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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: Tue, 26 Jan 2010 18:09:50 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/27/t12645546453a4mhkn8rajo50i.htm/, Retrieved Wed, 27 Jan 2010 02:10:49 +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/Jan/27/t12645546453a4mhkn8rajo50i.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:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

2,46 2,46 2,45 2,45 2,46 2,43 2,44 2,44 2,43 2,43 2,42 2,43 2,43 2,42 2,41 2,42 2,39 2,4 2,39 2,4 2,41 2,41 2,41 2,41 2,42 2,43 2,43 2,43 2,44 2,42 2,44 2,42 2,42 2,42 2,43 2,44 2,43 2,44 2,44 2,45 2,45 2,43 2,44 2,45 2,46 2,44 2,43 2,42 2,41 2,43 2,41 2,43 2,43 2,44 2,43 2,44 2,43 2,44 2,44 2,43 2,43 2,43 2,43 2,44 2,47 2,48 2,49 2,5 2,51 2,49 2,49 2,48 2,48 2,48 2,5 2,5 2,5 2,5 2,5 2,48 2,49 2,48 2,5 2,5 2,49 2,48 2,47 2,46 2,43 2,42 2,43 2,45 2,45 2,46 2,44 2,45 2,45 2,42 2,41 2,39 2,39 2,38 2,37 2,37 2,38 2,39 2,41 2,42 2,48 2,53 2,56 2,56 2,53 2,57 2,56 2,57 2,58 2,57 2,6 2,63 2,72 2,83 2,9 2,92 2,94 2,95 2,98 3,02 3,16 3,2 3,18 3,17

