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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 06 Aug 2010 12:28:25 +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/06/t1281097662vq6ufq92kkz09od.htm/, Retrieved Fri, 06 Aug 2010 14:27:47 +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/06/t1281097662vq6ufq92kkz09od.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 «

94 93 92 90 88 87 88 90 91 91 92 94 88 90 82 83 88 83 85 81 79 71 70 85 88 84 81 93 99 96 90 95 93 86 77 89 90 84 76 96 104 101 95 101 95 90 88 99 81 79 70 95 100 105 107 106 99 86 81 95 82 78 68 96 98 107 102 98 93 69 65 90 87 80 67 85 85 92 87 85 79 58 47 67

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	0.889089461093732
beta	0
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	92	92	0
4	90	91	-1
5	88	89.1109105389063	-1.11091053890627
6	87	87.1232116865467	-0.123211686546739
7	88	86.0136654745544	1.98633452544556
8	90	86.7796945673347	3.2203054326653
9	91	88.6428341890203	2.35716581097969
10	91	89.7385654696128	1.26143453038719
11	92	89.8600936164398	2.13990638356022
12	94	90.7626618297904	3.23733817020963
13	88	92.6409450789202	-4.64094507892023
14	90	87.5147297197374	2.48527028026257
15	82	88.7243573338883	-6.72435733388835
16	83	81.7458020956999	1.25419790430013
17	88	81.860896234539	6.13910376546104
18	83	86.3191086929712	-3.31910869297121
19	85	82.368124133826	2.63187586617408
20	81	83.7080972293482	-2.70809722934823
21	79	80.3003565231176	-1.30035652311759
22	71	78.1442232427492	-7.14422324274925
23	70	70.79236964992	-0.792369649920005
24	85	69.0878821448856	15.9121178551144
25	88	82.2351784335492	5.76482156645078
26	84	86.3606205333665	-2.36062053336647
27	81	83.2618176955089	-2.26181769550888
28	93	80.2508594195166	12.7491405804834
29	99	90.5859859476268	8.41401405237318
30	96	97.0667971670864	-1.06679716708638
31	90	95.1183190487052	-5.11831904870523
32	95	89.5676755239861	5.43232447601389
33	93	93.3974979648516	-0.397497964851595
34	86	92.0440867134958	-6.04408671349583
35	77	85.67035291459	-8.67035291459004
36	89	76.9616335142647	12.0383664857353
37	90	86.664818285516	3.33518171448405
38	84	88.6300931986962	-4.63009319869624
39	76	83.5135261318536	-7.51352613185364
40	96	75.8333292323702	20.1666707676298
41	104	92.7633036772169	11.2366963227831
42	101	101.753731955314	-0.753731955314052
43	95	100.083596817355	-5.08359681735476
44	101	94.563824462595	6.43617553740499
45	95	99.286160302651	-4.28616030265107
46	90	94.4753803490057	-4.47538034900568
47	88	89.4963668463187	-1.49636684631874
48	99	87.1659628533267	11.8340371466733
49	81	96.6874805626257	-15.6874805626257
50	79	81.7399069232824	-2.73990692328240
51	70	78.3038845534143	-8.30388455341426
52	95	69.9209883108346	25.0790116891654
53	100	91.2184732983181	8.78152670168193
54	105	98.0260361410967	6.97396385890332
55	107	103.226513910096	3.7734860899038
56	106	105.581480624213	0.418519375786531
57	99	104.953581790489	-5.9535817904888
58	86	98.6603149648057	-12.6603149648057
59	81	86.4041623554697	-5.40416235546968
60	95	80.5993785591821	14.4006214408179
61	82	92.4028193154137	-10.4028193154137
62	78	82.153782296417	-4.15378229641706
63	68	77.460698232995	-9.46069823299493
64	96	68.049291139451	27.9507088605490
65	98	91.8999718174643	6.10002818253568
66	107	96.3234425869315	10.6765574130685
67	102	104.815857263653	-2.81585726365287
68	98	101.312308246595	-3.31230824659487
69	93	97.3673698926535	-4.36736989265351
70	69	92.4843873483972	-23.4843873483972
71	65	70.6046660566943	-5.60466605669427
72	90	64.6216165327376	25.3783834672624
73	87	86.185269813076	0.814730186923981
74	80	85.909637835905	-5.90963783590506
75	67	79.6554411171211	-12.6554411171211
76	85	67.4036217943964	17.5963782056036
77	85	82.048376210418	2.95162378958199
78	92	83.6726338148489	8.3273661851511
79	87	90.076407328735	-3.07640732873506
80	85	86.3412059947252	-1.3412059947252
81	79	84.1487538796593	-5.1487538796593
82	58	78.5710510674888	-20.5710510674888
83	47	59.2815463597635	-12.2815463597635
84	67	47.3621529253637	19.6378470746363

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	63.8219557979932	45.0671900890184	82.576721506968
86	62.8219557979932	37.7264248367959	87.9174867591906
87	61.8219557979932	31.6917365546772	91.9521750413092
88	60.8219557979932	26.3854265147427	95.2584850812437
89	59.8219557979932	21.5607615340651	98.0831500619213
90	58.8219557979932	17.085120461232	100.558791134754
91	57.8219557979932	12.8774582331767	102.766453362810
92	56.8219557979932	8.88395105457829	104.759960541408
93	55.8219557979932	5.06669266001364	106.577218935973
94	54.8219557979932	1.39779297225093	108.246118623735
95	53.8219557979932	-2.14397679548101	109.787888391467
96	52.8219557979932	-5.57521920630965	111.219130802296

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/06/t1281097662vq6ufq92kkz09od/184zo1281097703.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/06/t1281097662vq6ufq92kkz09od/184zo1281097703.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/06/t1281097662vq6ufq92kkz09od/21vgr1281097703.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/06/t1281097662vq6ufq92kkz09od/21vgr1281097703.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/06/t1281097662vq6ufq92kkz09od/31vgr1281097703.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/06/t1281097662vq6ufq92kkz09od/31vgr1281097703.ps (open in new window)

Parameters (Session):

par1 = additive ; par2 = 12 ;

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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