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Workshop 8 (Smoothing model)

*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: Fri, 10 Dec 2010 15:44:28 +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/10/t12919958055rinm9jwcybe3sm.htm/, Retrieved Fri, 10 Dec 2010 16:43:29 +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/10/t12919958055rinm9jwcybe3sm.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	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.365156398722266
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	30	37	-7
3	47	34.4439052089441	12.5560947910559
4	35	39.0288435648615	-4.0288435648615
5	30	37.5576855577013	-7.5576855577013
6	43	34.7979483167758	8.20205168322419
7	82	37.7929799715559	44.2070200284441
8	40	53.9354562033856	-13.9354562033856
9	47	48.8468352016055	-1.84683520160546
10	19	48.1724515103537	-29.1724515103537
11	52	37.519944174933	14.480055825067
12	136	42.8074292133118	93.1925707866882
13	80	76.8372927494488	3.16270725055122
14	42	77.9921755392729	-35.9921755392729
15	54	64.8494023371723	-10.8494023371723
16	66	60.8876736514415	5.11232634855845
17	81	62.7544723299741	18.2455276700259
18	63	69.4169435067482	-6.41694350674823
19	137	67.0737555250198	69.9262444749802
20	72	92.6077711336764	-20.6077711336764
21	107	85.0827116408104	21.9172883591896
22	58	93.0859497278095	-35.0859497278095
23	36	80.2740906794521	-44.2740906794521
24	52	64.1071231702403	-12.1071231702403
25	79	59.6861296745085	19.3138703254915
26	77	66.7387130079538	10.2612869920462
27	54	70.485687612225	-16.4856876122250
28	84	64.4658332932847	19.5341667067153
29	48	71.5988592599492	-23.5988592599492
30	96	62.9815847986326	33.0184152013674
31	83	75.0384703850804	7.96152961491958
32	66	77.9456738675851	-11.9456738675851
33	61	73.583634617787	-12.5836346177871
34	53	68.9886399179191	-15.9886399179191
35	30	63.1502857450247	-33.1502857450247
36	74	51.0452467857574	22.9547532142426
37	69	59.4273218030286	9.5726781969714
38	59	62.9228464995618	-3.92284649956183
39	42	61.4903939990416	-19.4903939990416
40	65	54.3733519166735	10.6266480833265
41	70	58.2537404612699	11.7462595387301
42	100	62.5429622928896	37.4570377071104
43	63	76.2206392888222	-13.2206392888222
44	105	71.3930382573098	33.6069617426902
45	82	83.6648353792675	-1.66483537926752
46	81	83.0569100877088	-2.05691008770877
47	75	82.3058162075855	-7.30581620758554
48	102	79.6380506714968	22.3619493285032
49	121	87.8036595567029	33.1963404432971
50	98	99.9255156837356	-1.92551568373557
51	76	99.2224013109794	-23.2224013109794
52	77	90.742592878579	-13.7425928785790
53	63	85.7243971539308	-22.7243971539308
54	37	77.4264381260669	-40.4264381260669
55	35	62.6644655667838	-27.6644655667838
56	23	52.5626089478409	-29.5626089478409
57	40	41.7676331276127	-1.76763312761265
58	29	41.1221705804714	-12.1221705804714
59	37	36.6956824266095	0.30431757339052
60	51	36.8068059357767	14.1931940642233
61	20	41.9895415666347	-21.9895415666347
62	28	33.9599197586088	-5.95991975860879
63	13	31.7836169228815	-18.7836169228815
64	22	24.9246590123435	-2.92465901234348
65	25	23.8567010599055	1.14329894009448
66	13	24.2741839835334	-11.2741839835334
67	16	20.1573435615741	-4.15734356157409
68	13	18.6392629583785	-5.6392629583785
69	16	16.5800500050491	-0.580050005049131
70	17	16.3682410341266	0.631758965873445
71	9	16.5989318629654	-7.5989318629654
72	17	13.8241332697491	3.17586673025092
73	25	14.9838213277894	10.0161786722106
74	14	18.6412930606926	-4.64129306069257
75	8	16.9464952012354	-8.94649520123542
76	7	13.6796252323663	-6.67962523236626
77	10	11.240517337701	-1.24051733770101
78	7	10.7875344941136	-3.78753449411358
79	10	9.4044920382067	0.595507961793299
80	3	9.62194558094558	-6.62194558094558

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
81	7.20389978007267	-36.9330002321243	51.3407997922696
82	7.20389978007267	-39.7835399067165	54.1913394668618
83	7.20389978007267	-42.4707721760925	56.8785717362378
84	7.20389978007267	-45.019912600733	59.4277121608784
85	7.20389978007267	-47.4502869325532	61.8580864926985
86	7.20389978007267	-49.7770941639746	64.1848937241199
87	7.20389978007267	-52.0125440213287	66.420343581474
88	7.20389978007267	-54.1666205217587	68.574420081904
89	7.20389978007267	-56.24761168932	70.6554112494653
90	7.20389978007267	-58.2624874227007	72.670286982846
91	7.20389978007267	-60.2171755526185	74.6249751127638
92	7.20389978007267	-62.1167677343807	76.524567294526

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/10/t12919958055rinm9jwcybe3sm/12za91291995865.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t12919958055rinm9jwcybe3sm/12za91291995865.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t12919958055rinm9jwcybe3sm/22za91291995865.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t12919958055rinm9jwcybe3sm/22za91291995865.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t12919958055rinm9jwcybe3sm/3d89c1291995865.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/10/t12919958055rinm9jwcybe3sm/3d89c1291995865.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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