Home » date » 2010 » Jan » 19 »

Bruin brood triple

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 19 Jan 2010 13:01:48 -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/19/t12639313535mrq50po7m3nl91.htm/, Retrieved Tue, 19 Jan 2010 21:02:37 +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/19/t12639313535mrq50po7m3nl91.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 «

1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.38 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.44 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.48 1.57 1.58 1.58 1.58 1.58 1.59 1.6 1.6 1.61 1.61 1.61 1.62 1.63 1.63 1.64 1.64 1.64 1.64 1.64 1.65 1.65 1.65 1.65 1.65 1.66 1.66 1.67 1.68 1.68 1.68 1.68 1.69 1.7 1.7 1.71 1.72 1.73 1.74 1.74 1.75 1.75 1.75 1.76 1.79 1.83 1.84 1.85 1.87 1.87 1.87 1.88 1.88 1.88 1.88 1.89 1.89 1.89 1.9 1.89

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	1
beta	0.0330450901927309
gamma	0.00480500770391178

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	1.38	1.37990651709402	9.34829059822118e-05
14	1.38	1.38008321735619	-8.32173561877703e-05
15	1.38	1.38008046743115	-8.046743114698e-05
16	1.38	1.38007780837763	-7.78083776271643e-05
17	1.38	1.38007523719277	-7.52371927708051e-05
18	1.38	1.37798941763962	0.00201058236038354
19	1.38	1.38222252418172	-0.00222252418172175
20	1.38	1.38006574733635	-6.57473363481209e-05
21	1.38	1.38006357470969	-6.35747096884298e-05
22	1.38	1.38006147387767	-6.14738776727464e-05
23	1.38	1.38005944246784	-5.94424678406202e-05
24	1.43	1.38005747818613	0.0499425218138705
25	1.43	1.43170783332392	-0.00170783332392133
26	1.43	1.43165139781770	-0.00165139781769819
27	1.43	1.43159682722787	-0.00159682722786836
28	1.43	1.4315440599281	-0.00154405992810114
29	1.43	1.43149303632851	-0.00149303632851416
30	1.43	1.42936036547504	0.000639634524955968
31	1.43	1.43354816892228	-0.00354816892227805
32	1.43	1.43134758602689	-0.00134758602688922
33	1.43	1.43130305492509	-0.00130305492508809
34	1.43	1.43125999535756	-0.00125999535756249
35	1.43	1.43121835869733	-0.00121835869732934
36	1.43	1.43117809792429	-0.00117809792428902
37	1.43	1.43113916757213	-0.00113916757212507
38	1.43	1.43110152367696	-0.00110152367695959
39	1.43	1.43106512372771	-0.00106512372770506
40	1.43	1.43102992661806	-0.00102992661805668
41	1.43	1.43099589260007	-0.000995892600071047
42	1.43	1.42887964990595	0.00112035009405376
43	1.44	1.43308333864252	0.00691666135748203
44	1.48	1.44122856700758	0.0387714329924247
45	1.48	1.48250977250771	-0.00250977250771145
46	1.48	1.48242683684883	-0.00242683684883094
47	1.48	1.48234664180628	-0.00234664180627830
48	1.48	1.48226909681614	-0.00226909681613985
49	1.48	1.48219411430719	-0.00219411430719441
50	1.48	1.48212160960202	-0.00212160960202001
51	1.48	1.48205150082137	-0.00205150082136751
52	1.48	1.48198370879169	-0.00198370879169496
53	1.48	1.48191815695576	-0.00191815695575737
54	1.48	1.47977143795282	0.00022856204718269
55	1.48	1.48394565747295	-0.00394565747294751
56	1.48	1.48173193953255	-0.00173193953255102
57	1.48	1.48167470743449	-0.00167470743448961
58	1.48	1.48161936657627	-0.00161936657627049
59	1.48	1.48156585446170	-0.00156585446170254
60	1.48	1.48151411065979	-0.00151411065978690
61	1.48	1.48146407673647	-0.00146407673647242
62	1.48	1.48141569618867	-0.00141569618866666
63	1.48	1.48136891438043	-0.00136891438042652
64	1.48	1.48132367848126	-0.00132367848125936
65	1.48	1.48127993740646	-0.00127993740645982
66	1.48	1.47915430842609	0.00084569157391079
67	1.48	1.48334892104709	-0.00334892104709072
68	1.48	1.48115492231571	-0.00115492231570813
69	1.48	1.48111675780362	-0.00111675780361975
70	1.48	1.48107985444128	-0.00107985444127578
71	1.48	1.48104417055387	-0.00104417055386885
72	1.48	1.48100966584374	-0.00100966584373974
73	1.48	1.48097630134487	-0.000976301344868702
74	1.57	1.48094403937887	0.0890559606211279
75	1.58	1.57388690162980	0.00611309837020224
76	1.58	1.58408890951680	-0.00408890951679819
