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test (after main update)

*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: Mon, 29 Mar 2010 16:46:56 +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/Mar/29/t1269881244lcs8cz0nnitz4u7.htm/, Retrieved Mon, 29 Mar 2010 18:47:28 +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/Mar/29/t1269881244lcs8cz0nnitz4u7.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 «

112 118 132 129 121 135 148 148 136 119 104 118 115 126 141 135 125 149 170 170 158 133 114 140 145 150 178 163 172 178 199 199 184 162 146 166 171 180 193 181 183 218 230 242 209 191 172 194 196 196 236 235 229 243 264 272 237 211 180 201 204 188 235 227 234 264 302 293 259 229 203 229 242 233 267 269 270 315 364 347 312 274 237 278 284 277 317 313 318 374 413 405 355 306 271 306 315 301 356 348 355 422 465 467 404 347 305 336 340 318 362 348 363 435 491 505 404 359 310 337 360 342 406 396 420 472 548 559 463 407 362 405 417 391 419 461 472 535 622 606 508 461 390 432

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.275592474736350
beta	0.0326929527336615
gamma	0.87072922226501

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	115	111.081808708867	3.91819129113328
14	126	122.331452141086	3.66854785891434
15	141	137.439012569900	3.56098743009966
16	135	132.323380345381	2.67661965461949
17	125	123.479680462729	1.52031953727142
18	149	147.667288314870	1.33271168512962
19	170	162.443243712473	7.55675628752724
20	170	165.529589613321	4.47041038667871
21	158	153.88771229425	4.11228770575008
22	133	136.318641448733	-3.31864144873339
23	114	119.090610790114	-5.09061079011435
24	140	133.988719950498	6.01128004950164
25	145	134.830368289919	10.1696317100805
26	150	149.705143441365	0.294856558634905
27	178	166.540825999660	11.4591740003402
28	163	161.749728378189	1.25027162181149
29	172	149.757507993041	22.2424920069588
30	178	185.647723596323	-7.64772359632292
31	199	206.262153619027	-7.26215361902663
32	199	203.180886325985	-4.18088632598545
33	184	186.419252204207	-2.41925220420688
34	162	158.147799136752	3.85220086324750
35	146	138.368728198327	7.63127180167297
36	166	169.141340932275	-3.14134093227528
37	171	170.360941535351	0.639058464649423
38	180	177.43819047237	2.56180952763009
39	193	206.247937478342	-13.2479374783417
40	181	185.960743337438	-4.96074333743809
41	183	184.798362273963	-1.79836227396325
42	218	195.684395505420	22.3156044945797
43	230	227.498397718799	2.50160228120123
44	242	229.004771789439	12.995228210561
45	209	215.630984242776	-6.63098424277621
46	191	186.286597370310	4.71340262969036
47	172	166.037642761140	5.96235723886033
48	194	192.842517670216	1.15748232978419
49	196	198.309951792614	-2.30995179261362
50	196	206.984490574542	-10.9844905745424
51	236	224.192965596175	11.8070344038246
52	235	214.065423836271	20.9345761637291
53	229	222.675239689624	6.32476031037604
54	243	256.737994926100	-13.7379949260995
55	264	268.358000825093	-4.35800082509263
56	272	275.595138563011	-3.59513856301129
57	237	240.950054518830	-3.95005451882952
58	211	216.418708751084	-5.41870875108356
59	180	191.302349202140	-11.3023492021397
60	201	212.165209086813	-11.1652090868132
61	204	211.884606924302	-7.88460692430232
62	188	213.278507450624	-25.2785074506242
63	235	241.844292266099	-6.84429226609927
64	227	231.126648633712	-4.12664863371231
65	234	222.847577264956	11.1524227350442
66	264	244.403589556133	19.5964104438671
67	302	270.925430122293	31.0745698777072
68	293	288.46328100399	4.53671899600994
69	259	253.325564521034	5.67443547896596
70	229	228.457233710859	0.542766289141412
71	203	198.766723143806	4.23327685619387
72	229	226.325368143990	2.67463185601025
73	242	232.507692400678	9.49230759932206
74	233	226.155487496555	6.84451250344512
75	267	284.984109809782	-17.9841098097817
76	269	271.954044414959	-2.95404441495936
77	270	274.414349879443	-4.41434987944342
78	315	301.110875912758	13.8891240872424
79	364	337.481480217208	26.5185197827919
80	347	335.985533162042	11.0144668379583
81	312	297.836666071856	14.1633339281443
82	274	267.300445465088	6.69955453491184
