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holt winter 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: Sat, 18 Dec 2010 18:52:24 +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/18/t1292698265xgj228c861kruwl.htm/, Retrieved Sat, 18 Dec 2010 19:51:05 +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/18/t1292698265xgj228c861kruwl.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 «

101,76 102,37 102,38 102,86 102,87 102,92 102,95 103,02 104,08 104,16 104,24 104,33 104,73 104,86 105,03 105,62 105,63 105,63 105,94 106,61 107,69 107,78 107,93 108,48 108,14 108,48 108,48 108,89 108,93 109,21 109,47 109,80 111,73 111,85 112,12 112,15 112,17 112,67 112,80 113,44 113,53 114,53 114,51 115,05 116,67 117,07 116,92 117,00 117,02 117,35 117,36 117,82 117,88 118,24 118,50 118,80 119,76 120,09 120,16

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.799216301497526
beta	0.0327166432819145
gamma	0.178232667757671

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	104.73	103.368149038462	1.36185096153842
14	104.86	104.605955271144	0.254044728856243
15	105.03	104.979194049347	0.0508059506531282
16	105.62	105.610079540381	0.00992045961884003
17	105.63	105.625214744103	0.00478525589682022
18	105.63	105.60428759928	0.0257124007200389
19	105.94	106.116591422565	-0.176591422564854
20	106.61	106.115926610697	0.494073389303139
21	107.69	107.667520252880	0.022479747119732
22	107.78	107.851546361662	-0.0715463616618308
23	107.93	107.953971167219	-0.0239711672189173
24	108.48	108.105875386774	0.374124613226144
25	108.14	108.934878889200	-0.794878889200405
26	108.48	108.413765153321	0.066234846678725
27	108.48	108.629137151196	-0.149137151195887
28	108.89	109.093040757292	-0.203040757291632
29	108.93	108.926500713133	0.00349928686733847
30	109.21	108.893971676847	0.316028323153006
31	109.47	109.62732908891	-0.157329088909989
32	109.8	109.662831326913	0.137168673087061
33	111.73	110.899743846488	0.830256153511883
34	111.85	111.734554159189	0.115445840811191
35	112.12	112.001579099023	0.118420900976702
36	112.15	112.298705324744	-0.148705324744242
37	112.17	112.671523224133	-0.501523224132512
38	112.67	112.426853503090	0.243146496910157
39	112.8	112.791708040123	0.00829195987742537
40	113.44	113.399418170121	0.0405818298789029
41	113.53	113.461262337451	0.0687376625489833
42	114.53	113.520048719502	1.00995128049817
43	114.51	114.837197086984	-0.327197086983503
44	115.05	114.789171444357	0.260828555643485
45	116.67	116.194645785873	0.475354214127421
46	117.07	116.755880318670	0.314119681329529
47	116.92	117.222637946078	-0.302637946078235
48	117	117.203520780676	-0.203520780675873
49	117.02	117.548303100144	-0.528303100144043
50	117.35	117.336578987286	0.0134210127140051
51	117.36	117.531121441968	-0.171121441967898
52	117.82	118.013598569714	-0.193598569714439
53	117.88	117.900167842967	-0.0201678429666146
54	118.24	117.930135603758	0.309864396242048
55	118.5	118.630159634753	-0.130159634753085
56	118.8	118.756052810572	0.0439471894284225
57	119.76	119.985598209489	-0.225598209489263
58	120.09	119.952251008916	0.137748991084365
59	120.16	120.222768045257	-0.0627680452567176

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
60	120.371967043331	119.648151913234	121.095782173427
61	120.846166554290	119.907652747071	121.784680361508
62	121.068253839470	119.945453998008	122.191053680931
63	121.237311691034	119.947257936845	122.527365445223
64	121.852067686060	120.405623019414	123.298512352706
65	121.900952866359	120.305557513444	123.496348219274
66	121.960759387669	120.221734500787	123.699784274552
67	122.391195401520	120.512450543337	124.269940259704
68	122.624555728944	120.609009455557	124.640102002331
69	123.805393517070	121.655240600546	125.955546433595
70	123.967311481243	121.684201543424	126.250421419063
71	124.118920294351	121.704082112494	126.533758476209

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292698265xgj228c861kruwl/168x21292698340.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292698265xgj228c861kruwl/168x21292698340.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292698265xgj228c861kruwl/268x21292698340.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292698265xgj228c861kruwl/268x21292698340.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292698265xgj228c861kruwl/3hhe51292698340.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292698265xgj228c861kruwl/3hhe51292698340.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

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=0, beta=0)

if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)

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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