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Exponential Smoothing Eigen Reeks

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 19 Dec 2010 20:31:05 +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/19/t1292790789o446ar11cpunc5n.htm/, Retrieved Sun, 19 Dec 2010 21:33:13 +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/19/t1292790789o446ar11cpunc5n.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:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

95,05 96,84 96,92 97,44 97,78 97,69 96,67 98,29 98,2 98,71 98,54 98,2 96,92 99,06 99,65 99,82 99,99 100,33 99,31 101,1 101,1 100,93 100,85 100,93 99,6 101,88 101,81 102,38 102,74 102,82 101,72 103,47 102,98 102,68 102,9 103,03 101,29 103,69 103,68 104,2 104,08 104,16 103,05 104,66 104,46 104,95 105,85 106,23 104,86 107,44 108,23 108,45 109,39 110,15 109,13 110,28 110,17 109,99 109,26 109,11 107,06 109,53 108,92 109,24 109,12 109 107,23 109,49 109,04 109,02 109,23 109,46

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	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.651524078529005
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	96.84	95.05	1.79000000000001
3	96.92	96.216228100567	0.703771899433079
4	97.44	96.6747524388397	0.765247561160322
5	97.78	97.1733296509712	0.606670349028775
6	97.69	97.568589991093	0.121410008906935
7	96.67	97.6476915352704	-0.977691535270353
8	98.29	97.0107019586677	1.27929804133227
9	98.2	97.8441954362107	0.355804563789306
10	98.71	98.07601067677	0.633989323230054
11	98.54	98.4890699863846	0.0509300136153712
12	98.2	98.5222521165749	-0.322252116574859
13	96.92	98.3122971032694	-1.3922971032694
14	99.06	97.4051820160232	1.65481798397680
15	99.65	98.483335778167	1.16666422183309
16	99.82	99.2434456102495	0.576554389750513
17	99.99	99.6190846777535	0.370915322246461
18	100.33	99.8607449412925	0.469255058707546
19	99.31	100.166475911012	-0.856475911011955
20	101.1	99.6084612323076	1.49153876769239
21	101.1	100.580234653519	0.519765346481321
22	100.93	100.918874291936	0.0111257080637870
23	100.85	100.926122958630	-0.0761229586304637
24	100.93	100.876527018154	0.0534729818461699
25	99.6	100.911365953377	-1.31136595337736
26	101.88	100.056979458989	1.82302054101115
27	101.81	101.244721237111	0.56527876288942
28	102.38	101.613013962214	0.76698603778587
29	102.74	102.112723833727	0.627276166272807
30	102.82	102.521409359941	0.298590640058706
31	101.72	102.715948351563	-0.99594835156293
32	103.47	102.067064019548	1.40293598045159
33	102.98	102.981110591447	-0.00111059144730064
34	102.68	102.980387014378	-0.300387014377975
35	102.9	102.784677641633	0.115322358366711
36	103.03	102.859812934902	0.170187065098048
37	101.29	102.970693905668	-1.68069390566750
38	103.69	101.875681357488	1.81431864251182
39	103.68	103.057753639209	0.622246360791308
40	104.2	103.463162126041	0.73683787395872
41	104.08	103.943229742898	0.136770257102484
42	104.16	104.032338858626	0.127661141373608
43	103.05	104.115513166124	-1.06551316612378
44	104.66	103.421305682404	1.23869431759553
45	104.46	104.228344856255	0.231655143744987
46	104.95	104.37927376032	0.570726239680042
47	105.85	104.751115647720	1.09888435228018
48	106.23	105.467065262749	0.762934737250916
49	104.86	105.964135614414	-1.10413561441426
50	107.44	105.244764675662	2.19523532433804
51	108.23	106.675013347506	1.55498665249438
52	108.45	107.688124593397	0.761875406603068
53	109.39	108.184504765638	1.20549523436209
54	110.15	108.969913937377	1.18008606262322
55	109.13	109.738768421912	-0.608768421912316
56	110.28	109.342141136788	0.93785886321166
57	110.17	109.953178768433	0.216821231567423
58	109.99	110.094443021535	-0.104443021535076
59	109.26	110.026395878171	-0.766395878170641
60	109.11	109.527070509857	-0.417070509857098
61	107.06	109.255339030241	-2.19533903024083
62	109.53	107.825022791504	1.70497720849558
63	108.92	108.935856496182	-0.015856496182451
64	109.24	108.925525607118	0.314474392881507
65	109.12	109.130413246162	-0.0104132461615762
66	109	109.123628765552	-0.123628765551672
67	107.23	109.043081647996	-1.81308164799593
68	109.49	107.861815297988	1.62818470201246
69	109.04	108.922616835641	0.117383164358785
70	109.02	108.999094793635	0.0209052063651001
71	109.23	109.012715038948	0.217284961051632
72	109.46	109.154281422976	0.305718577024251

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	109.353464437161	107.532780286888	111.174148587433
74	109.353464437161	107.180446345334	111.526482528987
75	109.353464437161	106.877757572494	111.829171301827
76	109.353464437161	106.608242891983	112.098685982339
77	109.353464437161	106.362919639893	112.344009234428
78	109.353464437161	106.136249020560	112.570679853761
79	109.353464437161	105.92452992493	112.782398949391
80	109.353464437161	105.725144062453	112.981784811868
81	109.353464437161	105.536158372163	113.170770502159
82	109.353464437161	105.356097498009	113.350831376312
83	109.353464437161	105.183805062754	113.523123811567
84	109.353464437161	105.018354732559	113.688574141762

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292790789o446ar11cpunc5n/1forp1292790661.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292790789o446ar11cpunc5n/1forp1292790661.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292790789o446ar11cpunc5n/2forp1292790661.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292790789o446ar11cpunc5n/2forp1292790661.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292790789o446ar11cpunc5n/3qfqa1292790661.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t1292790789o446ar11cpunc5n/3qfqa1292790661.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Single ; par3 = multiplicative ;

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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