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*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: Wed, 22 Dec 2010 09:07:02 +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/Dec/22/t1293008813e9lzok38b1ni7c7.htm/, Retrieved Wed, 22 Dec 2010 10:06:54 +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/Dec/22/t1293008813e9lzok38b1ni7c7.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 «

377 370 358 357 349 348 369 381 368 361 351 351 358 354 347 345 343 340 362 370 373 371 354 357 363 364 363 358 357 357 380 378 376 380 379 384 392 394 392 396 392 396 419 421 420 418 410 418 426 428 430 424 423 427 441 449 452 462 455 461 461 463 462 456 455 456 472 472 471 465 459 465 468 467 463 460 462 461 476 476 471 453 443 442 444 438 427 424 416 406 431 434 418 412 404 409 412 406 398 397 385 390 413 413 401 397 397 409 419 424 428 430 424 433 456 459 446 441 439 454 460 457 451 444 437 443 471 469 454 444 436

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	3 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0767755995740817
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	358	363	-5
4	357	350.61612200213	6.3838779978704
5	349	350.106248063024	-1.10624806302388
6	348	342.021315204708	5.97868479529245
7	369	341.480332314531	27.5196676854694
8	381	364.593171301162	16.406828698838
9	368	377.852815411625	-9.85281541162453
10	361	364.096359600904	-3.09635960090429
11	351	356.858634736048	-5.85863473604792
12	351	346.408834541502	4.5911654584977
13	358	346.761324022322	11.2386759776778
14	354	354.624180108927	-0.624180108927305
15	347	350.576258306822	-3.57625830682218
16	345	343.301688931084	1.69831106891587
17	343	341.432077781663	1.56792221833655
18	340	339.552455950062	0.447544049938244
19	362	336.586816412832	25.4131835871684
20	370	360.537928819823	9.46207118017736
21	373	369.264385007893	3.7356149921066
22	371	372.55118908869	-1.55118908869031
23	354	370.432095616353	-16.4320956163534
24	357	352.170511623149	4.8294883768508
25	363	355.541298488918	7.45870151108204
26	364	362.113944769475	1.88605523052462
27	363	363.258747790629	-0.258747790628775
28	358	362.238882273865	-4.23888227386476
29	357	356.913439545765	0.0865604542351548
30	357	355.920085276538	1.07991472346185
31	380	356.002996376921	23.9970036230792
32	378	380.845380718064	-2.84538071806412
33	376	378.626924907418	-2.62692490741824
34	380	376.425241172615	3.57475882738493
35	379	380.69969542492	-1.69969542492032
36	384	379.569200289579	4.43079971042124
37	392	384.909377593939	7.09062240606102
38	394	393.453764380518	0.546235619482275
39	392	395.495701947712	-3.49570194771223
40	396	393.227317334744	2.77268266525567
41	392	397.440191708798	-5.44019170879801
42	396	393.022517728557	2.97748227144291
43	419	397.251115715168	21.7488842848317
44	421	421.920899346204	-0.920899346203612
45	420	423.850196746751	-3.85019674675141
46	418	422.554595583041	-4.55459558304142
47	410	420.204913776336	-10.204913776336
48	418	411.421425402556	6.57857459744406
49	426	419.926499411618	6.07350058838244
50	428	428.392796060804	-0.39279606080413
51	430	430.362638907726	-0.362638907725568
52	424	432.334797088156	-8.33479708815605
53	423	425.694888044385	-2.69488804438453
54	427	424.487986398992	2.51201360100811
55	441	428.680847749348	12.3191522506525
56	449	443.626658049636	5.37334195036419
57	452	452.039199599592	-0.0391995995915408
58	462	455.03619002683	6.96380997317016
59	455	465.57084071284	-10.57084071284
60	461	457.75925807911	3.24074192089046
61	461	464.008067983151	-3.0080679831508
62	463	463.777121760185	-0.777121760184798
63	462	465.717457771105	-3.71745777110453
64	456	464.432047721837	-8.43204772183668
65	455	457.784672202355	-2.78467220235535
66	456	456.570877324402	-0.570877324402261
67	472	457.527047875538	14.472952124462
68	472	474.638217452501	-2.63821745250056
69	471	474.435666725778	-3.43566672577805
70	465	473.17189135297	-8.17189135296974
71	459	466.544489494691	-7.54448949469122
