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additive methode

*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: Wed, 15 Dec 2010 19:06:40 +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/15/t1292439889oez96yvva3y48b0.htm/, Retrieved Wed, 15 Dec 2010 20:04:52 +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/15/t1292439889oez96yvva3y48b0.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 «

597 593 590 580 574 573 573 620 626 620 588 566 557 561 549 532 526 511 499 555 565 542 527 510 514 517 508 493 490 469 478 528 534 518 506 502 516 528 533 536 537 524 536 587 597 581 564 558

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	6 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.907995640815674
beta	0.174326898805076
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	557	582.066773504274	-25.0667735042737
14	561	560.294775085844	0.705224914155792
15	549	545.493600906272	3.50639909372796
16	532	529.332568462414	2.66743153758591
17	526	523.831979709242	2.16802029075768
18	511	508.304432789262	2.69556721073764
19	499	514.307572288637	-15.3075722886368
20	555	541.040933616536	13.9590663834637
21	565	555.599495542462	9.40050445753764
22	542	556.173557430937	-14.1735574309371
23	527	507.390635586568	19.6093644134315
24	510	502.969721177273	7.0302788227275
25	514	500.016942012003	13.9830579879970
26	517	523.392995833222	-6.39299583322224
27	508	508.600664042223	-0.600664042222547
28	493	494.179424078068	-1.17942407806777
29	490	490.077224430754	-0.0772244307538017
30	469	477.141411514237	-8.14141151423672
31	478	474.514759681558	3.48524031844158
32	528	526.845754622935	1.15424537706497
33	534	533.17252034648	0.827479653519504
34	518	526.250722148035	-8.25072214803527
35	506	489.348724650088	16.6512753499119
36	502	484.011157018115	17.9888429818855
37	516	496.309611698726	19.6903883012735
38	528	528.557832425678	-0.557832425678157
39	533	526.084981701922	6.91501829807805
40	536	526.112601258156	9.88739874184398
41	537	541.590082786025	-4.59008278602460
42	524	532.529989302095	-8.52998930209537
43	536	539.274021469171	-3.27402146917098
44	587	592.837072298615	-5.83707229861511
45	597	599.262943859248	-2.26294385924803
46	581	594.687898969429	-13.6878989694292
47	564	560.267499273585	3.73250072641531
48	558	546.40535315682	11.5946468431795

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
49	555.12488078002	534.852106432984	575.397655127056
50	566.585062319765	536.949615584372	596.220509055158
51	564.348226192678	525.688641063513	603.007811321843
52	556.31791671955	508.563425768233	604.072407670868
53	557.868040156977	500.801080162402	614.935000151552
54	549.722136854898	483.061821507585	616.38245220221
55	563.154033166462	486.590561899827	639.717504433098
56	618.431406978829	531.642381391265	705.220432566393
57	630.38742662323	533.046265231125	727.728588015336
58	627.075452707047	518.855953921443	735.294951492652
59	609.112462836496	489.691341672756	728.533584000236
60	594.419868249887	463.478167261278	725.361569238497

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292439889oez96yvva3y48b0/1zfyh1292439993.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292439889oez96yvva3y48b0/1zfyh1292439993.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292439889oez96yvva3y48b0/2zfyh1292439993.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292439889oez96yvva3y48b0/2zfyh1292439993.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292439889oez96yvva3y48b0/3sox21292439993.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292439889oez96yvva3y48b0/3sox21292439993.ps (open in new window)

Parameters (Session):

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

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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