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test

*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: Sun, 15 Mar 2009 03:22:02 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Mar/15/t1237108960yx67zeimlq5z3nv.htm/, Retrieved Sun, 15 Mar 2009 10:22:40 +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/2009/Mar/15/t1237108960yx67zeimlq5z3nv.htm/},
    year = {2009},
}
@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 = {2009},
    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	4 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.275592931492623
beta	0.0326927269946692
gamma	0.8707309723751

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	115	111.081808708867	3.91819129113324
14	126	122.331453874744	3.66854612525638
15	141	137.439015376159	3.56098462384080
16	135	132.323383220296	2.67661677970432
17	125	123.479682818149	1.52031718185103
18	149	147.66729023319	1.33270976680996
19	170	162.443244801901	7.55675519809901
20	170	165.529592394220	4.47040760577966
21	158	153.887714464935	4.11228553506479
22	133	136.318642929538	-3.31864292953784
23	114	119.090609201624	-5.09060920162416
24	140	133.988714960676	6.01128503932438
25	145	134.830370109666	10.1696298903343
26	150	149.705146015382	0.294853984617731
27	178	166.540824859925	11.4591751400746
28	163	161.749729120071	1.25027087992851
29	172	149.757505882891	22.2424941171085
30	178	185.647729927994	-7.64772992799351
31	199	206.262157804505	-7.26215780450494
32	199	203.180877899401	-4.18087789940057
33	184	186.419241979636	-2.41924197963596
34	162	158.147782759529	3.85221724047062
35	146	138.368716981075	7.63128301892496
36	166	169.141347816420	-3.14134781641982
37	171	170.360945870195	0.63905412980543
38	180	177.438178047914	2.56182195208552
39	193	206.247937689471	-13.2479376894715
40	181	185.960724160929	-4.960724160929
41	183	184.798364145757	-1.79836414575698
42	218	195.684359733551	22.3156402664486
43	230	227.498387941041	2.50161205895935
44	242	229.00476968852	12.9952303114799
45	209	215.630988418272	-6.63098841827184
46	191	186.286598351091	4.71340164890901
47	172	166.03764399356	5.96235600644013
48	194	192.842509510068	1.15749048993163
49	196	198.309952885671	-2.30995288567101
50	196	206.984486038046	-10.9844860380460
51	236	224.192940896220	11.8070591037796
52	235	214.065417855659	20.9345821443411
53	229	222.675252447109	6.32474755289078
54	243	256.738013695474	-13.7380136954740
55	264	268.357973304408	-4.35797330440784
56	272	275.595124348774	-3.59512434877428
57	237	240.950022441517	-3.95002244151664
58	211	216.418700337472	-5.41870033747205
59	180	191.302342357417	-11.3023423574168
60	201	212.165187519305	-11.1651875193053
61	204	211.884585973221	-7.88458597322119
62	188	213.278482377781	-25.2784823777809
63	235	241.844280631672	-6.84428063167161
64	227	231.126644343170	-4.12664434317026
65	234	222.847562357433	11.1524376425669
66	264	244.403573681984	19.5964263180161
67	302	270.925436787528	31.0745632124722
68	293	288.463304382644	4.53669561735649
69	259	253.325573114435	5.6744268855654
70	229	228.457242585487	0.54275741451346
71	203	198.766723711059	4.2332762889414
72	229	226.325370930041	2.67462906995868
73	242	232.507697921118	9.49230207888249
74	233	226.155470683088	6.84452931691163
75	267	284.984135370835	-17.9841353708349
76	269	271.954055875775	-2.95405587577505
77	270	274.414364054018	-4.41436405401839
78	315	301.110875438721	13.8891245612785
79	364	337.481483997024	26.5185160029757
80	347	335.985512136356	11.0144878636443
81	312	297.836655531173	14.1633444688269
82	274	267.300437713931	6.69956228606935
83	237	236.992541506197	0.00745849380322738
84	278	266.900682035766	11.0993179642339
85	284	281.633930499988	2.36606950001197
86	277	269.967232749700	7.03276725030031
87	317	320.174971097687	-3.17497109768715
88	313	321.27690151402	-8.27690151402027
89	318	322.045741716529	-4.04574171652934
