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ES faillissemten

*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: Sun, 19 Dec 2010 20:22:31 +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/19/t12927901002sgovgux0fpje4o.htm/, Retrieved Sun, 19 Dec 2010 21:21:41 +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/19/t12927901002sgovgux0fpje4o.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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.00799336056445855
beta	1
gamma	0.270233270298647

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	44	47.1768162393162	-3.17681623931624
14	36	38.0837799467711	-2.08377994677107
15	72	73.3578242829707	-1.35782428297071
16	45	46.7101511988013	-1.71015119880129
17	56	58.2543253167386	-2.25432531673864
18	54	56.3594633529885	-2.35946335298853
19	53	39.2782342750199	13.7217657249801
20	35	26.3518979470786	8.6481020529214
21	61	58.1208000605976	2.87919993940236
22	52	70.366603742715	-18.3666037427151
23	47	49.6291045027929	-2.62910450279289
24	51	59.7047187217592	-8.70471872175918
25	52	43.2272357871456	8.7727642128544
26	63	34.4792135675127	28.5207864324873
27	74	70.3936168612595	3.60638313874053
28	45	43.9319721404978	1.06802785950217
29	51	55.6154788027958	-4.61547880279583
30	64	53.9176891007579	10.0823108992421
31	36	41.5904402126777	-5.59044021267772
32	30	27.3388338763719	2.66116612362814
33	55	57.6547491391568	-2.65474913915676
34	64	64.258009503665	-0.25800950366505
35	39	48.1259311418164	-9.12593114181636
36	40	56.71084366957	-16.71084366957
37	63	44.9805529193299	18.0194470806701
38	45	41.8002135959526	3.19978640404735
39	59	70.8307886969427	-11.8307886969427
40	55	43.4393446626419	11.5606553373581
41	40	53.6410588108799	-13.6410588108799
42	64	55.6969951120199	8.30300488798012
43	27	39.0256436623309	-12.0256436623309
44	28	26.7547586151605	1.24524138483948
45	45	55.4431091661056	-10.4431091661056
46	57	62.3731685421579	-5.37316854215789
47	45	43.5286159649166	1.47138403508336
48	69	49.9552982659795	19.0447017340205
49	60	47.8972549418314	12.1027450581686
50	56	40.7257534564939	15.2742465435061
51	58	65.9489512508591	-7.94895125085908
52	50	45.0155858051311	4.98441419486888
53	51	48.5126937512844	2.48730624871565
54	53	56.812949246775	-3.81294924677496
55	37	34.7311215994065	2.26887840059351
56	22	26.3822645163909	-4.38226451639095
57	55	52.0975142803265	2.90248571967355
58	70	60.8052565706978	9.19474342930218
59	62	44.3403298041435	17.6596701958565
60	58	56.1650833395742	1.83491666042578
61	39	52.5286963972783	-13.5286963972783
62	49	46.2177996799159	2.78220032008407
63	58	65.2310652813551	-7.23106528135507
64	47	47.8917032636376	-0.891703263637588
65	42	50.7466401113247	-8.74664011132474
66	62	57.2525785389972	4.74742146100277
67	39	36.9223876970205	2.0776123029795
68	40	26.8403154285386	13.1596845714614
69	72	54.8401565631747	17.1598434368253
70	70	65.6541388561604	4.34586114383961
71	54	51.6864045054146	2.31359549458541
72	65	59.290363619393	5.70963638060702

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	51.7414124303452	33.0794356820062	70.4033891786842
74	50.1943460719829	31.5299847062871	68.8587074376786
75	66.7620216372809	48.092295996148	85.4317472784138
76	51.4986109248713	32.8193525977827	70.1778692519598
77	52.5808428822744	33.8866994648579	71.274986299691
78	63.1698730978866	44.4543159484312	81.8854302473421
79	42.4438627686134	23.6991984590622	61.1885270781646
80	35.6572154929169	16.874601600876	54.4398293849578
81	64.8602373409121	46.0297031596792	83.690771522145
82	72.2008402217756	53.3113128747534	91.0903675687978
83	57.7177044687576	38.7570408025164	76.6783681349988
84	66.2591969040138	47.214221401832	85.3041724061955

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927901002sgovgux0fpje4o/1gvms1292790147.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927901002sgovgux0fpje4o/1gvms1292790147.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927901002sgovgux0fpje4o/2943d1292790147.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927901002sgovgux0fpje4o/2943d1292790147.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927901002sgovgux0fpje4o/3943d1292790147.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927901002sgovgux0fpje4o/3943d1292790147.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=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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