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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: Tue, 07 Dec 2010 09:58:27 +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/07/t1291715800elkh2z8z8b5t1y0.htm/, Retrieved Tue, 07 Dec 2010 10:56:40 +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/07/t1291715800elkh2z8z8b5t1y0.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	0.00486104141907233
beta	0.816160950605529
gamma	0.253859759879226

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	44	46.6829275162342	-2.68292751623424
14	36	37.4196383690258	-1.41963836902578
15	72	73.8547395004858	-1.85473950048576
16	45	46.5003158720121	-1.50031587201206
17	56	58.5293158416863	-2.52931584168627
18	54	56.6179340105627	-2.61793401056273
19	53	39.8258696907352	13.1741303092648
20	35	26.743646417569	8.25635358243098
21	61	58.3026662710212	2.69733372897877
22	52	70.667386235984	-18.6673862359840
23	47	49.8742525002373	-2.87425250023728
24	51	60.2580225998112	-9.25802259981117
25	52	43.8871165582438	8.11288344175625
26	63	35.4193642077538	27.5806357922462
27	74	70.6891963385838	3.31080366141622
28	45	44.6291098145291	0.370890185470877
29	51	56.2747338131084	-5.2747338131084
30	64	54.6109523160435	9.38904768395653
31	36	42.3713431831259	-6.37134318312594
32	30	28.331511805726	1.66848819427402
33	55	58.0298335364493	-3.02983353644935
34	64	64.9666781000709	-0.966678100070894
35	39	48.6148066632519	-9.61480666325193
36	40	57.3813612933541	-17.3813612933541
37	63	45.5542957343008	17.4457042656992
38	45	42.1556080302253	2.84439196977471
39	59	70.9117520359552	-11.9117520359552
40	55	44.2410969906148	10.7589030093852
41	40	54.3989780908847	-14.3989780908847
42	64	56.31950068984	7.68049931015996
43	27	40.237866253895	-13.2378662538950
44	28	28.3092091538995	-0.309209153899509
45	45	56.2456489846546	-11.2456489846546
46	57	63.3572291256966	-6.35722912569665
47	45	45.0549821644299	-0.0549821644299016
48	69	51.6231072056786	17.3768927943214
49	60	48.836773674433	11.1632263255670
50	56	41.8713177071526	14.1286822928474
51	58	66.4498641015078	-8.44986410150784
52	50	46.0047125046752	3.99528749532485
53	51	49.7060980762021	1.29390192379785
54	53	57.2169843150172	-4.21698431501715
55	37	36.2146717814553	0.785328218544734
56	22	27.8192640714578	-5.81926407145777
57	55	52.6377454166685	2.36225458333146
58	70	61.0751314840978	8.92486851590216
59	62	44.7456387149647	17.2543612850353
60	58	56.0090796359372	1.99092036406280
61	39	51.7658097966268	-12.7658097966268
62	49	45.5049076490442	3.49509235095576
63	58	64.37374008907	-6.37374008907004
64	47	47.0997914298967	-0.0997914298967402
65	42	50.1236187423505	-8.12361874235045
66	62	56.1828073203417	5.81719267965832
67	39	36.4783195968937	2.52168040310625
68	40	26.4156824424678	13.5843175575322
69	72	53.743136032433	18.2568639675670
70	70	64.318554376582	5.68144562341796
71	54	50.0664397763046	3.93356022369539
72	65	57.721027194788	7.27897280521199

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	49.7677557536904	44.9723508258603	54.5631606815204
74	47.8303317985974	43.0323487033887	52.6283148938061
75	64.9540477058196	60.1436204573966	69.7644749542427
76	48.9580772001707	44.1454702954959	53.7706841048456
77	50.2149796710722	45.3871498023985	55.0428095397458
78	60.5764855821967	55.704945190105	65.4480259742883
79	39.1585032248659	34.3153763919981	44.0016300577338
80	31.6070558725343	26.7665075557883	36.4476041892803
81	61.7905483341838	56.7546042387015	66.8264924296661
82	69.5812497677764	64.3796245834013	74.7828749521514
83	54.0389592068271	48.9195948056013	59.1583236080529
84	63.0247265400554	39.4857059737818	86.5637471063289

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291715800elkh2z8z8b5t1y0/1ttzl1291715903.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291715800elkh2z8z8b5t1y0/1ttzl1291715903.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291715800elkh2z8z8b5t1y0/2ttzl1291715903.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291715800elkh2z8z8b5t1y0/2ttzl1291715903.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291715800elkh2z8z8b5t1y0/3ttzl1291715903.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t1291715800elkh2z8z8b5t1y0/3ttzl1291715903.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = 1 ; par3 = 1 ; par4 = 12 ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 12 ;

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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