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opgave 10 oef 2 verbetering

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 16 Jan 2011 17:15:18 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Jan/16/t1295197995bwab2i81qci0w6z.htm/, Retrieved Sun, 16 Jan 2011 18:13:18 +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/2011/Jan/16/t1295197995bwab2i81qci0w6z.htm/},
    year = {2011},
}
@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 = {2011},
    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 «

102,8 106,3 103,7 106,9 104,3 105,4 96,2 95,7 95,9 93,6 94,7 94,5 96,6 96,7 98,9 102 105,2 106,4 99,3 96,4 93,1 95,6 93,3 96,7 105,6 105,2 107 104,9 104,5 105,2 99,7 100,2 98,5 98,4 97,1 98,4 100,6 111,3 119 117,8 108,8 109,3 103,5 103,7 110 105,5 110,4 106,7 110,2 105,2 108 108,1 107,2 106 99,4 100,2 100,3 100,8 99,5 100,2 103 111 120,5 109,5 106,6 105,5 103,9 104,9 104,8 99,6 97 95,4 99,3 103,9 107,4 107,4 111 113,2 108,5 113,3 113,8 105,3 107,5 109,4 118,9 119 115 124,1 120,5 117,7 117,1 118,1 119,6 118,8 124,9 124 124,9 121,7 121,6 125,1 127,9 129 130,1 130,3 127,9 124,1 125,7 129,2 129,2 132,6 131,5 131 125,8 127,2 127,3 127,5 122 118,4 118,3 115,5

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	1 seconds
R Server	'Gwilym Jenkins' @ www.wessa.org