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	0.900361087365125
beta	0.157393226075154
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	2.43	2.45106837606838	-0.0210683760683770
14	2.42	2.41981582945203	0.000184170547967710
15	2.41	2.40647434776039	0.00352565223960877
16	2.42	2.41580769559908	0.00419230440092111
17	2.39	2.38591869897887	0.00408130102113136
18	2.4	2.39650812340718	0.00349187659282268
19	2.39	2.40456168941889	-0.0145616894188882
20	2.4	2.38846364604467	0.0115363539553281
21	2.41	2.38791475725939	0.0220852427406060
22	2.41	2.40957672679199	0.000423273208014052
23	2.41	2.40304508423965	0.00695491576034746
24	2.41	2.42337986471044	-0.0133798647104402
25	2.42	2.41057736623144	0.00942263376856367
26	2.43	2.41427411583034	0.0157258841696613
27	2.43	2.42283995440373	0.00716004559627015
28	2.43	2.44360825013825	-0.0136082501382502
29	2.44	2.40325499397821	0.0367450060217869
30	2.42	2.45339734278777	-0.0333973427877710
31	2.44	2.43141338004267	0.00858661995733367
32	2.42	2.44701284489899	-0.0270128448989913
33	2.42	2.41559929254193	0.00440070745806898
34	2.42	2.41946678627214	0.000533213727855308
35	2.43	2.41398688210335	0.0160131178966529
36	2.44	2.44203677083343	-0.00203677083342546
37	2.43	2.44491219797826	-0.0149121979782634
38	2.44	2.42707138323213	0.0129286167678688
39	2.44	2.43161329963331	0.0083867003666911
40	2.45	2.4509386467256	-0.000938646725600734
41	2.45	2.42832712052782	0.0216728794721806
42	2.43	2.45709169193994	-0.0270916919399391
43	2.44	2.44504339288516	-0.00504339288516498
44	2.45	2.4429673780756	0.00703262192440146
45	2.46	2.4483052050997	0.0116947949002988
46	2.44	2.46235646261533	-0.0223564626153276
47	2.43	2.43856807665296	-0.0085680766529559
48	2.42	2.43996221513687	-0.0199622151368728
49	2.41	2.42014982038177	-0.0101498203817703
50	2.43	2.4047802178352	0.0252197821647990
51	2.41	2.41708718398364	-0.00708718398364105
52	2.43	2.41650957906654	0.0134904209334632
53	2.43	2.4061454643738	0.0238545356261985
54	2.44	2.42932768189657	0.0106723181034329
55	2.43	2.45614127886923	-0.0261412788692317
56	2.44	2.43594677486229	0.00405322513770656
57	2.43	2.43831837567344	-0.00831837567343552
58	2.44	2.42737341463357	0.0126265853664287
59	2.44	2.43782942879536	0.00217057120464359
60	2.43	2.4506518752853	-0.0206518752853011
61	2.43	2.43399344837853	-0.00399344837852489
62	2.43	2.43136063103556	-0.00136063103555939
63	2.43	2.41641950522681	0.0135804947731857
64	2.44	2.43933234493077	0.000667655069228168
65	2.47	2.41947039707318	0.0505296029268201
66	2.48	2.47015110593411	0.00984889406589273
67	2.49	2.49723332970381	-0.00723332970381296
68	2.5	2.50442888684123	-0.004428886841227
69	2.51	2.50408635682978	0.00591364317021581
70	2.49	2.51621464035644	-0.0262146403564376
71	2.49	2.49332583718102	-0.00332583718102297
72	2.48	2.50081476438049	-0.0208147643804906
73	2.48	2.48753565957262	-0.00753565957262392
74	2.48	2.48334008836706	-0.00334008836706134
75	2.5	2.46918912757897	0.0308108724210334
76	2.5	2.50985431087844	-0.00985431087844457
77	2.5	2.48752131239287	0.0124786876071328
78	2.5	2.49653118075069	0.00346881924931042
79	2.5	2.51190495870566	-0.0119049587056574
80	2.48	2.51024975401399	-0.0302497540139908
81	2.49	2.47910650380814	0.0108934961918634
82	2.48	2.48463979002433	-0.00463979002432513
83	2.5	2.47863670998043	0.0213632900195657
84	2.5	2.50529085526093	-0.00529085526092743
85	2.49	2.50819056065946	-0.0181905606594572
86	2.48	2.49418843034905	-0.0141884303490531
87	2.47	2.47150413971845	-0.00150413971844499
88	2.46	2.47227425528616	-0.0122742552861648
89	2.43	2.44289668298617	-0.0128966829861699
90	2.42	2.41747487342962	0.00252512657037984
91	2.43	2.41964648114674	0.0103535188532646
92	2.45	2.42853767374426	0.0214623262557447
93	2.45	2.44771517972498	0.00228482027501853
94	2.46	2.44239163023426	0.0176083697657399
95	2.44	2.46060545010448	-0.0206054501044814
96	2.45	2.44246396773228	0.00753603226772137
97	2.45	2.45309208148258	-0.00309208148258167
98	2.42	2.45268730938122	-0.0326873093812163
99	2.41	2.41159421423757	-0.00159421423756534
100	2.39	2.40818036048418	-0.0181803604841848
101	2.39	2.36955643722626	0.0204435627737425
102	2.38	2.37654746506049	0.00345253493950493
103	2.37	2.38132347653303	-0.0113234765330308
104	2.37	2.3697219413628	0.000278058637201095
105	2.38	2.36283061899179	0.0171693810082090
106	2.39	2.36946016037513	0.0205398396248695
107	2.41	2.38394598870602	0.0260540112939807
108	2.42	2.41467121359233	0.00532878640766699
109	2.48	2.42599260208124	0.0540073979187623
110	2.53	2.48588031899439	0.0441196810056139
111	2.56	2.53975488255391	0.0202451174460863
112	2.56	2.58016210654684	-0.0201621065468354
113	2.53	2.56913192617182	-0.0391319261718244
114	2.57	2.53787763227208	0.0321223677279168
115	2.56	2.58814450077408	-0.0281445007740806
116	2.57	2.58132013547017	-0.0113201354701720
117	2.58	2.58279189600329	-0.00279189600329000
118	2.57	2.58607879445085	-0.0160787944508543
119	2.6	2.57724868737202	0.0227513126279781
120	2.63	2.61157185588040	0.0184281441195968
121	2.72	2.65003060372291	0.0699693962770889
122	2.83	2.73605959149173	0.0939404085082711
123	2.9	2.85222700587615	0.0477729941238461
124	2.92	2.93710916464554	-0.0171091646455368
125	2.94	2.95108627446372	-0.0110862744637235
126	2.95	2.98030593665009	-0.0303059366500880
127	2.98	2.98763614517666	-0.00763614517666156
128	3.02	3.02313560213474	-0.00313560213474151
129	3.16	3.05616851420426	0.103831485795738
130	3.2	3.1925831141371	0.00741688586290401
131	3.18	3.25055823275868	-0.0705582327586756
132	3.17	3.22899703712107	-0.0589970371210691

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
133	3.22046737489036	3.17268429702831	3.26825045275241
134	3.25355836785959	3.18454673752015	3.32256999819903
135	3.27490433979872	3.18567329808711	3.36413538151033
136	3.29789773659158	3.18847357737136	3.4073218958118
137	3.31789290974848	3.18793633387395	3.447849485623
138	3.34676376296595	3.19577013123447	3.49775739469743
139	3.37951829467517	3.2069018258927	3.55213476345763
140	3.41930283631193	3.22443744669639	3.61416822592747
141	3.46322272283419	3.24546367206635	3.68098177360203
142	3.47923652709980	3.23793256794994	3.72054048624967
143	3.50440504159922	3.23890548859986	3.76990459459859
144	3.53916316453042	3.24882208397466	3.82950424508619

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/27/t12645546453a4mhkn8rajo50i/1tbs31264554588.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/27/t12645546453a4mhkn8rajo50i/1tbs31264554588.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/27/t12645546453a4mhkn8rajo50i/2ds1d1264554588.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/27/t12645546453a4mhkn8rajo50i/2ds1d1264554588.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/27/t12645546453a4mhkn8rajo50i/3jz841264554588.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/27/t12645546453a4mhkn8rajo50i/3jz841264554588.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=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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