.86216755824093
118	106.4	108.525627964086	-2.12562796408612
119	110	106.979534093937	3.02046590606280
120	108.2	109.176496074707	-0.976496074706603
121	108.2	108.466233215525	-0.266233215524920

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
122	108.272586185326	104.467761022791	112.077411347861
123	108.272586185326	103.567737796666	112.977434573986
124	108.272586185326	102.814152142206	113.731020228446
125	108.272586185326	102.152667391264	114.392504979388
126	108.272586185326	101.556016384547	114.989155986105
127	108.272586185326	101.008206395450	115.536965975201
128	108.272586185326	100.498905102700	116.046267267951
129	108.272586185326	100.02097898326	116.524193387392
130	108.272586185326	99.5692577840759	116.975914586576
131	108.272586185326	99.139852251677	117.405320118975
132	108.272586185326	98.7297494505996	117.815422920052
133	108.272586185326	98.3365589717732	118.208613398879

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/18/t12926681307jdn3ie1xg1oukc/1jvgr1292668145.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t12926681307jdn3ie1xg1oukc/1jvgr1292668145.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t12926681307jdn3ie1xg1oukc/2u4xb1292668145.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t12926681307jdn3ie1xg1oukc/2u4xb1292668145.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t12926681307jdn3ie1xg1oukc/3u4xb1292668145.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t12926681307jdn3ie1xg1oukc/3u4xb1292668145.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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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