83	237	236.99254313544	0.00745686455996974
84	278	266.900689163386	11.0993108366135
85	284	281.633925908281	2.36607409171881
86	277	269.967245890601	7.03275410939943
87	317	320.174999871829	-3.17499987182867
88	313	321.276899149144	-8.27689914914367
89	318	322.045741325616	-4.04574132561623
90	374	367.951178474248	6.04882152575198
91	413	417.203225397332	-4.20322539733195
92	405	394.606247713423	10.3937522865770
93	355	352.30665533687	2.69334466312978
94	306	308.449808881235	-2.44980888123547
95	271	266.696337801515	4.30366219848491
96	306	309.394161372705	-3.39416137270507
97	315	315.103179025908	-0.103179025908162
98	301	304.405357956351	-3.40535795635083
99	356	349.058201817874	6.94179818212643
100	348	349.292551021806	-1.29255102180582
101	355	355.073176743192	-0.0731767431923913
102	422	414.360922266091	7.6390777339086
103	465	462.091146643931	2.90885335606902
104	467	448.979705968486	18.0202940315142
105	404	397.635010380021	6.3649896199791
106	347	345.450978117798	1.54902188220177
107	305	304.243038614503	0.756961385497391
108	336	345.615242815445	-9.61524281544519
109	340	352.616294292299	-12.6162942922995
110	318	334.810889595368	-16.8108895953683
111	362	386.941371143576	-24.941371143576
112	348	372.19085448139	-24.1908544813901
113	363	372.090123850004	-9.09012385000392
114	435	435.498537075613	-0.498537075613456
115	491	478.418383525416	12.5816164745842
116	505	476.297736428687	28.7022635713128
117	404	417.219138602199	-13.2191386021993
118	359	354.436906440644	4.56309355935639
119	310	311.87647452998	-1.87647452998021
120	337	345.975126181846	-8.97512618184646
121	360	350.643068831256	9.35693116874421
122	342	334.994586512654	7.00541348734612
123	406	390.685878839784	15.3141211602163
124	396	386.498863412812	9.50113658718794
125	420	407.130739664592	12.8692603354077
126	472	491.604975308879	-19.6049753088789
127	548	543.780022319873	4.21997768012739
128	559	549.935293999599	9.06470600040075
129	463	449.638769888322	13.3612301116776
130	407	399.913027267263	7.0869727327372
131	362	348.397215116609	13.6027848833913
132	405	386.652093911442	18.3479060885584
133	417	413.916764563464	3.08323543653609
134	391	392.451160571742	-1.45116057174164
135	419	460.1705013673	-41.1705013673003
136	461	435.421790272079	25.5782097279213
137	472	465.095112731698	6.90488726830233
138	535	534.352710870332	0.647289129667797
139	622	616.735355637602	5.26464436239837
140	606	627.551048082547	-21.5510480825469
141	508	510.133147348626	-2.13314734862615
142	461	446.162802943527	14.8371970564727
143	390	395.452817646612	-5.45281764661166
144	432	434.572462781261	-2.57246278126127

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
145	447.055931344916	427.306133026716	466.805729663116
146	419.712279855699	399.132585244972	440.291974466426
147	464.867131095767	442.963034360731	486.771227830803
148	496.083937621018	472.832900505232	519.334974736803
149	507.532637500571	483.137513327878	531.927761673263
150	575.450895961051	548.708256350216	602.193535571887
151	666.592293420418	636.628829419529	696.555757421307
152	657.913718340472	627.182084720006	688.645351960938
153	550.308766449002	521.639795163271	578.977737734733
154	492.985309235296	465.015309913896	520.955308556697
155	420.207279555462	393.4687785372	446.945780573723
156	465.634500936807	443.300414442854	487.96858743076

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Mar/29/t1269881244lcs8cz0nnitz4u7/1kgm81269881214.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Mar/29/t1269881244lcs8cz0nnitz4u7/1kgm81269881214.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Mar/29/t1269881244lcs8cz0nnitz4u7/2v73t1269881214.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Mar/29/t1269881244lcs8cz0nnitz4u7/2v73t1269881214.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Mar/29/t1269881244lcs8cz0nnitz4u7/3v73t1269881214.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Mar/29/t1269881244lcs8cz0nnitz4u7/3v73t1269881214.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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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