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exponential smoothing - verkocht aantal producten - mattias debbaut

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 14 Aug 2010 11:49:27 +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/Aug/14/t12817865605vas2ug2ze3kquu.htm/, Retrieved Sat, 14 Aug 2010 13:49:21 +0200

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/Aug/14/t12817865605vas2ug2ze3kquu.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:

mattias debbaut

Dataseries X:

» Textbox « » Textfile « » CSV «

376 375 374 372 370 369 370 372 373 373 374 376 371 374 369 363 357 366 362 366 361 362 358 363 360 360 348 345 332 333 323 327 332 337 336 337 343 337 326 321 309 302 293 287 292 292 289 302 310 295 276 264 257 243 227 226 226 229 224 240 244 226 208 199 193 180 167 164 166 173 169 191 193 166 143 147 139 129 115 108 106 116 108 135

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.999933983418648
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	375	376	-1
3	374	375.000066016581	-1.00006601658134
4	372	374.00006602094	-2.00006602093953
5	370	372.000132037521	-2.00013203752115
6	369	370.000132041879	-1.0001320418794
7	370	369.000066025298	0.999933974701719
8	372	369.999933987777	2.00006601222259
9	373	371.999867962479	1.00013203752059
10	373	372.999933974702	6.602529799693e-05
11	374	372.999999995641	1.00000000435875
12	376	373.999933983418	2.00006601658163
13	371	375.999867962479	-4.99986796247913
14	374	371.00033007419	2.99966992580988
15	369	373.999801972046	-4.99980197204633
16	363	369.000330069834	-6.00033006983364
17	357	363.000396121278	-6.00039612127819
18	366	357.000396125639	8.9996038743613
19	362	365.999405876919	-3.99940587691867
20	366	362.000264027103	3.99973597289659
21	361	365.999735951105	-4.99973595110475
22	362	361.000330065475	0.999669934524832
23	358	361.999934005208	-3.99993400520844
24	363	358.000264061969	4.99973593803134
25	360	362.999669934526	-2.99966993452568
26	360	360.000198027954	-0.000198027954240843
27	348	360.000000013073	-12.0000000130731
28	345	348.000792198977	-3.00079219897708
29	332	345.000198102042	-13.0001981020423
30	333	332.000858228636	0.999141771364407
31	323	332.999934040076	-9.99993404007597
32	327	323.000660161459	3.99933983854095
33	332	326.999735977256	5.00026402274381
34	337	331.999669899663	5.00033010033661
35	336	336.999669895301	-0.999669895301167
36	337	336.000065994789	0.99993400521106
37	343	336.999933987775	6.00006601222458
38	337	342.999603896154	-5.99960389615399
39	326	337.000396073339	-11.0003960733387
40	321	326.000726208542	-5.00072620854229
41	309	321.000330130849	-12.0003301308486
42	302	309.00079222077	-7.00079222077034
43	293	302.000462168369	-9.00046216836915
44	287	293.000594179743	-6.00059417974296
45	292	287.000396138714	4.99960386128618
46	292	291.999669943245	0.000330056755046826
47	289	291.999999978211	-2.99999997821078
48	302	289.000198049743	12.9998019502574
49	310	301.999141797517	8.00085820248302
50	295	309.999471810694	-14.9994718106936
51	276	295.000990213851	-19.000990213851
52	264	276.001254380416	-12.0012543804162
53	257	264.000792281786	-7.00079228178612
54	243	257.000462168373	-14.0004621683732
55	227	243.00092426265	-16.0009242626497
56	226	227.001056326318	-1.00105632631829
57	226	226.000066086316	-6.60863163943759e-05
58	229	226.000000004363	2.99999999563721
59	224	228.999801950256	-4.99980195025623
60	240	224.000330069832	15.9996699301678
61	244	239.998943756488	4.00105624351156
62	226	243.999735863945	-17.999735863945
63	208	226.001188281027	-18.001188281027
64	199	208.001188376911	-9.00118837691059
65	193	199.000594227685	-6.00059422768476
66	180	193.000396138717	-13.000396138717
67	167	180.000858241709	-13.0008582417093
68	164	167.000858272216	-3.00085827221577
69	166	164.000198106404	1.99980189359576
70	173	165.999867979916	7.00013202008441
71	169	172.999537875215	-3.99953787521503
72	191	169.000264035818	21.9997359641825
73	193	190.998547652641	2.00145234735899
74	166	192.999867870958	-26.9998678709583
75	143	166.001782438974	-23.0017824389738
76	147	143.001518499042	3.99848150095838
77	139	146.999736033921	-7.9997360339207
78	129	139.000528115225	-10.0005281152247
79	115	129.000660200678	-14.0006602006779
80	108	115.000924275723	-7.00092427572312
81	106	108.000462177087	-2.00046217708699
82	116	106.000132063674	9.99986793632594
83	108	115.999339842905	-7.99933984290487
84	135	108.00052808907	26.9994719109305

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	134.998217587166	117.2613133139	152.735121860432
86	134.998217587166	109.915274968125	160.081160206207
87	134.998217587166	104.278350275259	165.718084899073
88	134.998217587166	99.5261654208157	170.470269753517
89	134.998217587166	95.3393885307834	174.657046643549
90	134.998217587166	91.5542426383371	178.442192535995
91	134.998217587166	88.0734352585758	181.922999915756
92	134.998217587166	84.8335743230435	185.162860851289
93	134.998217587166	81.7906272353397	188.205807938993
94	134.998217587166	78.9125339568592	191.083901217473
95	134.998217587166	76.1750916458327	193.8213435285
96	134.998217587166	73.5594970378166	196.436938136516

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/14/t12817865605vas2ug2ze3kquu/199ff1281786562.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/14/t12817865605vas2ug2ze3kquu/199ff1281786562.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/14/t12817865605vas2ug2ze3kquu/210wi1281786562.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/14/t12817865605vas2ug2ze3kquu/210wi1281786562.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/14/t12817865605vas2ug2ze3kquu/310wi1281786562.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/14/t12817865605vas2ug2ze3kquu/310wi1281786562.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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