72	465	459.965256790256	5.03474320974408
73	468	466.351802218886	1.64819778111445
74	467	469.478343591747	-2.47834359174732
75	463	468.28806727654	-5.28806727654029
76	460	463.882072740796	-3.88207274079588
77	462	460.584024278531	1.41597572146895
78	461	462.692736663529	-1.69273666352916
79	476	461.562775791266	14.4372242087343
80	476	477.671202336077	-1.6712023360767
81	471	477.542894774715	-6.5428947747148
82	453	472.040560105436	-19.040560105436
83	443	452.578709687115	-9.57870968711478
84	442	441.84329850774	0.156701492259515
85	444	440.855329358763	3.14467064123716
86	438	443.096763332707	-5.09676333270687
87	427	436.705456271951	-9.7054562719511
88	424	424.960314047532	-0.960314047531995
89	416	421.886585360753	-5.88658536075332
90	406	413.434639240237	-7.43463924023746
91	431	402.863840354951	28.1361596450487
92	434	430.024010881412	3.97598911858807
93	418	433.329269829892	-15.3292698298916
94	412	416.152355947669	-4.15235594766875
95	404	409.833556330142	-5.8335563301415
96	409	401.385681545246	7.61431845475431
97	412	406.970275409957	5.02972459004252
98	406	410.35643553105	-4.35643553105047
99	398	404.021967581148	-6.02196758114826
100	397	395.55962740949	1.44037259051009
101	385	394.670212878736	-9.67021287873638
102	390	381.927776486962	8.07222351303761
103	413	387.547526287072	25.4524737129282
104	413	412.501655217025	0.498344782974527
105	401	412.539915936533	-11.539915936533
106	397	399.653931971471	-2.65393197147114
107	397	395.450174753133	1.54982524686739
108	409	395.569163515696	13.4308364843041
109	419	408.60032403956	10.3996759604402
110	424	419.398765396799	4.60123460320125
111	428	424.752027942241	3.24797205775945
112	430	429.001392944375	0.998607055625087
113	424	431.078061599809	-7.07806159980942
114	433	424.534639176662	8.46536082333824
115	456	434.184572329485	21.8154276705155
116	459	458.859464868853	0.140535131146635
117	446	461.870254537808	-15.8702545378084
118	441	447.651806230275	-6.65180623027481
119	439	442.141109818695	-3.14110981869487
120	454	439.899949229037	14.1000507709635
121	460	455.982489081002	4.01751091899774
122	457	462.290935890604	-5.29093589060369
123	451	458.884721115295	-7.88472111529461
124	444	452.279366924193	-8.27936692419343
125	437	444.643713564495	-7.64371356449465
126	443	437.056862872608	5.94313712739199
127	471	443.513150788915	27.4868492110855
128	469	473.623470117498	-4.62347011749802
129	454	471.268500427114	-17.2685004271142
130	444	454.942700953077	-10.9427009530772
131	436	444.102568526445	-8.10256852644488

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
132	435.480488969737	417.335462119549	453.625515819925
133	434.960977939474	408.296765647272	461.625190231676
134	434.441466909211	400.543147151057	468.339786667365
135	433.921955878948	393.33290533205	474.511006425846
136	433.402444848685	386.39195163814	480.41293805923
137	432.882933818422	379.586368691356	486.179498945488
138	432.363422788159	372.840615388385	491.886230187933
139	431.843911757896	366.10815177722	497.579671738572
140	431.324400727633	359.358562290774	503.290239164492
141	430.80488969737	352.571128986809	509.038650407931
142	430.285378667107	345.731314256543	514.839443077671
143	429.765867636844	338.828698056287	520.703037217401

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293008813e9lzok38b1ni7c7/1hcel1293008817.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293008813e9lzok38b1ni7c7/1hcel1293008817.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293008813e9lzok38b1ni7c7/2a3w61293008817.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293008813e9lzok38b1ni7c7/2a3w61293008817.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293008813e9lzok38b1ni7c7/3a3w61293008817.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/22/t1293008813e9lzok38b1ni7c7/3a3w61293008817.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

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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