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voorspelling 10.2 boeken

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 22 Dec 2010 14:12:30 +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/22/t12930271468ni6uky2g9fy43o.htm/, Retrieved Wed, 22 Dec 2010 15:12:27 +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/22/t12930271468ni6uky2g9fy43o.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:

voorspelling 10.2 boeken

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

90 69.3 87.3 57.4 56.2 61.6 77.7 177.2 97.6 81.6 96.8 191.3 106 75.1 72 63.5 57.4 62.3 79.4 178.1 109.3 85.2 102.7 193.7 108.4 73.4 85.9 58.5 58.6 62.7 77.5 180.5 102.2 82.6 97.8 197.8 93.8 72.4 77.7 58.7 53.1 64.3 76.4 188.4 105.5 79.8 96.1 202.5 97.3 89.5 64.7 61.2 57.8 62 76.3 195 110.9 81.4 101.7 202.2 97.4 68.5 86.8 59.1 62.4 66.2 68 198.5 120.4 90.2 103.2 207.3 106.4 75.5 97.3 60 67.5 71.2 73.7 213.3 114.6 96.1 117 229.2 105.6 99.9 79.3 72.5 67.4 78.3 85.7 177.4 113.6 94.1 105.7 228.3 100.3 70.3 94.2 66.5 64.4 73.7 87.9 152.2 97.3 89.3 107.6 228.4