90	374	367.951193908377	6.04880609162313
91	413	417.203241898457	-4.20324189845735
92	405	394.606219282427	10.3937807175729
93	355	352.306636964999	2.69336303500091
94	306	308.449783989775	-2.44978398977509
95	271	266.696313192658	4.30368680734244
96	306	309.394151440325	-3.39415144032546
97	315	315.103159698907	-0.103159698907120
98	301	304.405343346895	-3.40534334689534
99	356	349.05816545036	6.94183454964002
100	348	349.292530352989	-1.29253035298922
101	355	355.073171023921	-0.0731710239210202
102	422	414.360938373299	7.63906162670128
103	465	462.091156275837	2.90884372416303
104	467	448.979717852724	18.0202821472757
105	404	397.635009922124	6.36499007787643
106	347	345.450966287891	1.54903371210901
107	305	304.243031112075	0.756968887925495
108	336	345.615225431213	-9.61522543121265
109	340	352.616275490587	-12.6162754905871
110	318	334.810864863463	-16.8108648634627
111	362	386.941342201635	-24.9413422016352
112	348	372.190810667781	-24.1908106677807
113	363	372.090086438255	-9.09008643825496
114	435	435.49852015535	-0.49852015535015
115	491	478.418370094783	12.5816299052173
116	505	476.297754928989	28.7022450710107
117	404	417.219149854211	-13.2191498542109
118	359	354.436902962756	4.56309703724406
119	310	311.876475452214	-1.87647545221358
120	337	345.975115388033	-8.97511538803315
121	360	350.643058140312	9.3569418596877
122	342	334.994580207105	7.0054197928946
123	406	390.685875425544	15.3141245744561
124	396	386.498865844799	9.50113415520133
125	420	407.130762273235	12.8692377267649
126	472	491.605011219988	-19.6050112199878
127	548	543.780046558757	4.21995344124275
128	559	549.935327391724	9.06467260827571
129	463	449.63874670941	13.3612532905901
130	407	399.913034211776	7.08696578822429
131	362	348.397212667469	13.6027873325307
132	405	386.652084703312	18.3479152966877
133	417	413.916781467445	3.08321853255524
134	391	392.451160427231	-1.45116042723129
135	419	460.170497130598	-41.1704971305977
136	461	435.421755571338	25.5782444286623
137	472	465.095102857788	6.90489714221195
138	535	534.352674389893	0.647325610106805
139	622	616.735366186232	5.26463381376755
140	606	627.551069242213	-21.5510692422125
141	508	510.133139879417	-2.1331398794174
142	461	446.162791637766	14.8372083622340
143	390	395.452817969958	-5.45281796995783
144	432	434.572452493991	-2.57245249399091

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
145	447.055907793736	427.306081839850	466.805733747622
146	419.712252491671	399.132529133903	440.291975849439
147	464.867062938293	442.962936376519	486.771189500067
148	496.083938082045	472.832869325620	519.33500683847
149	507.532607460904	483.137451881795	531.927763040012
150	575.450839384531	548.708168067462	602.1935107016
151	666.592241551563	636.628745108619	696.555737994507
152	657.913647955733	627.181984104025	688.645311807442
153	550.308727275636	521.639727613372	578.9777269379
154	492.98528697611	465.015260234124	520.955313718097
155	420.207239449299	393.468712587961	446.945766310636
156	465.634459283957	443.300359438502	487.968559129412

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/15/t1237108960yx67zeimlq5z3nv/1mhw61237108915.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/15/t1237108960yx67zeimlq5z3nv/1mhw61237108915.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/15/t1237108960yx67zeimlq5z3nv/25ar91237108915.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/15/t1237108960yx67zeimlq5z3nv/25ar91237108915.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/15/t1237108960yx67zeimlq5z3nv/323t31237108915.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Mar/15/t1237108960yx67zeimlq5z3nv/323t31237108915.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=0, beta=0)

if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)

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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