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*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: Thu, 09 Dec 2010 16:35:12 +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/09/t1291912375fw1f4rorjcoj5tp.htm/, Retrieved Thu, 09 Dec 2010 17:32:56 +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/09/t1291912375fw1f4rorjcoj5tp.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 «

37 30 47 35 30 43 82 40 47 19 52 136 80 42 54 66 81 63 137 72 107 58 36 52 79 77 54 84 48 96 83 66 61 53 30 74 69 59 42 65 70 100 63 105 82 81 75 102 121 98 76 77 63 37 35 23 40 29 37 51 20 28 13 22 25 13 16 13 16 17 9 17 25 14 8 7 10 7 10 3

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	0.365156398722376
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	30	37	-7
3	47	34.4439052089434	12.5560947910566
4	35	39.0288435648624	-4.02884356486239
5	30	37.5576855577014	-7.55768555770143
6	43	34.7979483167751	8.20205168322494
7	82	37.7929799715563	44.2070200284437
8	40	53.9354562033907	-13.9354562033907
9	47	48.8468352016072	-1.84683520160717
10	19	48.1724515103546	-29.1724515103546
11	52	37.5199441749304	14.4800558250696
12	136	42.8074292133118	93.1925707866882
13	80	76.8372927494589	3.1627072505411
14	42	77.9921755392796	-35.9921755392796
15	54	64.8494023371727	-10.8494023371727
16	66	60.8876736514406	5.11232634855941
17	81	62.7544723299741	18.2455276700259
18	63	69.4169435067502	-6.41694350675019
19	137	67.0737555250204	69.9262444749796
20	72	92.6077711336843	-20.6077711336843
21	107	85.0827116408132	21.9172883591868
22	58	93.0859497278137	-35.0859497278137
23	36	80.274090679451	-44.2740906794509
24	52	64.1071231702347	-12.1071231702347
25	79	59.6861296745036	19.3138703254964
26	77	66.7387130079528	10.2612869920472
27	54	70.4856876122255	-16.4856876122255
28	84	64.4658332932832	19.5341667067168
29	48	71.5988592599504	-23.5988592599504
30	96	62.9815847986307	33.0184152013693
31	83	75.0384703850829	7.96152961491713
32	66	77.9456738675876	-11.9456738675876
33	61	73.5836346177873	-12.5836346177873
34	53	68.9886399179179	-15.9886399179179
35	30	63.1502857450222	-33.1502857450222
36	74	51.0452467857522	22.9547532142478
37	69	59.4273218030278	9.57267819697222
38	59	62.9228464995624	-3.92284649956236
39	42	61.4903939990415	-19.4903939990415
40	65	54.3733519166713	10.6266480833287
41	70	58.2537404612696	11.7462595387304
42	100	62.5429622928908	37.4570377071092
43	63	76.220639288827	-13.220639288827
44	105	71.3930382573114	33.6069617426886
45	82	83.6648353792722	-1.66483537927222
46	81	83.0569100877116	-2.05691008771157
47	75	82.3058162075871	-7.30581620758709
48	102	79.638050671497	22.361949328503
49	121	87.8036595567054	33.1963404432946
50	98	99.9255156837408	-1.92551568374081
51	76	99.2224013109826	-23.2224013109826
52	77	90.7425928785784	-13.7425928785784
53	63	85.724397153929	-22.7243971539289
54	37	77.4264381260632	-40.4264381260632
55	35	62.664465566777	-27.664465566777
56	23	52.5626089478336	-29.5626089478336
57	40	41.7676331276048	-1.76763312760479
58	29	41.1221705804663	-12.1221705804663
59	37	36.6956824266049	0.304317573395132
60	51	36.8068059357738	14.1931940642262
61	20	41.9895415666344	-21.9895415666344
62	28	33.9599197586062	-5.9599197586062
63	13	31.7836169228792	-18.7836169228792
64	22	24.92465901234	-2.92465901233998
65	25	23.856701059903	1.14329894009703
66	13	24.2741839835319	-11.2741839835319
67	16	20.1573435615719	-4.15734356157191
68	13	18.6392629583767	-5.63926295837666
69	16	16.5800500050473	-0.580050005047347
70	17	16.3682410341254	0.631758965874639
71	9	16.5989318629647	-7.59893186296472
72	17	13.8241332697478	3.17586673025219
73	25	14.9838213277889	10.0161786722111
74	14	18.6412930606934	-4.64129306069337
75	8	16.9464952012354	-8.94649520123543
76	7	13.6796252323653	-6.67962523236528
77	10	11.2405173376997	-1.24051733769967
78	7	10.7875344941126	-3.78753449411259
79	10	9.40449203820566	0.59550796179434
80	3	9.62194558094498	-6.62194558094498

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
81	7.20389978007156	-36.9330002321254	51.3407997922685
82	7.20389978007156	-39.7835399067192	54.1913394668624
83	7.20389978007156	-42.4707721760967	56.8785717362399
84	7.20389978007156	-45.0199126007386	59.4277121608818
85	7.20389978007156	-47.45028693256	61.8580864927031
86	7.20389978007156	-49.7770941639825	64.1848937241256
87	7.20389978007156	-52.0125440213376	66.4203435814808
88	7.20389978007156	-54.1666205217687	68.5744200819118
89	7.20389978007156	-56.2476116893309	70.655411249474
90	7.20389978007156	-58.2624874227125	72.6702869828556
91	7.20389978007156	-60.2171755526312	74.6249751127743
92	7.20389978007156	-62.1167677343942	76.5245672945373

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/09/t1291912375fw1f4rorjcoj5tp/1e55u1291912508.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/09/t1291912375fw1f4rorjcoj5tp/1e55u1291912508.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/09/t1291912375fw1f4rorjcoj5tp/206lz1291912508.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/09/t1291912375fw1f4rorjcoj5tp/206lz1291912508.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/09/t1291912375fw1f4rorjcoj5tp/306lz1291912508.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/09/t1291912375fw1f4rorjcoj5tp/306lz1291912508.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=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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