Home » date » 2010 » Aug » 15 »

Tijdreeks B - Stap 27

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 15 Aug 2010 14:22:15 +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/Aug/15/t1281882122k8xok8o3fzi3kch.htm/, Retrieved Sun, 15 Aug 2010 16:22:06 +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/Aug/15/t1281882122k8xok8o3fzi3kch.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:

Jacobs Jeff

Dataseries X:

» Textbox « » Textfile « » CSV «

335 334 333 331 329 328 329 331 332 332 333 335 335 333 325 322 322 315 321 324 329 332 322 324 324 323 309 306 305 300 301 302 308 311 301 301 308 302 290 286 286 275 284 289 292 293 285 280 281 280 265 260 254 238 247 246 247 237 222 216 212 209 185 186 178 158 166 162 164 147 132 124 117 120 89 81 71 52 63 62 74 67 53 42

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	0.425790716300489
beta	0.363870669843828
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	335	339.209935897436	-4.20993589743614
14	333	334.806502608273	-1.80650260827315
15	325	324.938209144871	0.0617908551287769
16	322	320.583324454149	1.41667554585115
17	322	320.358159862371	1.64184013762895
18	315	313.941576409506	1.05842359049399
19	321	321.482230754680	-0.482230754679506
20	324	322.375508777505	1.62449122249456
21	329	323.750829690947	5.2491703090534
22	332	326.8161070501	5.18389294990021
23	322	331.615078055856	-9.61507805585558
24	324	329.789760748247	-5.78976074824709
25	324	324.320486854875	-0.320486854874673
26	323	322.677783082907	0.322216917092931
27	309	314.84304297509	-5.84304297508982
28	306	307.891442956404	-1.89144295640426
29	305	305.013988640077	-0.0139886400766613
30	300	295.927808180145	4.07219181985499
31	301	302.704413151525	-1.70441315152510
32	302	302.935014611050	-0.935014611050349
33	308	303.553312836116	4.44668716388401
34	311	304.366553285318	6.6334467146819
35	301	299.636743470704	1.36325652929582
36	301	304.73505460785	-3.73505460784980
37	308	303.652127424538	4.34787257546185
38	302	305.460460076231	-3.46046007623073
39	290	292.983127039852	-2.98312703985152
40	286	290.469578026091	-4.46957802609114
41	286	288.124271799635	-2.12427179963527
42	275	280.710765506475	-5.71076550647479
43	284	278.714087744869	5.28591225513105
44	289	282.155120889326	6.84487911067407
45	292	290.173829347777	1.82617065222286
46	293	291.718512583454	1.2814874165461
47	285	281.446079019305	3.55392098069547
48	280	284.651445795878	-4.65144579587849
49	281	287.779429210233	-6.77942921023282
50	280	278.602069094362	1.39793090563762
51	265	267.456032914919	-2.45603291491886
52	260	263.383595893848	-3.38359589384788
53	254	262.085855751082	-8.0858557510823
54	238	248.389388125163	-10.3893881251626
55	247	248.304942615342	-1.30494261534224
56	246	246.403636761513	-0.403636761512843
57	247	243.899985521863	3.10001447813656
58	237	241.317437649324	-4.31743764932361
59	222	224.741569532128	-2.7415695321279
60	216	214.35508274905	1.64491725095002
61	212	213.717909759354	-1.71790975935434
62	209	206.951227370628	2.04877262937214
63	185	189.53018209015	-4.53018209014994
64	186	179.381473030181	6.61852696981944
65	178	176.531615812172	1.46838418782789
66	158	163.949963007576	-5.94996300757555
67	166	170.02938663195	-4.02938663195002
68	162	166.120700569598	-4.12070056959837
69	164	162.105416779896	1.89458322010435
70	147	152.622906454693	-5.62290645469275
71	132	134.066268925489	-2.06626892548874
72	124	124.260915470249	-0.260915470249202
73	117	118.360849366858	-1.36084936685826
74	120	111.443943579026	8.55605642097385
75	89	91.5590134459976	-2.55901344599764
76	81	87.4997715210797	-6.49977152107968
77	71	72.9230202749146	-1.92302027491462
78	52	50.92823095581	1.07176904419001
79	63	58.4787278140551	4.52127218594491
80	62	56.8616488247614	5.13835117523861
81	74	60.3805947251835	13.6194052748165
82	67	53.5281310002334	13.4718689997666
83	53	50.0568705898765	2.94312941012345
84	42	49.1099877428014	-7.1099877428014

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	44.2897769601159	34.9458582215414	53.6336956986905
86	48.4852466714746	37.6800247410051	59.2904686019442
87	22.0877965657826	9.2814119608429	34.8941811707223
88	20.7647596621920	5.49215792781678	36.0373613965673
89	16.5000120637975	-1.62982526374799	34.6298493913431
90	2.25804980161506	-19.061212598943	23.5773122021731
91	16.3812689970629	-8.41598400349236	41.1785219976181
92	17.5412485401203	-10.9905052094707	46.0730022897114
93	27.2939750888859	-5.20485789877787	59.7928080765497
94	15.9994292583440	-20.6807401287618	52.6795986454499
95	0.100689245159970	-40.9606619679016	41.1620404582215
96	-8.97351395682509	-54.6042591444928	36.6572312308426

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/15/t1281882122k8xok8o3fzi3kch/1jd7u1281882132.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/15/t1281882122k8xok8o3fzi3kch/1jd7u1281882132.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/15/t1281882122k8xok8o3fzi3kch/2jd7u1281882132.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/15/t1281882122k8xok8o3fzi3kch/2jd7u1281882132.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/15/t1281882122k8xok8o3fzi3kch/3cn7f1281882132.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Aug/15/t1281882122k8xok8o3fzi3kch/3cn7f1281882132.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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