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exponential smoothing faillissementen

*The author of this computation has been verified*

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 19:54:43 +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/t1292701968uiklwuhpr9kwk2m.htm/, Retrieved Sat, 18 Dec 2010 20:52:48 +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/t1292701968uiklwuhpr9kwk2m.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

46 62 66 59 58 61 41 27 58 70 49 59 44 36 72 45 56 54 53 35 61 52 47 51 52 63 74 45 51 64 36 30 55 64 39 40 63 45 59 55 40 64 27 28 45 57 45 69 60 56 58 50 51 53 37 22 55 70 62 58 39 49 58 47 42 62 39 40 72 70 54 65

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	0.0440224583015312
beta	0
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	62	46	16
3	66	46.7043593328245	19.2956406671755
4	59	47.5538008694966	11.4461991305034
5	58	48.0576906934302	9.94230930656983
6	61	48.4953755902996	12.5046244097004
7	41	49.0458598969519	-8.04585989695192
8	27	48.6916613651384	-21.6916613651384
9	58	47.7367411072007	10.2632588927993
10	70	48.1885549938467	21.8114450061533
11	49	49.1487484221263	-0.148748422126253
12	59	49.1422001509158	9.85779984908422
13	44	49.5761647337169	-5.57616473371694
14	36	49.3306882542444	-13.3306882542444
15	72	48.7438385864412	23.2561614135588
16	45	49.7676319825233	-4.7676319825233
17	56	49.5577491023756	6.44225089762438
18	54	49.8413528238843	4.15864717611571
19	53	50.0244266957856	2.97557330421438
20	35	50.1554187474935	-15.1554187474935
21	61	49.4882399576398	11.5117600423602
22	52	49.9950159340818	2.00498406591819
23	47	50.0832802615189	-3.08328026151892
24	51	49.9475466847743	1.05245331522573
25	52	49.9938782669581	2.00612173304189
26	63	50.0821926772987	12.9178073227013
27	74	50.6508663115096	23.3491336884904
28	45	51.678752575688	-6.67875257568802
29	51	51.3847374689185	-0.384737468918544
30	64	51.367800379736	12.6321996202640
31	36	51.9239008607757	-15.9239008607757
32	30	51.2228915991345	-21.2228915991345
33	55	50.2886077386737	4.71139226132631
34	64	50.4960148080401	13.5039851919599
35	39	51.0904934330576	-12.0904934330576
36	40	50.5582401900559	-10.5582401900559
37	63	50.0934405015516	12.9065594984484
38	45	50.6616189788883	-5.66161897888831
39	59	50.412380593471	8.58761940652897
40	55	50.7904287107044	4.20957128929562
41	40	50.9757443872547	-10.9757443872547
42	64	50.4925651376385	13.5074348623615
43	27	51.0871956256275	-24.0871956256275
44	28	50.0268180605975	-22.0268180605975
45	45	49.0571433810094	-4.05714338100941
46	57	48.8785379556956	8.12146204430441
47	45	49.2360646798885	-4.23606467988845
48	69	49.0495826991555	19.9504173008445
49	60	49.92784911288	10.0721508871200
50	56	50.371249955315	5.62875004468498
51	58	50.6190413694469	7.3809586305531
52	50	50.9439693129858	-0.943969312985757
53	51	50.9024134632669	0.0975865367330826
54	53	50.906709462511	2.09329053748896
55	37	50.9988612579106	-13.9988612579106
56	22	50.3825969719153	-28.3825969719153
57	55	49.13312528023	5.86687471976997
58	70	49.3913995279414	20.6086004720586
59	62	50.2986407828755	11.7013592171245
60	58	50.8137633810826	7.18623661891737
61	39	51.1301191829839	-12.1301191829839
62	49	50.5961215170583	-1.59612151705834
63	58	50.5258563241295	7.47414367587054
64	47	50.8548865024401	-3.85488650244013
65	42	50.6851849221293	-8.68518492212932
66	62	50.3028417310538	11.6971582689462
67	39	50.8177793931949	-11.8177793931949
68	40	50.2975316926413	-10.2975316926413
69	72	49.8442090330933	22.1557909669067
70	70	50.8195614170714	19.1804385829286
71	54	51.6639314747934	2.33606852520658
72	65	51.7667709540338	13.2332290459662

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	52.3493302279045	27.8299834175885	76.8686770382205
74	52.3493302279045	27.8062359544651	76.8924245013439
75	52.3493302279045	27.7825114467657	76.9161490090433
76	52.3493302279045	27.7588098280494	76.9398506277596
77	52.3493302279045	27.7351310321949	76.963529423614
78	52.3493302279045	27.7114749933991	76.98718546241
79	52.3493302279045	27.6878416461740	77.010818809635
80	52.3493302279045	27.6642309253454	77.0344295304636
81	52.3493302279045	27.6406427660505	77.0580176897585
82	52.3493302279045	27.6170771037356	77.0815833520734
83	52.3493302279045	27.5935338741545	77.1051265816545
84	52.3493302279045	27.5700130133661	77.1286474424429

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292701968uiklwuhpr9kwk2m/1d2qb1292702078.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292701968uiklwuhpr9kwk2m/1d2qb1292702078.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292701968uiklwuhpr9kwk2m/25upe1292702078.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292701968uiklwuhpr9kwk2m/25upe1292702078.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292701968uiklwuhpr9kwk2m/35upe1292702078.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292701968uiklwuhpr9kwk2m/35upe1292702078.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=0, beta=0)

if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)

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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