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.792089098495697
beta	0
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	96.6	97.6449252136752	-1.04492521367523
14	96.7	96.6754972639257	0.0245027360742682
15	98.9	98.8989848681327	0.00101513186729107
16	102	101.949701530431	0.0502984695690856
17	105.2	105.081121653927	0.118878346073132
18	106.4	106.258529816644	0.141470183355509
19	99.3	94.6038327273885	4.69616727261149
20	96.4	98.398528216149	-1.99852821614893
21	93.1	97.5320950571806	-4.43209505718056
22	95.6	92.042226799637	3.55777320036292
23	93.3	96.0435460873106	-2.74354608731063
24	96.7	93.507825727744	3.19217427225605
25	105.6	97.6648067468625	7.93519325313748
26	105.2	104.030778467002	1.16922153299844
27	107	107.15610202213	-0.15610202213044
28	104.9	110.092614442731	-5.19261444273108
29	104.5	109.085438907981	-4.58543890798077
30	105.2	106.541305747153	-1.34130574715311
31	99.7	94.6590891857357	5.04091081426432
32	100.2	97.3349521012511	2.86504789874886
33	98.5	99.8149394868075	-1.3149394868075
34	98.4	98.4553168871981	-0.0553168871981313
35	97.1	98.284633930865	-1.18463393086506
36	98.4	98.2178118669663	0.182188133033733
37	100.6	100.976741030751	-0.376741030750779
38	111.3	99.3522009373226	11.9477990626774
39	119	110.739569035869	8.26043096413089
40	117.8	119.295579644212	-1.4955796442121
41	108.8	121.343023482929	-12.5430234829292
42	109.3	113.170264979995	-3.87026497999506
43	103.5	100.611819778583	2.88818022141652
44	103.7	101.130142639191	2.5698573608086
45	110	102.507247872059	7.49275212794144
46	105.5	108.385991053644	-2.88599105364376
47	110.4	105.738364624043	4.66163537595726
48	106.7	110.586485952449	-3.88648595244908
49	110.2	110.006455261471	0.193544738528786
50	105.2	111.396038550367	-6.19603855036718
51	108	107.645226645198	0.35477335480212
52	108.1	107.910871084086	0.189128915914125
53	107.2	108.995870199595	-1.79587019959548
54	106	111.138975691126	-5.13897569112636
55	99.4	98.9807530008759	0.419246999124127
56	100.2	97.4772779782737	2.72272202172627
57	100.3	99.9989891316444	0.301010868355576
58	100.8	98.023378610945	2.77662138905507
59	99.5	101.430279581408	-1.9302795814078
60	100.2	99.2797693223174	0.920230677682596
61	103	103.355369332751	-0.355369332751238
62	111	102.981699747944	8.01830025205578
63	120.5	111.851895859287	8.64810414071262
64	109.5	118.652157919295	-9.15215791929545
65	106.6	111.925322611123	-5.32532261112334
66	105.5	110.577719247255	-5.07771924725547
67	103.9	99.6236322086994	4.27636779130063
68	104.9	101.654258085703	3.24574191429681
69	104.8	104.086747445195	0.71325255480491
70	99.6	102.95237548541	-3.35237548540977
71	97	100.525948822834	-3.52594882283444
72	95.4	97.7041785105199	-2.30417851051985
73	99.3	98.960548005761	0.339451994239027
74	103.9	100.878216011742	3.02178398825835
75	107.4	105.921669154336	1.47833084566402
76	107.4	103.341963416741	4.05803658325864
77	111	107.874419941881	3.12558005811931
78	113.2	113.272163893365	-0.072163893365385
79	108.5	108.227739351478	0.272260648521694
80	113.3	106.872477256277	6.42752274372337
81	113.8	111.298688378778	2.50131162122211
82	105.3	110.735330121946	-5.43533012194581
83	107.5	106.622930010048	0.87706998995185
84	109.4	107.542762266878	1.85723773312245
85	118.9	112.644983804499	6.25501619550066
86	119	119.805991788761	-0.805991788761162
87	115	121.496604732586	-6.49660473258601
88	124.1	113.136388407773	10.9636115922268
89	120.5	122.944807739605	-2.44480773960522
90	117.7	123.265462414386	-5.56546241438573
91	117.1	113.94146561622	3.15853438378014
92	118.1	116.152135573199	1.94786442680051
93	119.6	116.213756083905	3.38624391609488
94	118.8	114.70122871101	4.09877128899019
95	124.9	119.453103188588	5.4468968114125
96	124	124.196433011817	-0.196433011817177
97	124.9	128.586310425202	-3.68631042520201
98	121.7	126.404841433083	-4.70484143308323
99	121.6	123.824077609704	-2.22407760970408
100	125.1	122.478252758505	2.62174724149479
101	127.9	122.891415725964	5.00858427403639
102	129	128.467002834847	0.532997165152693
103	130.1	125.787343426278	4.31265657372221
104	130.3	128.660469506063	1.63953049393731
105	127.9	128.776916846176	-0.87691684617559
106	124.1	124.035728516796	0.0642714832035693
107	125.7	125.872209673035	-0.172209673035312
108	129.2	124.991396715614	4.20860328438636
109	129.2	132.144871798543	-2.94487179854281
110	132.6	130.338924559746	2.26107544025425
111	131.5	133.791565395702	-2.29156539570246
112	131	133.399784018277	-2.39978401827739
113	125.8	130.331696256294	-4.5316962562945
114	127.2	127.420007809943	-0.220007809943283
115	127.3	124.929733764502	2.37026623549787
116	127.5	125.708541579273	1.79145842072658
117	122	125.422132538882	-3.42213253888217
118	118.4	118.860589920037	-0.460589920036497
119	118.3	120.232167070165	-1.93216707016535
120	115.5	118.868129815959	-3.36812981595936

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
121	118.532871754513	110.57149365463	126.494249854396
122	120.141898547411	109.98558519966	130.298211895162
123	120.857022515837	108.902196695855	132.811848335819
124	122.257865275459	108.741763028342	135.773967522575
125	120.647372477763	105.732541619758	135.562203335769
126	122.221638265603	106.028450219659	138.414826311548
127	120.444176219933	103.066417484707	137.821934955159
128	119.225181534467	100.738601044064	137.71176202487
129	116.435815412123	96.9032575203225	135.968373303924
130	113.200643666661	92.6753427586366	133.725944574685
131	114.631092139411	93.1588976327161	136.103286646106
132	114.498951048951	92.1198917188148	136.878010379087

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295197995bwab2i81qci0w6z/1zcuz1295198117.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295197995bwab2i81qci0w6z/1zcuz1295198117.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295197995bwab2i81qci0w6z/223681295198117.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295197995bwab2i81qci0w6z/223681295198117.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295197995bwab2i81qci0w6z/3q31c1295198117.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295197995bwab2i81qci0w6z/3q31c1295198117.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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