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Faillissementen detailhandel Denemarken

*Unverified author*

R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)

Title produced by software: Exponential Smoothing

Date of computation: Sat, 15 Jan 2011 11:38:00 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Jan/15/t1295091457b62m4pirh0gvilr.htm/, Retrieved Sat, 15 Jan 2011 12:37:40 +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/2011/Jan/15/t1295091457b62m4pirh0gvilr.htm/},
    year = {2011},
}
@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 = {2011},
    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:

KDGP2W102 - PAUWELS

Dataseries X:

» Textbox « » Textfile « » CSV «

12 13 23 24 21 20 18 13 12 25 21 17 10 15 23 12 10 21 9 13 17 14 20 12 13 14 23 14 21 21 21 7 15 28 28 18 22 30 1 26 29 24 26 19 19 41 36 54 49 33 50 43 51 46 45 23 56 41 48 43

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	1 seconds
R Server	'Gwilym Jenkins' @ www.wessa.org

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.292518976579315
beta	0.00735790797960356
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	23	14	9
4	24	17.6520417386215	6.34795826137854
5	21	20.5419738284961	0.458026171503942
6	20	21.7099748337406	-1.70997483374061
7	18	22.2401139774867	-4.24011397748669
8	13	22.0210132934853	-9.02101329348529
9	12	20.3839926575377	-8.38399265753772
10	25	18.9152675463438	6.08473245365623
11	21	21.6920154353636	-0.692015435363558
12	17	22.4849465233526	-5.48494652335261
13	10	21.8640489122671	-11.8640489122671
14	15	19.3516074776318	-4.35160747763176
15	23	19.0273316377023	3.97266836229768
16	12	21.1466149314395	-9.14661493143955
17	10	19.4085723898511	-9.4085723898511
18	21	17.5736519895362	3.42634801046384
19	9	19.500563992972	-10.500563992972
20	13	17.3309892953794	-4.33098929537942
21	17	16.9568105659756	0.0431894340244128
22	14	17.8622550796877	-3.86225507968769
23	20	17.6169701225228	2.38302987747725
24	12	19.2036785907176	-7.20367859071762
25	13	17.970588231973	-4.97058823197304
26	14	17.3800208447811	-3.38002084478114
27	23	17.2474496893398	5.75255031066017
28	14	19.798710275274	-5.79871027527405
29	21	18.9585272115907	2.04147278840928
30	21	20.4161403923462	0.583859607653775
31	21	21.4486307144321	-0.448630714432056
32	7	22.1781324238542	-15.1781324238542
33	15	18.5663070526812	-3.56630705268125
34	28	18.3434850938027	9.6565149061973
35	28	22.0093734664593	5.99062653354065
36	18	24.6158137155926	-6.6158137155926
37	22	23.5203915655439	-1.52039156554388
38	30	23.9122047071674	6.08779529283257
39	1	26.542659812741	-25.542659812741
40	26	19.8656303875421	6.13436961245795
41	29	22.4679363645875	6.53206363541253
42	24	25.200634531798	-1.20063453179804
43	26	25.6687875859647	0.331212414035292
44	19	26.58574781866	-7.58574781865996
45	19	25.170519931222	-6.17051993122204
46	41	24.1559920759988	16.8440079240012
47	36	29.9099041804769	6.09009581952312
48	54	32.53120080393	21.46879919607
49	49	39.6972678916596	9.30273210834043
50	33	43.3245520140049	-10.3245520140049
51	50	41.1882612524371	8.8117387475629
52	43	44.6686644294642	-1.66866442946421
53	51	45.0797592823152	5.92024071768476
54	46	47.7234952003259	-1.72349520032594
55	45	48.1275837838765	-3.1275837838765
56	23	48.1142182266906	-25.1142182266906
57	56	41.6152908360158	14.3847091639842
58	41	46.7015098698039	-5.70150986980394
59	48	45.8998571507876	2.10014284921237
60	43	47.3848560964186	-4.38485609641863

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	46.9634321400664	30.0580682771238	63.8687960030091
62	47.8246618014862	30.2006178605696	65.4487057424028
63	48.685891462906	30.3614171000595	67.0103658257524
64	49.5471211243257	30.5383788531169	68.5558633955345
65	50.4083507857455	30.7297497462353	70.0869518252557
66	51.2695804471653	30.9340406963617	71.6051201979688
67	52.130810108585	31.149974928566	73.111645288604
68	52.9920397700048	31.3764483966228	74.6076311433868
69	53.8532694314245	31.6124991765255	76.0940396863236
70	54.7144990928443	31.8572834696186	77.57171471607
71	55.5757287542641	32.1100565535301	79.041400954998
72	56.4369584156838	32.3701574908999	80.5037593404677

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Jan/15/t1295091457b62m4pirh0gvilr/1ac5w1295091479.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/15/t1295091457b62m4pirh0gvilr/1ac5w1295091479.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/15/t1295091457b62m4pirh0gvilr/2xka81295091479.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/15/t1295091457b62m4pirh0gvilr/2xka81295091479.ps (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/15/t1295091457b62m4pirh0gvilr/3aj4s1295091479.png (open in new window)

http://www.freestatistics.org/blog/date/2011/Jan/15/t1295091457b62m4pirh0gvilr/3aj4s1295091479.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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