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.388480381575032
beta	0.079378799348397
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	87.3	48.6	38.7
4	57.4	44.1275867792093	13.2724132207907
5	56.2	30.1863377607131	26.013662239287
6	61.6	21.997000089345	39.602999910655
7	77.7	20.3080954183551	57.3919045816449
8	177.2	27.2996314817916	149.900368518208
9	97.6	74.8513845066085	22.7486154933915
10	81.6	73.7086774716441	7.8913225283559
11	96.8	67.0375491477881	29.7624508522119
12	191.3	69.780712960143	121.519287039857
13	106	111.916910673859	-5.91691067385916
14	75.1	104.3641852701	-29.2641852700999
15	72	86.8390789316744	-14.8390789316744
16	63.5	74.4602491540468	-10.9602491540468
17	57.4	63.250286280699	-5.850286280699
18	62.3	53.8450378345352	8.45496216546477
19	79.4	50.2578243299821	29.1421756700179
20	178.1	55.605847789181	122.494152210819
21	109.3	100.996647903667	8.30335209633299
22	85.2	102.282613768227	-17.0826137682267
23	102.7	93.179851551105	9.52014844889507
24	193.7	94.7053143803685	98.9946856196315
25	108.4	134.04258919058	-25.6425891905805
26	73.4	124.169984676402	-50.769984676402
27	85.9	102.970280563629	-17.0702805636285
28	58.5	94.3358523079252	-35.8358523079252
29	58.6	77.3062935949926	-18.7062935949926
30	62.7	66.3543844237556	-3.65438442375563
31	77.5	61.1371560300039	16.3628439699961
32	180.5	64.2008109189472	116.299189081053
33	102.2	109.674105741473	-7.47410574147283
34	82.6	106.833423969598	-24.2334239695977
35	97.8	96.7347871875331	1.06521281246687
36	197.8	96.4970225565805	101.302977443419
37	93.8	138.323553657549	-44.5235536575489
38	72.4	122.126360757447	-49.7263607574465
39	77.7	102.374562299322	-24.6745622993225
40	58.7	91.5940039658122	-32.8940039658122
41	53.1	76.6059979017651	-23.5059979017651
42	64.3	64.5401910606676	-0.240191060667613
43	76.4	61.5052869415902	14.8947130584098
44	188.4	64.8093059990854	123.590694000915
45	105.5	114.15076057243	-8.65076057243009
46	79.8	111.852239990084	-32.0522399900841
47	96.1	99.4743054237077	-3.37430542370771
48	202.5	98.133132005557	104.366867994443
49	97.3	141.865662946582	-44.5656629465819
50	89.5	126.366551354878	-36.8665513548784
51	64.7	112.721535810545	-48.0215358105447
52	61.2	93.26218244586	-32.06218244586
53	57.8	79.0140198389737	-21.2140198389737
54	62	68.3259765970259	-6.32597659702591
55	76.3	63.2265712620959	13.0734287379041
56	195	66.0666010251793	128.933398974821
57	110.9	117.8918891598	-6.9918891598
58	81.4	116.697259865209	-35.2972598652093
59	101.7	103.418084005214	-1.71808400521401
60	202.2	103.130778457253	99.0692215427473
61	97.4	145.052371938275	-47.6523719382755
62	68.5	128.5060435415	-60.0060435415
63	86.8	105.31014334553	-18.5101433455298
64	59.1	97.6637870342588	-38.5637870342588
65	62.4	81.0377879722635	-18.6377879722635
66	66.2	71.577913180987	-5.37791318098701
67	68	67.1034003280445	0.896599671955514
68	198.5	65.0940611617671	133.405938838233
69	120.4	118.675853748708	1.72414625129198
70	90.2	121.155020986148	-30.9550209861484
71	103.2	109.984409594208	-6.78440959420841
72	207.3	107.994394979144	99.3056050208558
73	106.4	150.280567217266	-43.8805672172662
74	75.5	135.588570914034	-60.0885709140336
75	97.3	112.747125503834	-15.4471255038337
76	60	106.771661190078	-46.7716611900785
77	67.5	87.1849266142028	-19.6849266142028
78	71.2	77.5138308482658	-6.31383084826578
79	73.7	72.8424431947817	0.857556805218323
80	213.3	70.9834435236719	142.316556476328
81	114.6	128.467120796611	-13.8671207966114
82	96.1	124.848881649245	-28.7488816492445
83	117	114.562838049069	2.43716195093079
84	229.2	116.467115588559	112.732884411441
85	105.6	164.695473411175	-59.0954734111746
86	99.9	144.349551828394	-44.4495518283938
87	79.3	128.322587897676	-49.0225878976756
88	72.5	109.007374417674	-36.5073744176737
89	67.4	93.4282940616907	-26.0282940616907
90	78.3	81.1174935712128	-2.81749357121281
91	85.7	77.7367503632958	7.96324963670418
92	177.4	78.7896779656735	98.6103220343265
93	113.6	118.098071820628	-4.49807182062801
94	94.1	117.212169968524	-23.112169968524
95	105.7	108.382343724036	-2.6823437240355
96	228.3	107.406388456074	120.893611543926
97	100.3	158.165276589424	-57.8652765894245
98	70.3	137.69544596786	-67.3954459678596
99	94.2	111.445050980946	-17.2450509809459
100	66.5	104.145313105131	-37.6453131051313
101	64.4	87.7596010946749	-23.3596010946749
102	73.7	76.2032654359678	-2.50326543596778
103	87.9	72.6720135499667	15.2279864500333
104	152.2	76.4985921987252	75.7014078012747
105	97.3	106.152321005549	-8.85232100554869
106	89.3	102.685605018411	-13.3856050184113
107	107.6	97.0450238038641	10.5549761961359
108	228.4	101.030373637203	127.369626362797

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
109	154.323634043264	47.272984601823	261.374283484706
110	158.136293398837	42.0553178321554	274.21726896552
111	161.94895275441	36.2628137538313	287.63509175499
112	165.761612109984	29.9371870635074	301.58603715646
113	169.574271465557	23.1147393626518	316.033803568461
114	173.38693082113	15.8269079760202	330.946953666239
115	177.199590176703	8.10089664849966	346.298283704905
116	181.012249532276	-0.0397086291137612	362.064207693665
117	184.824908887849	-8.57438260678703	378.224200382484
118	188.637568243422	-17.4851774468497	394.760313933693
119	192.450227598995	-26.7563131865662	411.656768384555
120	196.262886954568	-36.3738354169099	428.899609326045

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/22/t12930271468ni6uky2g9fy43o/1my3m1293027146.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t12930271468ni6uky2g9fy43o/1my3m1293027146.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t12930271468ni6uky2g9fy43o/2eplp1293027146.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t12930271468ni6uky2g9fy43o/2eplp1293027146.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t12930271468ni6uky2g9fy43o/3eplp1293027146.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t12930271468ni6uky2g9fy43o/3eplp1293027146.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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