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Tripple Exponential Smoothing (additive): 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, 11 Dec 2010 16:41:33 +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/11/t129208563269o9lny8up6ld8r.htm/, Retrieved Sat, 11 Dec 2010 17:40:32 +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/11/t129208563269o9lny8up6ld8r.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	0.00547273897852051
beta	0
gamma	0.283796808383624

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	44	47.3857323232323	-3.38573232323233
14	36	38.5338697606428	-2.53386976064281
15	72	74.061669219504	-2.06166921950393
16	45	47.6753862420055	-2.67538624200552
17	56	59.4940778847696	-3.49407788476964
18	54	57.8916223752023	-3.89162237520234
19	53	41.1203245417399	11.8796754582601
20	35	28.3520055713391	6.64799442866086
21	61	60.2217216429112	0.778278357088801
22	52	72.5593142905455	-20.5593142905455
23	47	52.1134651965227	-5.11346519652266
24	51	62.4604805362263	-11.4604805362263
25	52	46.2338254930999	5.76617450690009
26	63	37.6724817373835	25.3275182626165
27	74	73.4860349106542	0.513965089345817
28	45	46.9406299672454	-1.94062996724536
29	51	58.5322722115789	-7.53227221157892
30	64	56.7955123055187	7.20448769448126
31	36	44.5362894494873	-8.53628944948731
32	30	30.1796304171774	-0.179630417177368
33	55	60.3552905180826	-5.35529051808256
34	64	66.6369154458488	-2.63691544584883
35	39	50.64864398173	-11.6486439817300
36	40	59.1684891381623	-19.1684891381623
37	63	47.7617643883987	15.2382356116013
38	45	44.7733240562875	0.226675943712529
39	59	73.4460387434385	-14.4460387434385
40	55	46.1259677051388	8.87403229486119
41	40	56.1985901865845	-16.1985901865845
42	64	58.5737588740304	5.42624112596959
43	27	41.862069546533	-14.862069546533
44	28	29.8294052226966	-1.82940522269663
45	45	58.5352392738363	-13.5352392738363
46	57	65.5393416137178	-8.53934161371778
47	45	46.9752644441634	-1.97526444416337
48	69	53.425620843247	15.5743791567530
49	60	51.9201147520066	8.07988524799342
50	56	44.6555810559099	11.3444189440901
51	58	69.2478595159965	-11.2478595159965
52	50	48.5272335380874	1.47276646191262
53	51	51.4827620251635	-0.482762025163474
54	53	60.0474109291823	-7.0474109291823
55	37	37.5412094491569	-0.541209449156923
56	22	29.2653063658442	-7.26530636584425
57	55	54.637493673371	0.36250632662896
58	70	63.1277152005227	6.87228479947728
59	62	46.5006510210163	15.4993489789837
60	58	57.9999171041062	8.28958938114965e-05
61	39	54.2939035450508	-15.2939035450508
62	49	47.8228451507844	1.17715484921555
63	58	65.9829534109177	-7.9829534109177
64	47	48.8705114775701	-1.87051147757007
65	42	51.2558075547797	-9.25580755477974
66	62	57.919613320685	4.08038667931505
67	39	37.3106455072468	1.68935449275322
68	40	27.1491159772013	12.8508840227987
69	72	54.7842957353716	17.2157042646284
70	70	65.2040941342166	4.79590586578341
71	54	51.0006006656771	2.99939933432294
72	65	58.0568881613235	6.94311183867649

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	50.0722412396403	31.3423579300858	68.8021245491948
74	48.3337342343557	29.6035704387332	67.0638980299781
75	63.9020177287652	45.171573451275	82.6324620062553
76	48.5584624139734	29.8277376588157	67.2891871691312
77	48.8695422985678	30.1385370699423	67.6005475271933
78	59.3480589880769	40.6167732901833	78.0793446859704
79	38.0419066018529	19.3103404388907	56.773472764815
80	31.0214026496053	12.2895560257739	49.7532492734368
81	59.8181957252078	41.0860686447061	78.5503228057094
82	66.6383676803266	47.9059601473537	85.3707752132995
83	51.9015748876225	33.1688869063771	70.6342628688679
84	60.0545353148076	41.3215668894883	78.787503740127

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/11/t129208563269o9lny8up6ld8r/11ir61292085689.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/11/t129208563269o9lny8up6ld8r/11ir61292085689.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/11/t129208563269o9lny8up6ld8r/2brrr1292085689.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/11/t129208563269o9lny8up6ld8r/2brrr1292085689.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/11/t129208563269o9lny8up6ld8r/3brrr1292085689.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/11/t129208563269o9lny8up6ld8r/3brrr1292085689.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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