77	1.58	1.58395379113303	-0.00395379113302563
78	1.58	1.58173980441510	-0.00173980441509825
79	1.59	1.58584897908795	0.00415102091204989
80	1.6	1.59390281661505	0.00609718338495258
81	1.6	1.60410429858992	-0.00410429858992489
82	1.61	1.60396867167284	0.00603132832715714
83	1.61	1.61416797746140	-0.00416797746139586
84	1.61	1.61403024627026	-0.00403024627026261
85	1.62	1.61389706641876	0.00610293358123704
86	1.63	1.62409873840940	0.00590126159060467
87	1.63	1.63429374613091	-0.00429374613090761
88	1.64	1.63415185890275	0.00584814109725285
89	1.64	1.64434511125277	-0.00434511125276571
90	1.64	1.64211819332619	-0.00211819332618735
91	1.64	1.64621486410334	-0.00621486410334415
92	1.64	1.64392616002518	-0.00392616002518054
93	1.65	1.64379641971304	0.00620358028696266
94	1.65	1.65400141758314	-0.00400141758313777
95	1.65	1.65386919037820	-0.00386919037820421
96	1.65	1.65374133263318	-0.00374133263318366
97	1.65	1.65361769995888	-0.00361769995887906
98	1.66	1.65349815273745	0.00650184726255243
99	1.66	1.66371300686666	-0.00371300686665799
100	1.67	1.66359031021986	0.0064096897801369
101	1.68	1.67380211899676	0.00619788100324481
102	1.68	1.68192359520018	-0.00192359520017793
103	1.68	1.68602669648996	-0.00602669648996024
104	1.68	1.68374421042755	-0.00374421042755202
105	1.69	1.68362048265627	0.00637951734372688
106	1.7	1.69383129438228	0.00616870561771732
107	1.7	1.70403513981579	-0.00403513981579251
108	1.71	1.70390179825664	0.00609820174336062
109	1.72	1.71410331388326	0.00589668611673777
110	1.73	1.72429817040783	0.00570182959217203
111	1.74	1.73448658788096	0.00551341211903522
112	1.74	1.74466877908171	-0.00466877908170815
113	1.75	1.74451449885586	0.00548550114413682
114	1.75	1.75261243440259	-0.00261243440259018
115	1.75	1.7566927729388	-0.00669277293880044
116	1.76	1.75438827632007	0.0056117236799349
117	1.79	1.76457371623521	0.0254262837647947
118	1.83	1.79541393007548	0.0345860699245211
119	1.84	1.83655682987555	0.00344317012445328
120	1.85	1.84667060974286	0.00332939025714185
121	1.87	1.85678062974419	0.0132193702558077
122	1.87	1.87721746502659	-0.0072174650265866
123	1.87	1.87697896324382	-0.00697896324382019
124	1.88	1.87674834277398	0.00325165722602350
125	1.88	1.88685579408029	-0.00685579408028603
126	1.88	1.88454591041323	-0.00454591041322705
127	1.88	1.88856235706028	-0.00856235706028041
128	1.89	1.88619607986563	0.00380392013437225
129	1.89	1.89632178074955	-0.00632178074955414
130	1.89	1.89611287693451	-0.00611287693450646
131	1.9	1.89591087636487	0.00408912363513148
132	1.89	1.9060460018242	-0.0160460018242008

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
133	1.89551576024669	1.87305534603914	1.91797617445424
134	1.90103152049337	1.86873861399600	1.93332442699074
135	1.90654728074006	1.86634545799856	1.94674910348156
136	1.91206304098675	1.86488639239692	1.95923968957657
137	1.91757880123344	1.86398512238925	1.97117248007763
138	1.92101122814679	1.86136873480422	1.98065372148936
139	1.92861032172681	1.86317660172650	1.99404404172712
140	1.93412608197350	1.86308793549109	2.00516422845591
141	1.93964184222019	1.86313780062387	2.0161458838165
142	1.94515760246687	1.86329171318116	2.02702349175259
143	1.95067336271356	1.86352414389728	2.03782258152984
144	1.95618912296025	1.86381565460201	2.04856259131848

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/19/t12639313535mrq50po7m3nl91/143a41263931306.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/19/t12639313535mrq50po7m3nl91/143a41263931306.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/19/t12639313535mrq50po7m3nl91/2jys31263931306.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/19/t12639313535mrq50po7m3nl91/2jys31263931306.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/19/t12639313535mrq50po7m3nl91/3e6s61263931306.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/19/t12639313535mrq50po7m3nl91/3e6s61263931306.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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